Recent changes to this web site are posted below.

August 13, 2010 (T-Model 8.2)

A new PDF file for Fingerprint Experiments 10-12 was posted under Validation Study with 2 corrected images.

August 1, 2010 (T-Model 8.2)

The below example about the need to consider the plausible number of people who could be the source of a latent fingerprint was refined.  See Relevant Fingerprint Population.

Example

Based on a conservative upper bound world fingerprint population of 66 billion, the excellent agreement of 9 excellent non-diminishing area bifurcations in sequence, the  estimated number of look-alikes is approximately .088 (less than 1).  As a result, there is valid basis to infer positive identification.  However based on a fingerprint population of 77 million, only 7 excellent bifurcations in excellent agreement will have approximately .09 look-alikes (also less than 1) and consequently there is valid basis to infer positive identification. 

For crimes in which a suspect is apprehended within minutes the geographic perimeter may involve only a radius of only 1-2 miles and a subsequent conservative upper bound relevant fingerprint population of only, for example, 100,000.  As a result , only 5 bifurcations would be needed to establish an estimated number of look-alikes to be less than 1, i.e. .12, and therefore valid basis for sufficiency to individualize.

July 30, 2010 (T-Model 8.2)

The preamble was slightly re-worded on the Introduction page.  In addition the following "challenge" to the fingerprint community was posted: 

A Challenge to the Fingerprint Community

The T-Model and this web site will be maintained and offered to the fingerprint community for testing and critical scrutiny until another model, method or procedure is shown to be more accurate.  At this time the author considers the T-Model the most accurate tool to make correct fingerprint conclusions, i.e., more accurate than human decision making by the expert latent print examiner using any model, method or procedure, and more accurate than any other statistical probability model currently in existence. 

The author challenges the fingerprint community to a "competition" to find out which model, method or procedure is most accurate and reliable to make correct fingerprint conclusions.  Requirements for the competition are as follows:

• Test samples must be distal segments of fingerprints, i.e., no medial or proximal phalanges and no palm prints.
• Test samples of latent fingerprints must be consistent with normal handling and processed using conventional latent fingerprint processing methods, e.g., fingerprint powder, ninhydrin, DFO, etc..  Image manipulation of test samples using digital imaging software is prohibited.
• Test samples of exemplar fingerprints must be consistent with conventional exemplar fingerprint recording methods, e.g., ink or livescan.  Image manipulation of test samples using digital imaging software is prohibited.
• Test samples must include AFIS database fingerprint population if AFIS was used to find fingerprint "look-alikes" which were used in test samples.  
  
• Test conditions, design and administration must be well-controlled, reproducible, and honest.
• Test conditions, design and administration must be carried out by an uninterested team of scientists.
  

Comments and suggestions about the above "competition" are welcome and may be submitted to the author at the following email address:  henry@henrytempleman.com 

July 29, 2010 (T-Model 8.2)

1.  The following note regarding "underlying assumptions" of the T-Model formulae was included in The Formulae:

Underlying Assumption

The discriminating value of 10^120 for the average flat fingerprint is not directly testable and therefore remains an underlying assumption in the T-Model formulae.  Although this value is not directly testable, it can be indirectly tested by "close match" experiments in order to determine it's influence on the accuracy for the model to predict numbers of close matches likely to be present in a given population group.  Based on results from these experiments, the value 10^120 has, at this time, shown to be a relatively accurate, yet conservative, vlaue needed to make the most accurate, reliable predictions for the number of close matches likely to be present in a given population group (see Validation Study).

2.  The term "likelihood ratio" was included in the Introduction to describe as a like term  the total quantitative-qualitative weighting or discriminating value for fingerprint evidence.

July 17, 2010 (T-Model 8.2)

A 40-hour T-Model training course is offered by Henry Templeman.  Information how participates can attend for free by hosting a course at their agency has been included at Examiner Training 1/2.

A contact link to Mr. Robert Ramotowski, Chief Research Scientist, Forensic Services Division, US Secret Service, has been added to the list of recommended individuals for training on how to conduct  and document research, e.g., experiments, and what is the scientific method (see Examiner Training 1/2.

For purposes of consistency with other forensic science disciplines in expressing the significance of a "match", the T-Model includes the "Likelihood Ratio" value to express the chance a different source shares the same ridge features in the population for the case at hand (see Fingerprint Match Probability and Fingerprint Calculator)  

The following passage (in bold) was referenced in the NAS report and has been sited as a reference for clarification (see Introduction):

"The model takes into consideration all levels of fingerprint ridge detail, e.g., Level I, II and III.  It uses simple statistics to assign match probabilities based on population distributions of "friction ridge feature shapes in position".   It has "matured past mere counts of corresponding minutiae by taking into consideration ridge feature clarity" (a variable that the National Academy of Sciences stated no statistical probability model has addressed [91]),..." 

The following information regarding "IAI Resolution 2010-18" and "The Justified Opinion" was posted and modified on the Introduction as follows:

IAI Resolution 2010-18 

On July 16, 2010 at the International Association for Identification Conference in Spokane, WA, members voted to adopt Resolution 2010-18 which in effect rescinds Resolution 1979-7 and Resolution 1980-5 forbidding latent print examiners to provide oral or written reports, or give testimony of possible, probable or likely friction ridge identification.  The adoption of this resolution ushers in a new paradigm for the field of fingerprints by allowing the significance of a fingerprint match to be expressed in terms of probability theory.   

The full resolution is scheduled to be published in the Journal of Forensic Identification.  For subscription information, see International Association for Identification.

The Justified Opinion

The T-Model sets the demarcation for sufficiency to infer positive identification at 1, where if the Fingerprint Match Probability (FMP) divided by the Relevant Population (RP) for the case at hand is greater than 1, then there is valid basis to infer positive identification.  As a result, the inference for positive identification is considered a justified opinion. 

The justified opinion to infer positive identification may be considered to bridge the gap between the individualization to the exclusion of all others opinion and the qualified opinion by setting the demarcation for sufficiency to absolute 1. 

The justified opinion for fingerprint source attribution can be made on partial, fragmented parts of whole, complete fingerprints.  For purposes of performing routine latent print casework in a timely manner, the human population group of 300 million people (e.g., approximately the total United States human population) is recommended for use as the default T-Value (or Likelihood Ratio) that needs to be exceeded in order to establish inference for positive identification.

*It is significant to note here that 300 million people is the same default human population group used by the FBI to match DNA profiles for routine criminal casework [84].  

July 10, 2010 (T-Model 8.1) 

Quotes on "probability" by notable scientists were added throughout the web site.  See Probability Theory, Statistics is More Accurate than Humans, Foundations for the T-Model, Fingerprint Match Probability, Friction Skin Elasticity, Validation Study, and Pre-Determined Minimum to Individualize.

Also a quote by Edward Teller is included on the page Product Rule.

Lastly, since no amount of experiment can "prove the truth" of an idea, the word "verified" was replaced with the more accurate descriptive term "corroborated" on the Santamaria v. Osterburg page.   The author apologizes in advance if the word "verify", "verified" or "verification" is similarly used on this web site and has yet to be corrected. 

July 8, 2010 (T-Model 8.1)

The following [more complete] quote by Glenn Langenburg regarding how to test the T-Model is included under Validation Study:

"I would recommend that you do calculate some very simple probabilities for 3-5 minutiae in arrangements using your approach.  Predict the value based on your model, and then go and search and see how often they appear."

"If you calculate a small 3 or 4 arrangement is not likely to appear 1/1000, then go and look at 1000 fingerprints.  If you find it 20 times, you're off a bit.  If you find it 0-3 times, you might be in the ballpark.  Its tedious, but that's the only way to see how well this independence holds up.  Personally I think you are overestimating by assuming this, BUT maybe...not by much.  Empirically testing will help determine the soundness of the assumptions."  

July 3, 2010 (T-Model 8.1)

The following information has been included on the Introduction page of the web site:

The T-Model is grounded in experimental research that estimates the discriminating value of the various ridge formations and clusters of ridge formations in a flat fingerprint, e.g., the area of friction skin most often found at the scenes of crimes.

The T-Model speaks to the following concern raised in the NAS Report:

"More research is needed regarding the discriminating value of the various ridge formations and clusters of ridge formations.”

The T-Model provides standard values for the most frequently occurring ridge formations used in fingerprints, e.g., ending ridges, bifurcations and dots, and formula to estimate the discriminating value for clusters of ridge formations and the number of close matches likely to be present in a given population group.  Based on these estimates, the T-Model forms demarcations to establish inference for identification to a single source. 

June 30, 2010 (T-Model 8.1)

The number of ending ridges in Example No. 1 under Pre-Determined Minimum to Individualize should read 11, and not 8, which changes the values in the equation, but not the outcome.  

Readers are asked to notify the author of any errors, e.g., math, spelling, etc., regardless how minor, that are observed on this web site.  Any help to improve this web site is greatly appreciated.   

June 27, 2010 (T-Model 8.1)

Based on results gathered from experiments on "dots", see Validation Study, the T-Model defines different types of dots, e.g., single dots and cluster dots, and estimates conservative lower-bound values for each, and their corresponding probabilities (also see Ridge Unit Weights 1/3).

It is significant to note that the emergence of different dot types and values slightly impacts the standard theoretical value for the average flat fingerprint and The Formulae used to estimate numbers of "parts" per fingerprint when calculating numbers of close matches likely to occur in a given fingerprint population.   However, at this time and for purposes of conservatism on behalf of the defendant, the T-Model retains the upper-bound value of 10^120 for the average flat fingerprint.

June 16, 2010 (T-Model 8.0.5)

Quotes by physicist Brian Cox about what are science and equations are included in the Introduction and The Formulae.

June 3, 2010 (T-Model 8.0.5)

The following note was added to Ridge Unit Weights (1/3) and Validation Study regarding the value for "dots": 

Preliminary results from close-match experiments performing June 2010 involving "dots" indicate that dots come in different types in terms of their positional relationship with other dots.  As a result some dots have more value than others.   Extended validation studies are in progress to better define these different dot types and their respective values.  Pending completion of these studies the value "98" for a "dot" is deemed "a poor guess" and therefore should not be used at this time.  

June 2, 2010 (T-Model 8.0.4)

For purposes of further clarification, images displaying fingerprint "funnels" were added to the section on Pattern Force (2/2).

May 24, 2010 (T-Model v. 8.0.4)

In the "Preamble" on the Introduction page, the default 300 million population group represents human population, not fingerprint population.  

May 1, 2010 (T-Model v. 8.0.4)

1.  Results from fingerprint experiments 10, 11 and 12 were completed and posted under Validation Study.

2.  Thresholds for spatial relationship between ridge features based on triangulation from Level II ridge features to the nearest 3 neighbors according to friction skin elasticity thresholds defined by experiment (see Friction Skin Elasticity) was deemed simplest and adequate for purposes of routine criminal casework.   As a result, the idea of applying an additional "ridge vector" measurement to define "rotational thresholds" between Level II ridge features and the nearest neighbor was deemed overkill.  Subsequently the section and concept of a "ridge vector" was discarded. 

3.  As a result of discarding the idea of a "ridge vector", the pages Friction Skin Elasticity and Quality of Agreement Level II were updated. 

April 24, 2010 (T-Model v. 8.0.3)

Results from "close match" fingerprint experiments are simplified and put in PDF format for download and review.  See Validation Study.

April 17, 2010 (T-Model v. 8.0.3)

Results from fingerprint experiments 7, 8 and 9 were completed and are posted under Validation Study in PDF format.  The result from these studies provide strong support that the latest version of the T-Model is able to estimate numbers of close matches more accurately than any other model tested.  It corroborates the standard value for a "bifurcation in a funnel with 0-1 intervening ridge counts to the nearest neighbor" as 18.75, which equates to a match probability of 1/18.75.

Fingerprint experiments 10 - 12 are currently in progress.

April 4, 2010 (T-Model v. 8.0.2)

Comment regarding use of "likelihood ratios" to express the significance of a fingerprint match is expanded (see Fingerprint Match Probability).

March 28, 2010 (T-Model v. 8.0.1)

Fingerprint experiment no. 6 was completed and provides further support that T-Model v. 8.0 is more accurate than latent print examiner professional judgment decision-making or any other statistical model tested, to estimate what is the number of "close matches" for an arrangement of fingerprint ridge features present in a given flat fingerprint population group.

Statistics for results from the 6 "close match" experiments are included.  See Validation Study.

The quote made by Richard Feynman was slightly off and has been corrected.  See Validation Study.

The definition for "borders for funnel sides" was refined to include "the outside ridge of bifurcations" (see Pattern Force 2 of 2).  This change will be tested in fingerprint experiments involving arrangements of "3 bifurcations in a funnel", e.g., Fingerprint Experiment no. 7 (bifurcations) is currently in progress (see Validation Study).

March 9, 2010  (T-Model v. 8.0)

Further detailed explanation of the basis of the new T-Model Formulae was added.

March 8, 2010  (T-Model v. 8.0)

Text under pages "Madrid Error" and "More Look-alikes and Shirley McKie" were refined. 

Arie Zeelenberg [103] was referenced for being the first [to the author's knowledge] to describe the concept of according less weight or discriminatory value to [directional] ridge features present in "diminishing areas in fingerprints caused by pattern force".

Summary comments by Mr. Zeelenberg regarding the T-Model have been included in the Comments page. 

March 6, 2010 (T-Model v. 8.0)

The T-Model's expression to define the pre-determined minimum amount of corresponding ridge features needed in two fingerprint impressions in order to establish inference for identification is simplified.  See Pre-Determined Minimum to Individualize.

March 5, 2010 (T-Model v. 8.0)

Links to videos of Richard P. Feynman describing the "Key to Science" and the series "Take the World from Another Point of View" were added.  See Validation Study. 

March 2, 2010 (T-Model v. 8.0)

Results from a latent print examiner survey regarding estimated number of close matches present in a 1000 flat fingerprint sample are reported.  Also the numbers of "intervening ridge counts to each nearest neighbor" for the "close match" experiments were included (see Validation Study).

February 27, 2010  (T-Model v. 8.0)

Based on results from broader experimentation (see Validation Study) using a 1000 fingerprint sampling (e.g., a significantly larger fingerprint sample used than in any previous experiments performed by the author) the formulae for T-Model version 7.0 has been refined, e.g., made significantly more accurate (see The Formulae).  As a result, most all sections of the previous version of the T-Model have undergone revision in order to reflect the change in the modified formulae. 

February 13, 2010

The Preamble of the Introduction was simplified. 

February 9, 2010

Comments are included on the Clark Non-Match page by Christophe Champod regarding the need to exceed the largest and best amount of matching ridge features ever seen in a non-match in order to infer identification.

December 1, 2009 (Version 7.0.2

Fingerprint Calculator v. 7.0 has been completed. 

November 28, 2009  (Version 7.0.1)

The author has recently accepted to serve as the fingerprint expert for "Art Experts, Inc.".  The Author page has been updated to reflect new position.

November 20, 2009 (Version 7.0.1)

The author offers a 40-hr "Dactyloscopy" course and an additional source of examiner training in probability theory and statistics is included in Examiner Training 1/2.

November 16, 2009 (Version 7.0)

Contact information for recommended sources of information for examiner training is included in Examiner Training 1/2.

November 14, 2009  (Version 7.0)

The concept of using "likelihood ratios" to establish inference for positive identification is discarded due to the difficulty in defining the numerator (see Fingerprint Match Probability page for comments and references). 

Subsequently, the "likelihood ratio" term to express the significance of a fingerprint match was replaced by the previous term "T-Value" which represents the aggregate quantitative-qualitative weight for an arrangement of fingerprint ridge features and a mathematical expression for the reciprocal of the fingerprint match probability. 

The changes made were largely in terminology only, yet significant enough to update the T-Model version to 7.0. 

November 6, 2009 (Version 6.0.1)

Based on new criteria to establish inference for fingerprint exclusion [with a degree of probability that borders on certainty], the page "More Look-alikes and Shirley McKie" has been updated. 

October 31, 2009 (Version 6.0)

The concept of Fingerprint Match Probability (FMP) was updated to reflect the need to consider "Likelihood Ratio" and "prior odds" and not simply as an inverse function of the Likelihood Ratio.   As a result, various sections on the following pages were refined:

Introduction

Likelihood Ratio

Probability Theory

Product Rule

Ridge Unit Frequency

Fingerprint Analysis

Fingerprint Evaluation

Relevant Fingerprint Population

The Formulae

Pre-Determined Minimum To Individualize

Fingerprint Calculator 

October 25, 2009 (Version 5.0)

1.  A new standard and criteria in order to infer fingerprint exclusion is introduced (see Pre-Determined Minimum to Exclude). 

As a result of the above change, the following pages were revised:  

More Look-alikes & Shirley McKie (see Shirley McKie)

Non-Corresponding Ridge Events

Examiner Training 2/2

Validation Study

 2.  A validation study to determine the error rate for the T-Model to perform fingerprint analysis is presented in a format in line with the National Academy of Sciences, e.g., NAS Report (See Error Rate in Terms of Best Look-alikes).

September 12, 2009 (Version 4.0)

A preamble was included on the Introduction page.

September 11, 2009 (Version 4.0)

Quotes by Ludwig Wittgenstein are referenced on the following pages:  Probability Theory and Error Rate in Terms of Best Look-alikes.

September 5, 2009 (Version 4.0)

Based on new 5-tier qualitative numeric scales for use during the analysis phase of latent v. exemplar impressions, likelihood ratios and estimated numbers of look-alikes for the Chesapeake IAFIS Non-Match and Clark Non-Match have been refined to reflect these changes (see Chesapeake IAFIS Non-Match, Clark Non-Match, Ridge Unit Quality and Quality of Agreement Level II). 

See also minor modifications to the following pages based on this change:  County of Santa Clara Non-Match, Fingerprint Analysis, Fingerprint Comparison,  Quality of Agreement Level II, Ridge Connectivity Disagreement, Fingerprint Evaluation.

The newly adopted qualitative grading scales are significant enough to upgrade this version of the T-Model to 4.0. 

September 1, 2009 (Version 3.0.3)

For improved clarification, the page "Pre-Determined Minimum To Individualize" has been further modified.  See link here. 

August, 24, 2009 (Version 3.0.3)

1.  The following information was added to the Chesapeake IAFIS Non-Match page:

Note:  It is significant to note here that based on preliminary test results utilizing the two (2) refined 5-tier qualitative reduction factor scales, the estimated likelihood ratio for the Chesapeake IAFIS non-match decreased to approximately 1 billion and the estimated number of look-alikes subsequently increased to approximately 12.8 (see Ridge Unit Quality and Quality of Agreement Level II).  The comparative weaker likelihood ratio value and larger number of predicted look-alikes results are appealing since they more clearly establish the Chesapeake impression as bearing insufficient corresponding ridge features to infer positive identification.  

2.  The following information was added to the Clark Non-Match page:

3.  The following information was added to the Ridge Vector page:

During experimentation to observe the effects of fingerprint deposition pressure combined with rotational twisting, Alice Maceo reported a maximum 30-35 degree rotational movement from the core before slippage occurred [97].  Macae video-recorded deliberate fingerprint rotational movement under heavy deposition pressure and recorded these results. 

August 23, 2009 (Version 3.0.3)

1.  The following information was added to the Introduction:

*Note: The plausible number of people who could be the source of any latent print for any crime is always restricted to a number less than the total number of people on earth based on the time and location for a crime at hand.  It is illegitimate to set [a priori] the size of the relevant population at its maximum, e.g., the total number of persons on earth [34] and therefore is determined, or may be refined, on a case by case basis (see Relevant Fingerprint Population).

Fingerprint Source Attribution

The "Individualization to the Exclusion of All Others" Opinion

The "individualization to the exclusion of all other sources" opinion traditionally used by latent print examiners has been qualified as inherently subjective and unscientific by the most eminent scientific organization in the United States, the National Academy of Sciences (NAS) [91].  The NAS Report (released February 2009) rejects the idea that ACE-V has a zero error  rate or can be used to reliably establish fingerprint source attribution.   In addition the report  points out the need for scientific research regarding the rarity of ridge features and sufficiency thresholds to infer positive identification, e.g., based on experiment, and the application of the science of probability to justify conclusions.

The T-Model uses the science of probability to define the rarity of ridge features types in position and sufficiency thresholds to infer positive identification for amounts of corresponding fingerprint ridge features found in two impressions based on the relevant population for the case at hand.  The model calculates posterior odds utilizing prior odds (e.g., relevant fingerprint population) and a likelihood ratio (LR) such that when the posterior probability is greater than or equal to 1, inference for positive identification is established.  In essence a posterior probability greater than or equal to 1 for an amount of corresponding ridge features found in two impressions is a qualification of the acceptable level of reasonable doubt tantamount to a judgment of moral certainty [34].   

The Qualified Probability Opinion

Traditional statements for fingerprint source attribution are "identification, exclusion and inconclusive" and have excluded gray-scale probability statements as "highly likely", "likely", unlikely" and so on [34].   The gray-scale probability statement or "qualified opinion" attempts to assess the value of evidence with amounts of corresponding ridge features that fails to exceed a posterior probability of 1, however is deemed significant enough to report if it tends to make inference for positive identification more or less probable that otherwise.

The greatest strength, or weakness, of any probability based fingerprint evidence (PBFE) model is its ability, or inability, to reliably establish a posterior probability greater than or equal to 1 for amounts of matching ridge features in two impressions when utilizing Automated Fingerprint Identification System (AFIS) technology.   All AFIS technology is designed to find the largest and best friction ridge arrangement "look-alikes" that exist in its database.  As a result, any PBFE model that uses likelihood ratios to measure the aggregate weight of friction ridge arrangements present in two impressions must successfully pass validation testing against the largest and best fragmentary friction ridge look-alikes ever recorded in a given fingerprint population.  The model must either demonstrate zero specificity, e.g., a zerp false positive error rate, or at the very least show an improved error rate over that found in human decision-making.       

The T-Model discards qualified probability opinion when the posterior odds for an amount of corresponding ridge features found in two impressions (based on an AFIS search) is calculated to be less than 1.  Only a model that demonstrates zero specificity, e.g., a zero false positive error rate, when pitted against the largest and best friction ridge look-alikes AFIS can find, should be considered reliable enough for use in criminal casework.

The Justified Opinion

The T-Model sets the demarcation for sufficiency to infer positive identification, e.g., the posterior probability, at 1.  Therefore, based on prior odds, e.g., the relevant population for the case at hand, and the aggregate weight assigned to the amount of corresponding ridge features found in two impressions, e.g., the likelihood ratio, any posterior probability found to be greater than or equal to 1 is considered sufficient to infer positive identification.  As a result, the inference for positive identification is considered a justified opinion. 

The justified opinion to infer positive identification may be considered to bridge the gap between the individualization to the exclusion of all others opinion and the qualified opinion by setting the demarcation for sufficiency to infer positive identification to a posterior odds defined as absolute 1. 

The justified opinion for fingerprint source attribution can be made on partial, fragmented parts of whole, complete fingerprints.  For purposes of conservatism, the number of parts in the average fingerprint, each sufficient to establish source attribution, is set at 22 (see The Formulae), which is multiplied against the fingerprint population group of 3 billion (i.e. 10 fingers multiplied by 300 million people) in order to establish the total number of parts per fingerprint in the total [default] fingerprint population in the United States.  Subsequently the total fingerprint part population is set at 66 billion.  As a result the match probability used to establish positive identification for routine casework is 1/66 billion*.

*It is significant to note here that 1/66 billion is the rough equivalent of the match probability used by the FBI to match DNA profiles for routine casework [84].  

2.  The following information was added/revised to Likelihood Ratio:

*Note:  "The numerator of the likelihood ratio asks for the probability of the evidence if the suspect has left the recovered evidence.  This probability is not systematically equal to one and must be assessed in each case taking into account the intra-variability of the whole process that generates the mark." [34]  In other words, the numerator takes into account discrepancies which speaks to the strength of the non-corresponding ridge features found in two impressions.  For example, on rare occasion, both corresponding and non-corresponding ridge features (absent clear distortion markers) are observed in fingerprints (see Non-Corresponding Ridge Events).  Dissimilarities observed in two impressions which also bear similar features should not be "explained away" without clear elicitation and ability to demonstrate how the dissimilarity occurred, e.g., reproduce it to the satisfaction of the trier of fact.  

For purposes of a timely work product the default value for the denominator that the suspect of the fingerprint evidence is not the source is based on the FBI population standard used to match DNA profiles and subsequently defined as the match probability equal to the numbers of parts per fingerprint in a total United States human population of 300 million, e.g.,  approximately 66 billion (see The Formulae).

However, if the likelihood ratio is borderline and the examiner is unclear about whether or not it clearly and beyond doubt exceeds the relevant population group for the case at hand, then posterior odds based on the relevant population and likelihood ratio should be calculated.

August 7, 2009 (Version 3.0.3)

The Fingerprint Analysis page has been updated to emphasize the importance of rendering a best estimate of the likelihood ratio for a given aggregate amount of ridge features in a friction ridge impression prior to comparison.

August 4, 2009 (Version 3.0.3)

Sample latent v. exemplar documentation has been added to the Bench Notes page.  Also, the following additional information is included:

It is significant to note here that SWGFAST latest definition for the "V" in ACE-V, e.g., verification [95], as "The final step of the ACE-V method. A review and independent analysis of the conclusion of another examiner", fails to speak to the root meaning of the word "verify", e.g., to prove the truth of, and is inconsistent with basic dictionary definition.  Instead, it describes the simple process used to either corroborate or refute, e.g., agree or disagree with, the initial conclusions made by the first examiner.  

It is important for examiners to understand the fact that all knowledge is provisional, conjectural, hypothetical - we can never finally prove our scientific theories, we can merely (provisionally) confirm or (conclusively) refute them [Karl Popper].  This simply means when a fingerprint examiner makes an identification, for example, a second examiner can only agree or disagree with it; he cannot prove the truth of it.  Therefore, the word "verification" implies a much greater strength for the evidence, compared to a "review" or "corroboration", and therefore, again, is considered misleading and an exaggeration to the trier of fact.  

August 1, 2009 (Version 3.0.3)

The Bench Notes page has been further refined.

July 29, 2009 (Version 3.0.3)

The Bench Notes page has been updated to reflect recommendations by SWGFAST and the NAS Report.

July 5, 2009 (Version 3.0.3)

The "Fingerprint Calculator" was refined. The calculator is now on 1 page, has 20 entries for ridge features instead of 14, the term "shape" replaced "type" and the term "position" replaced "IRC" (Intervening Ridge Count to nearest neighbor), and it includes calculation for the actual number of look-alikes with the confidence interval for a confidence level of 99% (see Validation Study).

For easy access to any future updates for the calculator, a Fingerprint Calculator page was created.

June 30, 2009 (Version 3.0.2

For purposes of quick independent experimentation and validation study of the T-Model, a "fingerprint calculator" was created using Microsoft Excel.  The calculator automatically calculates the estimated likelihood ratio, fingerprint match probability, number of look-alikes in the relevant population group for the case at hand, and whether or not there is a sufficient amount of matching ridge features to infer positive identification. See bottom page of "Validation Study".

June 20, 2009 (Version 3.0.1)

Links to translate the web site were included on the Introduction and Fingerprint Consulting Services pages.

June 19, 2009 (Version 3.0.1)

Information regarding the author has been updated (see Author). 

June 5, 2009 (Version 3.0.1)

1.  For purposes of refinement, two new friction ridge "clarity" and "quality of agreement" scales are under review and will be tested against the largest and best look-alikes ever recorded.  See Ridge Unit Quality and Quality of Agreement Level II.

2.  The following was added to the page Clark Non-Match:

Note

Research is underway to test refining the value for fingerprint parts (P) based on the presence of unambiguous pattern types, e.g., whorls, right slant and left slant loops, arches, and core and/or delta formations, in order to reduce relevant population according to the statistical frequencies for each.  It is hypothesized that such a reduction will more accurately reflect relevant population and consequently reduce the calculated number of look-alikes for the Clark Non-Match. 

Note

May 20, 2009 (Version 3.0)

Following recent corroborative test results and information providing further support for the T-Model, on May 15, 2009 Henry Templeman applied the T-Model to a "Question of  Identification" corporate (not criminal) fingerprint case.  It was the first time a probability estimate was calculated using T-Model statistical probability theory and formally presented in a report to describe the quantitative and qualitative weight of fingerprints. The change from theory to application was significant enough to update the previous "T-Model BETA Version 2.0.3" to a working "T Model Version 3.0". 

In addition the following six (6) updates were included:

1.  Results from the following experiment were included in the section Validation Study:

CORROBORATION BY INDEPENDENT EXPERIMENT

The following experiment corroborates, in part, the use of the Osterburg study to define frequency values for ridge features, and corroborates the idea that the ratio of the most common, significantly weighted friction ridge features used in fingerprint identification, e.g., the ending ridge, bifurcation and dot, are the same across all fingerprint regions, and corroborates the assumption that Osterburg consolidated immature, e.g., incipient, ridge features with mature, e.g., normal ridge features in his frequency study:

The Michel–Tallerico–Verceluz (MTV) Experiment

Dawn Michel, Frances Tallerico and Cesar Verceluz, Latent Print Examiners at San Jose Police Department Central Identification Unit, performed an independent frequency study of 218 fingerprints that were largely comprised of right flat thumbs from different individuals (the experiment was conducted as a classroom training exercise for new examiner trainees).  The impressions were selected at random from criminal ten-print records.  Only clear, reliable, e.g., absent distortion marker, flat fingerprint impressions were used.  Individual mature and incipient friction ridge features, e.g., ending ridge units, bifurcating ridge units and single ridge units (dots), were combined and counted in each sample.  The results were then verified in the rolled fingerprint sample on the same ten-print record. 

The results from the MTV study were compared to the extrapolated results from the Osterburg study. The ratio of the frequency results for the different ridge feature types were as follows:

Osterburg Study

Ratio of bifurcations to ending ridges - 1 : 1.88           
Ratio of bifurcations to dots - 1 : 3.89
Ratio of dots to ending ridges - 1 : 6.42

MTV Study

Ratio of bifurcations to ending ridges - 1 : 1.87           
Ratio of bifurcations to dots -  1 : 3.84
Ratio of dots to ending ridges - 1 : 6.64

Conclusions

The MTV study corroborates the theory that numerical ratios for the most frequently used friction ridge features used in fingerprint identification defined by the Osterburg study are valid.

The Osterburg study utilized roughly a 221mm2 surface area, e.g., or about 13mm x 17mm, to count the number of ridge features observed in each fingerprint sample.  The area used to place the millimeter grid was the center portion of each fingerprint.  The center portion of fingerprints generally contains the core and not the periphery regions of fingerprints.  The MTV study utilized predominantly right thumbs which are known to contain significant amounts of distal periphery regions of the thumb, e.g., the tip area.  Subsequently, the MTV study corroborates the theory that the ratios of the most common, significantly weighted fingerprint ridge feature types, e.g., the ending ridge unit, the bifurcating ridge unit and the single ridge unit, e.g., dot, are the same across all fingerprint regions.

Osterburg did not distinguish between the immature, e.g., incipient, ridge unit type and the mature or normal ridge unit type in his frequency table (see Osterburg Frequency Table). The MTV study corroborates the theory that Osterburg consolidated these ridge feature types.

2.  Results from the following experiment were included in the section Validation Study:

The T-Model is More Accurate than ACE-V

The following experiment was performed to test the accuracy of expert fingerprint examiners to correctly identify amounts of corresponding ridge features in a look-alike as insufficient to identify:

Experiment

The Chesapeake IAFIS Non-Match, the largest and best look-alike ever seen, was used for this experiment (see Chesapeake IAFIS Non-Match) . The Chesapeake look-alike images were rotated 90 degrees clockwise and horizontally mirrored (to help guard against recognition).  Nine (9) sections of the look-alike were cropped using Adobe Photoshop in a manner so that only corresponding ridge features were left showing.  Each section displayed incrementally larger numbers of corresponding Level II ridge features, so that in each image there were from 4 to 12 matching Level II ridge features.

Then, nine (9) expert fingerprint examiners (including 6 CLPEs) were shown each image in succession and asked whether or not the amount of matching ridge detail present in the two images was enough to establish positive identification based on conventional "ACE" fingerprint methodology, e.g., utilizing only human intuition and subjective judgment to render an "expert opinion".

Note:  The fingerprint examiners tested conformed to no pre-determined minimum standard needed to establish positive fingerprint identification.  In addition they were not given any prior knowledge regarding the latent v exemplar in terms of relevant population (the fact that the "match" was found as a result of an FBI IAFIS search of a fingerprint database containing roughly 530 million fingerprints was not revealed to the examiners).  

The results for the above experiment were as follows: 

At different stages during the experiment, three (3) expert latent print examiners (including at least 1 CLPE) were prepared to establish "positive identification" based on the amount of matching ridge features displayed in the look-alike images.  As a result, 1 out of 3, or 33.3%, of the expert fingerprint examiners tested were fooled by the look-alike.   

Conclusion

The 33.3% error rate for "ACE" alone reflects significant inability for expert latent print examiners to reliably and accurately identify amounts of matching ridge features in two impressions as insufficient to establish positive identification when faced with the largest and best look-alike ever recorded. 

As a result, the error rate for "ACE-V", which represents  the error rate for 2 expert examiners performing an independent examination when faced with the largest and best look-alike ever seen, is calculated as 1/3 x 1/3 = 1/9, or 11.1%.

Note:  It is significant to note here that sufficiency to establish positive identification with a reasonable degree of scientific certainty depends on relevant population because as the population increases so does the number of look-alikes.  

In contrast to the above study, the T-Model was able to accurately and reliably identify each successive amount of matching ridge features in this look-alike, including every largest and best look-alike ever recorded as well as the the most notable erroneous fingerprint identifications ever recorded, as insufficient to establish positive identification [Link].  

As a result, when faced with the largest and best look-alikes ever recorded, the T-Model has a 0% error rate.

Prediction

The T-Model empirical probability approach to fingerprint identification is more accurate than conventional ACE-V fingerprint methodology, e.g., fingerprint expert decision-making based solely on human intuition and subjective judgment, to reliably and accurately identify amounts of matching ridge features in two impressions as insufficient to establish positive identification when faced with the largest and best look-alike ever recorded.

Based on deductively testing both theories, the T-Model theory, while unfalsified, is better than conventional ACE-V fingerprint methodology, e.g., an ACE-V which fails to define pre-determined minimum threshold probability estimates needed in two impressions in order to establish inference for positive identification and also fails to consider what is the relevant population for the case at hand.

Based on the above results, T-Model Theory has greater predictive power than conventional ACE-V fingerprint methodology.  This idea is consistent with the fact that the T-Model is grounded in empirical content, e,g., simple experimentation.  For Karl Popper, one of the greatest philosophers of science in the 20th century, the following statement supports this idea:

"[For Popper] any theory X is better than a ‘rival’ theory Y if X has greater empirical content, and hence greater predictive power, than Y."

[Stanford Encyclopedia of Science]

It is significant to note here that conventional ACE-V is not entirely replaced by T-Model theory but rather refines it with statistical probability theory, as well as with the following significant exception:

The "V" for "verification" in "ACE-V" comes from the word "verify" which means "to prove true" or "authenticate".  That is the root meaning and true implication of the word.  Not only can no scientific theory be proved true or authenticated (this idea is supported by Karl Popper and noble prize scientist Richard Feynman), but also no latent fingerprint identification can be proved true or authenticated.  There is always the theoretical chance the "identification" can be a look-alike and you can be wrong.

The National Academy of Science report makes it clear that fingerprint identification is probabilistic in nature and therefore fingerprint identification can never be verified or proved true with absolute certainty.  As a result, the "verification" in ACE-V is misleading and exaggerates the weight of fingerprint evidence.  Subsequently, the idea that fingerprint examination requires the examination by two independent examiners in order to be "scientific" is a fallacy.  For purposes of quality assurance, and for that reason only, should a second examiner perform a technical review or check of the initial examiner's work.

Lastly, it is significant to note that unlike conventional ACE-V fingerprint methodology, the T-Model forbids positive identification for amounts of corresponding ridge features in two impressions that fail to meet the minimum probabilistic threshold for the case at hand.  All true scientific theories are prohibitive. 

3. The last paragraph in the section  "Error rates in Look-alikes Calculated v. Observed" was revised to read as follows:

Based on results from 50 validation studies (Link] the T Model calculates roughly a 23.6% larger number of look-alikes compared to what is the actual number observed.  For example, if the number of look-alikes for an amount of matching fingerprint ridge features in two impressions is calculated by the T Model to have 1.12 look-alikes based on an AFIS fingerprint population of X, e.g., greater than 1 and therefore exculpatory in favor of a defendant, then the actual number of look-alikes observed, if all fingerprints were compared, is predicted to be roughly 0.91, e.g., less than 1 and therefore inculpatory in favor of the procecution.  As a result, T-Model calculations slightly favor the defendant.  For purposes of performing criminal casework in a conservative manner, e.g., to provide additional quality assurance to help guard against the erroneous fingerprint identification of an innocent person, these results are appealing.

4.  The following section under "Quality of Agreement Level II" was re-written for purposes of clarification:

"Precise" and "Relative" Agreement of Ridge Formations in Two Impressions

The terms "precise" and "relative" are used to refine levels of agreement between ridge features in two impressions as follows:

"Precise" agreement between ridge formation shapes in two impressions was defined in terms of ridge types and ridge paths.  Precise agreement is used when  ridge types precisely match and ridge paths, i.e. the slants, curves or angles observed between the ridge unit features in the two impressions, are found to be in relative close or near precise agreement. 

It is significant to note here that relative level II ridge path agreement should not be confused with level III ridge unit width and ridge unit edge contour in agreement.   The agreement of level III ridge detail should expand the quantitative weight for a continuous ridge unit in agreement.  Pending validation studies this value is tentatively set at 1.15.

"Relative" agreement between ridge formation shapes in two impressions was defined in terms of ridge types and ridge paths.  Relative agreement is used when ridge types precisely match, however ridge paths, i.e. the slants, curves or angles, observed between the ridge unit features in the two impressions, are found to be not close and not in near precise agreement but bordering on and just within tolerance to include. 

5.  The Disclaimer section was updated (see Disclaimer).

6.  A new section titled "Services" was included.

May 1, 2009 (Version 2.0.3)

1.  The following additional foundational support for the T Model was included on the Foundation for the T Model page:

In addition to using a ridge unit approach, ridge unit frequency, and relevant population, to define discrimination values for individual amounts of ridge features, and define match probabilities for amounts of corresponding ridge features found in two impressions, the following additional variables serve to complete the foundations for the T Model:

Pattern Force [Link]

Friction Ridge Skin Elasticity Threshold [Link]

Intervening Ridge Count to Nearest Neighbor (Level II) [Link]

Ridge Unit Clarity and Reliability [Link]

Ridge Unit Quality of Agreement [Link]

2.  The last paragraph in section Ridge Unit Frequency was simplified to read as follows (Note:  The figures in the below study remain unchanged):

It is significant to note the Osterburg model is convenient because the aggregate grid of 8,591 1mm^2 cells in the 39 randomly selected fingerprints corresponds more to a flat fingerprint impression, as opposed to a rolled fingerprint impression.  Based on a simple study, friction ridge skin most often contacting a given substrate is generally the central portion of a finger and not its periphery.  Thus it may be inferred that the flat fingerprint impression represents ridge formations that are typically found in the chance, accidental or latent fingerprint impression.  See the below study.

Osterburg took the center portion of a fingerprint which most reflects information found in a flat fingerprint on an exemplar ten-print record compared to its counterpart rolled impression.  It was also hypothesized that a flat fingerprint best represented ridge detail found in the average "useable" latent fingerprint, e.g., latent print impression bearing "value" for a conclusion of identification or exclusion. In order to corroborate this general idea, the following study was performed:

Study

A frequency of occurrence study was performed on a random sample of 50 identified latent fingerprints at the San Jose Police Department Central Identification Unit as follows:  The numbers of identified latent fingerprints with delta, out-of-delta, core and periphery regions were counted with the following results:

Region of Interest        Percentage Distribution

Core                                 81%   
Out-of-Delta                      75%   
Delta                                35%   
Periphery                           6%   

As a result of the above study, it was found that approximately 94% of latent print identifications examined displayed no periphery, and 81% displayed a core, which are both consistent with information found in the flat fingerprint impression as opposed to information found in a rolled fingerprint impression which includes periphery ridge feature information. 

April 13, 2009 (Version 2.0.2)

On The Formulae page, the equation "(P) Log (6 billion) = 240" should read "(P) Log (66 billion) = 240".  The equation has been corrected to read as follows:

T ^ P = F

(66 billion) ^ P = 10 ^ 240

Log (66 billion) ^ P = Log (10 ^ 240)

(P) Log (66 billion) = 240

(P) (10.8195) = 240

P =  22.1820

L = (R) (P) / T

L = (3 billion) (22.1820) / 66 billion

March 28, 2009 (Version 2.0.1)

The following information was included on the page Probability Theory:

The Three Major Methods Used to Determine Probability Values:

Subjective Probability
Prior Probability (Classic or Theoretical)
Empirical Probability (Frequentist)

Subjective Probability

Subjective probability is a probability value based on an individual's best available knowledge and personal judgment about how likely a particular event is to occur. It is not based on any formal calculations but is a reasonable assessment by a knowledgeable person that reflect the subject’s opinions and past experience. 

Like all probabilities, a subjective probability is conventionally expressed on a scale from 0 to 1; a rare event has a subjective probability close to 0, a very common event has a subjective probability close to 1.  A person's subjective probability of an event describes his/her degree of belief in the event.  Absent a probability model, only verbal statements can be used to describe a fingerprint examiner’s degree of belief for positive identification, i.e. bordering on certainty (with a reasonable degree of certainty), highly likely, likely, and so on.   

Subjective probability thresholds can be tested based on the following theory:

The more you are willing to pay for entering a bet in which you win some fixed amount if your belief turns out to be true, the higher is your subjective probability.

In the above theory, your willingness to bet serves as an indicator of how likely you think the belief is to be true.  For example, how much are you, the fingerprint examiner for the case at hand, willing to bet that the fingerprint identification is correct and not an unexpected look-alike or a clerical error?  Are you willing to bet 1 year in prison?  Are you willing to bet 20 years in prison?  Life in prison?  Are you willing to bet your life?

It is significant to note that the subjective approach to assigning probability value is used when prior and empirical approaches cannot be used.


Priori Probability (Classic or Theoretical)

Priori probability is a probability value that can be determined prior to any experimentation or trial. For example, the probability of obtaining a tail in tossing a coin once is fifty percent. The coin is not actually tossed to determine this probability.  No experiments are carried out.  It is simply observed that there are two faces to the coin, one of which is tails and that heads and tails are equally likely.  A priori probability is a situation where probability is assigned based on prior knowledge of the process involved.  Examples of this are that we can assign probability in card games, coin flipping, and die tossing.  This is sometimes called the classical method of assigning probability.


Empirical Probability (Frequentist)

Empirical probability is a relative frequency method, which determines probability value by observation and experimentation. An example of this is a manufacturing process where after checking one hundred parts, five are found defective. If the sample of one hundred parts was representative of the total population, then the probability of finding a defective part is .05 (5/100).  The question may be asked:  How is it known that this sample is representative of the total population?  If repeated trials average .05 defective, with little variation between trials, then it can be said that the empirical probability of a defective part is .05. 

The empirical approach to assigning probability is used when data is available about the past history of the experiment.  The probability of an outcome is the relative frequency of the outcome.  You can form this probability by taking the ratio of the number of times the outcome came up over the total number of times of the experiment.  As an example, if one takes a random sampling of 100 fingerprints and let's say it is found that a total of 100,000 ridge units, i.e. continuous ridge units, ending ridge units, bifurcating ridge units, and so on, are observed, and more specifically one observes 87,000 continuous ridge units, 8000 ending ridge units, 4000 bifurcating ridge units, and 1000 single ridge units (dots) are found, then the empirical probability of finding 1 ending ridge unit is 8000/100000, or 1 out of 12.5.  Similarly, the empirical probability of finding a bifurcating ridge unit is 1/25, and for a dot it is 1 out of 100.

Empirical probability can be thought of as the most accurate scientific "guess" based on the results of experiments to collect data about an event.  Because some problems are so complicated for analysis, we can only estimate probabilities from experience and observation. This is empirical probability.  Experience has shown that empirical probabilities, if carefully determined on the basis of adequate statistical samples, can be applied to large groups with the result that probability and relative frequency are approximately equal. By adequate samples we mean a large enough sample so that accidental runs of "luck," both good and bad, cancel each other. With enough trials, predicted results and actual results agree quite closely.

The empirical approach to determining probabilities relies on data from actual experiments to determine approximate probabilities instead of the assumption of equal likeliness. Probabilities in these experiments are defined as the ratio of the frequency of the occurrence of an event to the number of trials in the experiment.  If an experiment involves flipping a coin, the empirical probability of heads is the number of heads divided by the total number of flips.  The relationship between these empirical probabilities and the theoretical or true probabilities is suggested by the Law of Large Numbers.

Law of Large Numbers

The Law of Large Numbers states that as the number of trials of an experiment increases, the empirical probability approaches the theoretical probability [6][see Ridge Unit Frequency]. This makes sense as we would expect that if we roll a die numerous times, each number would come up approximately 1/6 of the time.

The study of empirical probabilities is known as statistics.  The T Model utilizes, in most part, the frequency method of empirical probability based on observation and experimentation to define relative probability values for ridge formation shapes in position.   It is significant to mention here that based on a sufficiently large fingerprint sampling, definitive probability values for all ridge formation types in position can be established.

March 24, 2009

Under "Quality of Agreement Level III" the match probability value for the single pore feature, defined as 1/5, was included.

March 20, 2009

1.  Under "Validation Study", the phrase "duplication likelihood was defined as" was replaced with the phrase "the number of look-alikes was calculated to be".  Also the phrase "based on an aggregate QQ Value" was replaced with the phrase "based on an aggregate weight, e.g., likelihood ratio,".  Also under "Standard Deviation" the phrase "predicted duplication likelihood" was replaced with the phrase the number of look-alikes calculated".

March 19, 2009

The following clerical errors were corrected:

1.  Under the "Chesapeake IAFIS Non-Match" in the last paragraph, the phrase "duplication likelihood" was replaced with the phrase "the number of likely look-alikes". 

2.  The number "10" ridge feature in the Chesapeake IAFIS Non-Match evaluated by the author was omitted in the evaluation of the first group of ridge features. 

2.  Under the "Clark Non-Match" the number "26,26,523,299" was corrected to read "26,523,299".

March 9, 2009

1.  A photo of the author courtesy of Lipo Ching, San Jose Mercury is included (see Author).

2.  Update of the Top 10 reads (see Examiner Training 1/2) that includes NAS and IAI recommendations.

3.  The phrase "with a high level of confidence" has been inserted in the statement that infers attribution to a single source in the Introduction to read as follows: 

“Fingerprint exemplar X is the source of fingerprint evidence Y with a high level of confidence and reasonable degree of scientific certainty.”

March 6, 2009

1.  The following quote by Christophe Champod is included in Likelihood Ratio:

“The future lies in an assessment of forensic evidence in the perspective of its likelihood ratio, as it constitutes a coherent way of describing objectively the weight of scientific evidence.”  

March 5, 2009

1.  As a result of the National Academy of Sciences report released on 2/18/2009 titled Identifying the Needs of the Forensic Science Community [Link], the International Association for Identification (IAI) made the following recommendations to members [Link] on 2/19/2009:

"Although the IAI does not, at this time, endorse the use of probabilistic models when stating
conclusions of identification, members are advised to avoid stating their conclusions in absolute terms when dealing with population issues."
 
The IAI acknowledgment that fingerprint identification conclusions should not be stated in absolute terms supports the fact that, absent an accepted probabilistic model at this time, examiners must rely on subjective probability to establish positive identifications.  As a result of this acknowledgment, the IAI comment (under Comments) expressing "general concerns about [the author's] proposed statistical modeling approach to fingerprint identification" has been removed.

2.  The following information was added to the Introduction: 

NAS and IAI Recommendations

It is significant to note here that as a result of the National Academy of Sciences (NAS) report released on 2/18/2009 titled Identifying the Needs of the Forensic Science Community [Link], the International Association for Identification (IAI) made the following recommendations to members [Link] on 2/19/2009:

"It is suggested that members not assert 100% infallibility (zero error rate) when addressing the reliability of fingerprint comparisons." 

"Although the IAI does not, at this time, endorse the use of probabilistic models when stating
conclusions of identification, members are advised to avoid stating their conclusions in absolute terms when dealing with population issues." 

Absent an accepted probabilistic model at this time, the IAI acknowledgment of a non-zero error rate for ACE-V methodology and that fingerprint identification conclusions should not be stated in absolute terms supports the use of subjective probability to establish positive identifications.  The use of subjective probability in fingerprint identification was supported by forensic scientists Joshua Bergeron, Glenn Langenburg and Cedric Neumann during the State of Minnesota v. Jeremy Jason Hull Frye-Mack hearing [Link] in 2008.

February 19, 2009

The section under "Pre-Determined Minimum to Individualize" incorporates Francis Galton's calculation for the match probability of two people having the same fingerprint as follows:

The number of look-alikes likely to occur is calculated to be precisely 1.00 inclusive of the evidence fingerprint.  As a result, based on a population group of 300 million people there is valid basis to define any amount of matching ridge formations present in two impressions bearing a T Value (T) or Likelihood Ratio (LR) of 66 billion as the pre-determined minimum threshold needed to establish sufficiency to individualize.

The Likelihood Ratio of 66 billion represents a match probability of 1/66 billion which is nearly in agreement with Francis Galton's calculation for the statistical probability of two people having the same fingerprint as 1 in 64 billion [89].  The T Model provides scientific independent corroboration of Galton's fingerprint match probability (FMP) calculation, albeit performed in a different manner.  It may be stated that Galton's calculation has been verified.  Consequently it may also be stated that at this time scientific basis exists to require a pre-determined minimum amount of corresponding quantitative-qualitative ridge formations in two impressions in order to establish valid basis for sufficiency to individualize. 

February 17, 2009

1.  The terms "Likelihood Ratio" and  “Match Probability” are incorporated throughout the model to define fingerprint identification in terms similar to those used by the FBI and general forensic science community. 

2.  Final estimates for ridge formation weights are expressed in terms of Likelihood Ratio  (the reciprocal of the Fingerprint Match Probability (FMP) defined by the model) in order to be in line with standard probability theory. 

3.  The term "duplication likelihood" is replaced with the phrase "number of look-alikes".

4.  A new Introduction , and new pages titled "Likelihood Ratio" and "Probability Theory" have been included.

5.   The changes made to the model are significant enough to designate this version as  “T Model BETA VERSION 2.0”. 

NOTE:  As a result of these latest updates, sections throughout the web site have been significantly changed.  Readers are encouraged to visit each section to review these changes. 

January 4, 2009

The term "It has been said that" is inserted in the first paragraph on web page Pattern Force 2/2 to modify and more correctly describe the Golden Ratio that is reflected in some aspects of nature.   Also the quote "Nature does, it seem, favor the golden ratio.", by Stanford University Mathematician Keith Devlin [83], is included.

December 20,2008

1.  The following comment was posted on the Comments Page:

“I should say that the T-model is the most advanced modeling system that I have ever seen in my 5 years’ research. It has integrated identification technology, mathematics and art of nature to define and measure the quantitative weights and qualitative metrics for all levels of individual and aggregate amounts of fingerprint ridge formations. It is really a very dedicatedly fulfilled work.”

Wang Wei is a visiting scholar from the Education Ministry of China to the Henry C. Lee College of Criminal Justice and Forensic Sciences, University of New Haven.  Wang Wie has worked with the Fingerprint Information and Identification Center of Liaoning Provincial Police Forensic Science Institute for 8 years.
 

2.  The following information is included on the Relevant Fingerprint Population page:

November 30, 2008

The following information is included on the Product Rule page:

The work of Newell and Kuchen, see "A model for fingerprint formation", provides additional foundation for the fact that individual ridge formation types do not depend on each other specifically and are fundamentally dependent on the stresses and forces that occur at the basal layer during fetal development.  The observations by Newell and Kuchen provides further support of the fallacy to consider "compound" ridge formation types, i.e. enclosures, short ridges, spurs, etc., as independent events and use them in frequency studies and apply any weights accorded to them to the product rule in order to attempt to define quantitative weights or match probabilities for aggregate ridge formation types.

November 23, 2008 

Additional photographs displaying how thresholds for friction ridge skin elasticity were measured and defined are included on the Friction Skin Elasticity page. 

November 21, 2008 

Video clips describing the Golden Ratio, an interview with Richard P. Feynman, and a presentation by Gerry Spence on the erroneous FBI fingerprint identification to Brandon Mayfield, were added on the Pattern Force 2/2 , Validation Study and Madrid Error pages respectively. 

November 1, 2008 

The following statistical data and conclusions are included in the Validation Study:

Standard Deviation

Standard deviation is a measure that shows how spread out values are around a particular mean or average. The larger the value of the standard deviation, the more the values are spread out.  Standard deviation also serves as a measure of uncertainty. In physical science for example, the reported standard deviation of a group of repeated measurements should give the precision of those measurements. When deciding whether measurements agree with a theoretical prediction, the standard deviation of those measurements is of crucial importance: if the mean of the measurements is too far away from the prediction (with the distance measured in standard deviations), then the theory being tested probably needs to be revised.
The results from all 50 experiments were used to calculate standard deviation and show how spread out values are around the average.  In order to calculate the standard deviation, a standard deviation calculator was used [78].

Based on results from all 50 experiments in which the predicted duplication likelihood was set at precisely 3.0, the mean value was determined to be 2.22 (just slightly lower than the 2.3 mean for the results from the 5 grouped experiments) with a standard deviation of 1.88. 

Confidence Interval

Confidence interval is the range around a test result for which there is a high statistical probability that it contains the true population parameter.  In order to determine the range for the true population mean a “confidence interval for means calculator” was used [79].

Based on a confidence level of 99%, a sample size of 50, and a standard deviation of 1.88, the confidence interval was defined as ± 0.68. 


Range for True Population Mean

The "true population mean" was defined as the actual mean or average numbers of look-alikes  you would get based on a study of a larger number of experiments, i.e. 5000 experiments instead of 50.  Based on a confidence interval of ± 0.68, the range for the true population mean was subsequently defined as 1.54 – 2.90. 

Conclusions 

6.  Based on a standard deviation of 1.88, a sample size of 50 experiments, and a confidence interval of ± 0.68, a true population mean range of 1.54 - 2.90 with a 99% confidence level is extremely appealing because it is both close and under the predicted amount of 3.0.

7.  Based on results from all 50 experiments, the 99% confidence level for the range of the true duplication likelihood of 1.54 – 2.90 compared to the predicted 3.0, provides significant support that the T Model is a relatively accurate statistical model able to predict conservative upper bound numbers of look-alikes likely to exist in a given fingerprint population.

October 12, 2008

1.  Recommended top 10 books, articles and/or reports about fingerprints and current issues in the practice of fingerprint identification are included in [Examiner Training 1/2].

2.  The following information was added to Validation Study:

The consequence for a 23.4% error rate may be demonstrated as follows:  Let’s say there are three (3) different latent fingerprints with 11, 12, and 13 strong ending ridges in a funnel that are in excellent agreement with 3 different exemplar impressions.  The T-Values for these amounts of corresponding ridge formations are defined as 10^11, 10^12 and 10^13 respectively (given that there are no corresponding pores or continuous ridge edge contours and widths in any of the latents v. exemplars).  Using the T Model, based on an upper bound conservative 18-65 year old world fingerprint population of 24,552,000,000, the number of look-alikes likely to exist for each is 5.35, 0.49, and 0.04 respectively.  A 23.4% error rate translates to 4.09, 0.37 and 0.03 actual look-alikes respectively.  As a result, duplication likelihoods defined by the T Model are barely, yet conservatively, just above the actual or true number of look-alikes found.  Based on “individualization” defined as the number of look-alikes likely to occur in a given fingerprint population as less than or equal to 1, the above values mean there is no change in terms of whether or not any of the 3 amounts are sufficient or insufficient to individualize.  In other words a 23.4% error rate is small enough to be considered of little or no consequence when defining whether or not amounts of corresponding ridge formations in two impressions are sufficient or insufficient to individualize, especially in terms of performing routine casework which for the most part utilizes the presence of matching Level II ridge formations in sequence only.

October 11, 2008

Recommended top 10 web sites to learn about fingerprints and current issues in the practice of fingerprint identification are included in [Examiner Training 1/2].

October 10, 2008

The paragraph under the fingerprint images in "Madrid Error" was re-worded to include reference to the report of the FBI's handling of the Brandon Mayfield case by the U.S Department of Justice Office of the Inspector General [77].  The changes are highlighted in red as follows:

The fingerprint examiners involved in the Madrid error were accused of violating the Patriot Act, not following proper examination procedure, succumbing to the pressures of a high profile case, and so on.  However, based on the Review of the FBI's Handling of the Brandon mayfield case by the U.S. Department of Justice office of the Inspector General the No. 1 major contributing cause of the error was "the unusual similarity of the prints" [77].  In other words, after searching a database of over 500 million fingerprints, the fingerprint examiners came across a portion of a fingerprint with similar looking features.  they came across a double, a twin.  They came across a look-alike. 

The FBI fingerprint examiners only had “professional judgment” to determine whether or not the amount of poorly corresponding ridge formations present in the two impressions was enough to individualize.  There was no other tool available that could more reliably and more accurately identify look-alikes as insufficient to individualize. 

It may be stated that the fundamental cause for the error, which is the same for every erroneous fingerprint identification ever made, was that the fingerprint examiners had no tool available to them more accrurate than "training and experience", and subsequently failed, to establish that the amount of poorly corresponding ridge formations present in the two impressions were insufficient to individualize.  There were not simply enough matching ridge formations in terms of quantity and quality, i.e. visually clear, absent distortion markers, and level of agreement, present in the two fingerprint impressions to warrant a claim of sufficiency to individualize. 

September 28, 2008

The following information was included under Comments:

Excerpts from Super Crunchers by Ian Ayres [74]:

"First and foremost, Super Crunchers (e.g. statistical models) are better at making predictions because they do a better job at figuring out what weights should be put on individual factors in making a prediction.  Indeed, regression equations are so much better than humans at figuring out appropriate weights that even very crude regressions with just a few variables have been found to outperform humans."

"Unlike self-involved experts, statistical regressions don't have egos or feelings....Statistical predictions are also not overconfident."

"Decisions that are backed by quantitative prediction are at least as good as and often substantially better than decisions based on mere lived experience.  The mounting evidence of statistical superiority has led many to suggest that we should strip experts of at least some of their decisionmaking authority."

"In context after context, decision makers who wave off the statistical predictions tend to make poorer decisions."

"Humans do make better predictions when they are provided with the results of statistical prediction.  The problem is that even with Super Crunching assistance (e.g. statistical modeling), humans don't predict as well as the Super Crunching prediction by itself....so the experts get better if you give them the model.  But still the model by itself performs better."

"The most important thing that is left to humans is to use their minds and intuitions to guess at what variables should and should not be included in statistical analysis.  A statistical regression can tell us the weights to place upon various factors....humans, however, are crucially needed to generate the hypotheses about what causes what."

"In the new world of database decision making, [these] assessments are merely inputs for a formula and it is statistics, and not experts, which determine how much weight is placed on the assessments."

An introduction to Ian Ayres work is presented on YouTube.


September 27, 2008

The following information was added to the Introduction for the T Model:

There have been numerous studies showing that simple statistical methods are more accurate than humans and that the more complicated the problem the less likely an “expert” will beat a statistical model.  One reason why humans perform poorer than statistical models is because they fail to assign the right weights to the overall “equation”, but they think they do [53][74][75][76].

Fingerprint experts currently rely almost exclusively on a non-statistical professional judgment or personal opinion approach to define relative weights for fingerprint ridge formations in order to exceed sufficiency thresholds to establish positive identification or exclusion.  However, notable erroneous fingerprint identifications, i.e. [Brandon Mayfield] and [Shirley McKie], and recent fingerprint studies indicate that fingerprint expert opinion can be an inaccurate and unreliable methodology, and in some cases reliably so.

A recent study performed by Christophe Champod, Cedric Neumann et al, shows fingerprint experts do not agree how much weight to accord fingerprint ridge formations [72].  The study is significant because it reveals that fingerprint expert opinion cannot accurately or reliably measure and define weights for partial and subsequently total amounts of corresponding ridge formations in two impressions.  Without the ability to reliably measure and define total weights for aggregate ridge formations, fingerprint examiners have no valid basis to establish sufficiency thresholds for positive identification or exclusion.

In general fingerprint examiners receive no training in statistical modeling in terms of how to measure and define weights for ridge formations.  As a result fingerprint examiners are for the most part unaware of how much it could likely help them make more accurate, reliable judgments.  Based on works by Meehl [53], Ayres [74][75], Trout and Bishop [76], Champod and Neumann, et al [72], there is overwhelming evidence for the need of fingerprint experts to apply statistical models when making decisions about fingerprint identifications or exclusions, especially if the amount or volume of ridge detail present in two impressions is extremely distorted, highly fragmented, or “borderline”.

In an effort to make more accurate and reliable decisions about how much weight to accord individual and aggregate fingerprint ridge formations and at what precise point a positive fingerprint identification or exclusion can be made....


September 26, 2008

1.  Links that provide additional information regarding a statistical approach as more accurate that a non-statistical approach were added under the author's response in Comments.

2.  The above information with further explanation was added to Court as follows:

There have been numerous studies showing that simple statistical methods are more accurate than humans and that the more complicated the problem the less likely an “expert” will beat a statistical algorithm. One reason why humans perform poorer than statistical models is because they fail to assign the right weights to the overall “equation”, but they think they do [53][74][75][76].

Fingerprint examiner “experts” currently rely almost exclusively on a non-statistical professional judgment or personal opinion approach to define relative weights for fingerprint ridge formation types and to make decisions regarding positive identification or exclusion.  The Champod/Neumann study illustrates how fingerprint examiners consistently fail to agree on relative weights given to specific fingerprint ridge formation types.  The results from this study shows that the attribution of fingerprint ridge formation weights based on expert opinion cannot be accurate or reliable.  If examiners who rely only on expert opinion cannot reliably make decisions about the weight accorded to different amounts of ridge formation types, then the decisions they make regarding what is the threshold for sufficiency to establish positive identification and at what point it is exceeded must also be unreliable.

This is a significant issue for the field of fingerprint identification especially in light of the Maryland v. Bryan Rose case in which fingerprint evidence was not admitted based on the State’s witness failure to elaborate on “sufficiency”.  This issue is easily remedied by assigning quantitative weights to specific ridge formation types based on frequency of occurrence and application of the product rule to calculate aggregate values and compare these values against the largest and best amounts ever recorded in a non-match.  Total values that exceed the total value for the largest and best look-like ever recorded [even for a given fingerprint population] may be considered valid, scientific basis to establish sufficiency to individualize.

3.  A training exercise that demonstrates a statistical modeling approach to define weights for ridge formations is more reliable than expert opinion is included in Examiner Training 1/2.  


September 9, 2008

The following information was added to the Validation Study:

The central values for the numbers of look-alikes found in the 50 experiments were relatively equivalent and calculated as follows:

Mode (most common number of look-alikes)= 2
Median (middle number of look-alikes) = 3
Mean (average number of look-alikes) = 2.22

The similar central values are consistent with a normal curve or normal distribution.


September 5, 2008

1. A new page has been included called "Court" that discusses Illinois v. Thomas Jennings and Maryland v. Bryan Rose, and the problem facing fingerprint examiners about what scale to use to weigh ridge formations and the need to be able to better elaborate on "sufficiency" to individualize.

2. Comment by Pat Wertheim is included regarding how weights or values for ridge formations are determined as well as results from a survey by Christophe Champod, Cedric Neumann and others, that show examiner disagreement regarding perceived weight or value for ridge formation types.  See Ridge Unit Weights (1/3).


September 1, 2008

Further explanation and an image of a directional ridge formation impacted by pattern force located between a delta region and diverging type lines are included (see Pattern Force 1/2).


August 29, 2008

1.  The definition of "individualization" as "exclusion of all others in a group based on duplication likelihood less than or equal to 1" and the phrase "duplication likelihood" defined as "number of look-alikes that are likely to occur in a given fingerprint population" was included in the first paragraph of the first page (see Introduction).

2. Pore and ridge edge formations are illustrated in "Poroscopy: A Method of Personal Identification Revisited" and captured under 50x magnification (see Reference No. 69 and Quality of Agreement Level III).

3. Image of friction skin magnified 50x showing pores is included.  See Ridge Unit Weights (1/3).


August 28, 2008

1.  Additional images are displayed of common look-alikes found in nature (see Error Rate in Terms of Look-alikes).


August 18, 2008

1.  The error rate for the T Model to correctly define duplication likelihood based on validation study was included in the "Error Rate in Duplication Likelihood" with a link to the "Validation Study" page.


August 17, 2008

1.  PDF version of Bench Notes included.

2.  Images depicting the Golden Ratio found in nature are included (see Pattern Force 2/2).


August 16, 2008

In order to assist a judge and jury better understand the probative value of fingerprint evidence at trial, duplication likelihood can be expressed graphically in terms of relevant fingerprint population.  A sample graph that displays this relationship is included.  See Relevant Fingerprint Population and Bench Notes.

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Suggestions how to improve the T Model may be submitted to the author by email at:

henry@henrytempleman.com