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NEAFS Probabilistic DNA MixtureInterpretation Workshop9/25/2015Likelihood Ratio (LR)Pr(𝐸 𝐻𝑝 )Pr(𝐸 𝐻𝑑 ) 1if 𝑃𝑟 𝐸 𝐻𝑝 Pr 𝐸 𝐻𝑑0Likelihood Ratio (LR)We have the DNA typing results of only one marker,called NEW.crime scene:Albert:8NEW: 8If Albert left this DNA on the crime scene, we would expect toobserve a peak for allele 8.The probability of this observation if Albert left this DNA onthe crime scene is 1.Pr 𝐸 𝐻𝑝 1Cedar Crest CollegeForensic Science Training Institute24

NEAFS Probabilistic DNA MixtureInterpretation Workshop9/25/2015Likelihood Ratio (LR)We have the DNA typing results of only one marker,called NEW.crime scene:Albert:NEW: 88In the population of potential donors, 1 out of 10people have genotype {8,8}.Pr 𝐸 𝐻𝑝 11Pr 𝐸 𝐻𝑑 10𝐿𝑅 Pr(𝐸 𝐻𝑝 )1 101Pr(𝐸 𝐻𝑑 )10Likelihood Ratio (LR)We have the DNA typing results of only one marker,called NEW.crime scene:Albert:NEW: 88In the population of potential donors, everyone hasgenotype {8,8}.Pr 𝐸 𝐻𝑝 1Pr 𝐸 𝐻𝑑 1Cedar Crest CollegeForensic Science Training Institute𝐿𝑅 Pr(𝐸 𝐻𝑝 )1 1Pr(𝐸 𝐻𝑑 )125

NEAFS Probabilistic DNA MixtureInterpretation Workshop9/25/2015Likelihood Ratio (LR)We have the DNA typing results of only one marker,called NEW.crime scene:Albert:NEW: 88In the population of potential donors, Albert is theonly one who has genotype {8,8}.Pr 𝐸 𝐻𝑝 1Pr 𝐸 𝐻𝑑 0𝐿𝑅 Pr(𝐸 𝐻𝑝 )1 𝑖𝑛𝑓𝑖𝑛𝑖𝑡𝑦Pr(𝐸 𝐻𝑑 )0individualizationLikelihood Ratio (LR)We have the DNA typing results of only one marker,called NEW.crime scene:Albert:NEW: 188In the population of potential donors, 1 out of 10people have genotype {8,8}.Pr 𝐸 𝐻𝑝 01Pr 𝐸 𝐻𝑑 10Cedar Crest CollegeForensic Science Training Institute𝐿𝑅 Pr(𝐸 𝐻𝑝 )0 01Pr(𝐸 𝐻𝑑 )10exclusion26

NEAFS Probabilistic DNA MixtureInterpretation Workshop9/25/2015True or False?Pr(𝐸 𝐻𝑝 )Pr(𝐸 𝐻𝑑 ) 100, or abbreviated as 𝐿𝑅 100A)B)Given the availableinformation, the probability ofthese DNA typing results is100 times greater if theprosecution’s proposition istrue than if the defense’sproposition is true.Pr(𝐸 𝐻𝑝 )Pr(𝐸 𝐻𝑑 )A.B.Given the available information,these DNA typing results indicatethat the probability of theprosecution’s proposition beingtrue is 100 times greater than theprobability of the defense’sproposition being true. 100, or abbreviated as 𝐿𝑅 100Given the available information,the probability of these DNAtyping results is 100 timesgreater if the prosecution’sproposition is true than if thedefense’s proposition is true.Given the available information,these DNA typing resultsindicate that the probability ofthe prosecution’s propositionbeing true is 100 times greaterthan the probability of thedefense’s proposition being true.0%A.Cedar Crest CollegeForensic Science Training Institute0%B.27

NEAFS Probabilistic DNA MixtureInterpretation Workshop9/25/2015True or False?Pr(𝐸 𝐻𝑝 )Pr(𝐸 𝐻𝑑 ) 100, or abbreviated as 𝐿𝑅 100Given the availableinformation, the probability ofthese DNA typing results is100 times greater if theprosecution’s proposition istrue than if the defense’sproposition is true.Given the available information,these DNA typing results indicatethat the probability of theprosecution’s proposition beingtrue is 100 times greater than theprobability of the defense’sproposition being true.Exercise 1: Likelihood RatioThe DNA typing results of a biological stain recovered on acrime scene in Washington DC show the same genotype as thatof a person of interest (POI) living in Washington DC. If thebiological stain came from the POI, the forensic scientist wouldexpect to obtain these typing results. According to populationdata, we would expect to see this genotype in one person outof 500,000. The forensic scientist formulates:𝐻𝑝 : The DNA recovered on the crime scene came from the POI.𝐻𝑑 : The DNA recovered on the crime scene came fromsomeone else, unrelated to the POI.What is the likelihood ratio for these DNA typing results withregard to propositions 𝐻𝑝 and 𝐻𝑑 ?Cedar Crest CollegeForensic Science Training Institute28

NEAFS Probabilistic DNA MixtureInterpretation Workshop9/25/2015Exercise 1: Likelihood RatioWrite a sentence describing your likelihood ratio inwords:Bayes’ theoremCedar Crest CollegeForensic Science Training Institute29

NEAFS Probabilistic DNA MixtureInterpretation Workshop9/25/2015Logical Framework for Updating Uncertainty𝐻𝑝 : The crime stain came from the POI.𝐻𝑑 : The crime stain did not come from the POI. It came from someother person.𝐸: The DNA typing results of the crime stain and the POI’s sampleboth show a peak for allele 8.Pr(𝐻𝑝 )Pr(𝐻𝑑 )Pr(𝐻𝑝 𝐸)Pr(𝐻𝑑 𝐸)Pr(𝐸 𝐻𝑝 )Pr(𝐸 𝐻𝑑 )forensicscientistfactfinderLogical Framework for Updating UncertaintyOdds form of Bayes’ theorem:Pr(𝐻𝑝 )Pr(𝐻𝑑 )prior oddsCedar Crest CollegeForensic Science Training Institute Pr(𝐸 𝐻𝑝 )Pr(𝐸 𝐻𝑑 )LikelihoodRatioThomas Bayes Pr(𝐻𝑝 𝐸)Pr(𝐻𝑑 𝐸)posteriorodds30

NEAFS Probabilistic DNA MixtureInterpretation Workshop9/25/2015Logical Framework for Updating UncertaintyPr(𝐻𝑝 )Pr(𝐻𝑑 )odds 3211/21/30:certainty that 𝐻𝑝 is true𝐻𝑝 is 3 times more probable to be true than 𝐻𝑑𝐻𝑝 is 2 times more probable to be true than 𝐻𝑑𝐻𝑝 is just as probable to be true as 𝐻𝑑𝐻𝑑 is 2 times more probable to be true than 𝐻𝑝𝐻𝑑 is 3 times more probable to be true than 𝐻𝑝certainty that 𝐻𝑑 is trueFrom Probabilities to Odds andback againPr(𝐻)Pr(𝐻)𝑜𝑑𝑑𝑠 Pr(𝑛𝑜𝑡 𝐻) 1 Pr(𝐻)𝑜𝑑𝑑𝑠Pr 𝐻 1 𝑜𝑑𝑑𝑠Cedar Crest CollegeForensic Science Training Institute31

NEAFS Probabilistic DNA MixtureInterpretation Workshop9/25/2015Transposed ConditionalPr(𝐻𝑝 ) Pr(𝐸 𝐻𝑝 )Pr(𝐻𝑝 𝐸) Pr(𝐻𝑑 ) Pr(𝐸 𝐻𝑑 ) Pr(𝐻𝑑 𝐸)100100The probability of these DNAtyping results is 100 timesgreater if the prosecution’sproposition is true than if thedefense’s proposition is true.These DNA typing results indicatethat the probability of theprosecution’s proposition beingtrue is 100 times greater than theprobability of the defense’sproposition being true.Logical Framework for Updating UncertaintyPr(𝐻𝑝 )Pr(𝐻𝑑 )prior oddsfactfinderCedar Crest CollegeForensic Science Training Institute Pr(𝐸 𝐻𝑝 )Pr(𝐸 𝐻𝑑 ) Likelihood Ratioexpert witnessPr(𝐻𝑝 𝐸)Pr(𝐻𝑑 𝐸)posterior oddsfactfinder32

NEAFS Probabilistic DNA MixtureInterpretation Workshop9/25/2015Role of the FactfinderPr(𝐻𝑝 𝐸)Pr(𝐻𝑑 𝐸)Given the evidence, what is theprobability that theprosecution’s proposition istrue?Given the evidence, what is theprobability that the defense’sproposition is true?Role of the FactfinderPr(𝐻𝑝 𝐸)Pr(𝐻𝑑 𝐸)The chance that the crime staincame from the POI is 0.9.The probability that the crimestain came from someone otherthan the POI is 0.1.There is a 1 in 10 chance that the crimestain did not come from the POI.Cedar Crest CollegeForensic Science Training Institute33

NEAFS Probabilistic DNA MixtureInterpretation Workshop9/25/2015Role of the Forensic ScientistWhat is the probability ofthe analytical results if theprosecution’s propositionis true?Pr(𝐸 𝐻𝑝 )Pr(𝐸 𝐻𝑑 )What is the probability of theanalytical results if thedefense’s proposition is true?Role of the Forensic ScientistThe probability of obtainingthese DNA results if the crimestain came from the suspect isvery close to 1.Pr(𝐸 𝐻𝑝 )Pr(𝐸 𝐻𝑑 )The chance of obtaining theseDNA results if the crime staincame from some other person,unrelated to the suspect, is 1 in1 million.Cedar Crest CollegeForensic Science Training Institute34

NEAFS Probabilistic DNA MixtureInterpretation Workshop9/25/2015Prosecutor’s FallacyPr 𝐸 𝐻𝑑 , I 1 in 7 millionIn layman’s terms, just so I get thisright, are you saying that theprobability that the DNA that wasfound in the question samplescame from anyone else besidesA.L. is one in 7 million ( )?State v. Lee, No. 90CA004741 (Ohio App. Dec. 5, 1990), transcript at 464Prosecutor’s FallacyPr 𝐸 𝐻𝑑 , I 1 in 10 millionThe witness concludes that thegenetic profile of the twoanalyzed samples matchperfectly, and he deduces thatthe probability of someone otherthan the suspect being the sourceof the trace found on the victim’scloths is 1 in 10 million.modified from:State of Arizona v. Michael Steven Gallegos [178 Ariz. 1; 870 P.2d 1097 (1994)]Cedar Crest CollegeForensic Science Training Institute35

NEAFS Probabilistic DNA MixtureInterpretation Workshop9/25/2015Prosecutor’s FallacyLR 4.73 quadrillionThe DNA mixture profile obtainedfrom [the item of evidence] is 4.73quadrillion times more likely to haveoriginated from [suspect] and[victim/complainant] than from anunknown individual in the U.S.Caucasian population and[victim/complainant].Holder, E.H., Leary M.L., Laub J.H. DNA for the Defense Bar 2012.Prosecutor’s FallacyThe fallacy is to transpose the conditional:Pr 𝐸 𝐻𝑑 , 𝐼 Pr 𝐻𝑑 𝐸, 𝐼orPr(𝐸 𝐻𝑝 , 𝐼) Pr(𝐻𝑝 𝐸, 𝐼) Pr(𝐸 𝐻𝑑 , 𝐼) Pr(𝐻𝑑 𝐸, 𝐼)Cedar Crest CollegeForensic Science Training Institute36

NEAFS Probabilistic DNA MixtureInterpretation Workshop9/25/2015Prosecutor’s Fallacywhich means that a low Pr 𝐸 𝐻𝑑 , 𝐼 is expressedas a low Pr 𝐻𝑑 𝐸, 𝐼 or highPr(𝐻𝑝 𝐸,𝐼)Pr(𝐻𝑑 𝐸,𝐼)when theprior odds are not necessarily equal to 1.Defense Attorney’s FallacyPr 𝐸 𝐻𝑑 , I 1 in 1,000The city where the crime occurredhas a population of 200,000. In thiscity, this genotype would be found in200 people. Therefore the evidencemerely shows that the person ofinterest is one of 200 people in thecity who might have left the crimestain.modified from: W.C. Thompson and E.L. Schumann. Interpretation of statistical evidence in criminal trials:The prosecutor’s fallacy and defence attorney’s fallacy. Law and Human Behaviour, 11: 167-187, 1987.Cedar Crest CollegeForensic Science Training Institute37

NEAFS Probabilistic DNA MixtureInterpretation Workshop9/25/2015Defense Attorney’s FallacyThe fallacy is:1. 200 individuals in the population plus thegenotyped POI is equal to 2012. To assume that each of these 200 individuals hasthe same prior probability of being the source ofthe crime stain as the POI3. To assume that the actual number of individualsin this city having the genotype in question isequal to the expected number of individualshaving this genotype. The actual number couldbe anywhere between 1 and 200,000.CorrectPr 𝐸 𝐻𝑑 , I 1 in 1,000The city where the crime occurred hasa population of 200,000. In this city,we would expect to find thisgenotype in 200 untyped people inaddition to the POI.Cedar Crest CollegeForensic Science Training Institute38

NEAFS Probabilistic DNA MixtureInterpretation Workshop9/25/2015Uniqueness FallacyPr 𝐸 𝐻𝑑 , I 1 in 200,000The city where the crime occurred hasa population of 200,000. In this city,this genotype can therefore onlycome from the person of interest.Uniqueness FallacyThe fallacy is:1. 1 individual in the population plus the genotypedPOI is equal to a total of two individuals2. To assume that the actual number of individuals inthis city having the genotype in question is equal tothe expected number of individuals having thisgenotype. The actual number could be anywherebetween 1 and 200,000.Cedar Crest CollegeForensic Science Training Institute39

NEAFS Probabilistic DNA MixtureInterpretation Workshop9/25/2015CorrectPr 𝐸 𝐻𝑑 , I 1 in 200,000The city where the crime occurred hasa population of 200,000. In this city,we would expect to find thisgenotype in 1 untyped person inaddition to the POI.Exercise 1: Moot CourtA) CorrectB) Transposed Conditional / Prosecutor’s FallacyC) Defense Attorney’s FallacyD) Uniqueness FallacyE) ?Cedar Crest CollegeForensic Science Training Institute40

NEAFS Probabilistic DNA MixtureInterpretation Workshop9/25/2015Principles of Evidence Interpretation1. To evaluate the uncertainty of a proposition, it isnecessary to consider at least one alternativeproposition.2. Scientific interpretation is based on questions of thekind ‘‘What is the probability of the evidence giventhe proposition?’’3. Scientific interpretation is conditioned not only bythe competing propositions, but also by theframework of circumstances within which they areto be evaluated.I.W. Evett and B.S. Weir. Interpreting DNA Evidence: Statistical Genetics for Forensic Scientists. SinauerAssociates, Sunderland, 1998: page 29.Conditioning on the Framework of Circumstances𝐿𝑅 Pr(𝐸 𝐻𝑝 , 𝐼)Pr(𝐸 𝐻𝑑 , 𝐼)where 𝐼 is the available informationcase circumstances and evidence presented so far where was the crime committed when was the crime committed description of the offender(s) information about the commission of the crime(activities performed, modus operandi, crimescene entry/exit points) information about the crime scene before andafter the commission of the crime information about how rare particularcharacteristics are in a populationCedar Crest CollegeForensic Science Training Institute41

NEAFS Probabilistic DNA MixtureInterpretation Workshop9/25/2015Conditioning on the Framework of Circumstances𝐿𝑅 Pr(𝐸 𝐻𝑝 , 𝐼)Pr(𝐸 𝐻𝑑 , 𝐼)with 𝐼:What do we know or assume about theoffender? What population does theoffender come from?What are the genetic properties of thispopulation? What do we know about therarity of the observed genotype in thispopulation?Conditioning on the Framework of Circumstances𝐿𝑅 Pr(𝐸 𝐻𝑝 , 𝐼)Pr(𝐸 𝐻𝑑 , 𝐼)The LR will vary according to the information in 𝐼.It is therefore imperative for the forensicscientist to make explicit to the court whatinformation makes up the 𝐼 in his/her LR. Ifthe court disagrees, or new informationbecomes available, the forensic scientistmust re-assign the probabilities formingthe LR conditioned on the new 𝐼.Cedar Crest CollegeForensic Science Training Institute42

NEAFS Probabilistic DNA MixtureInterpretation Workshop9/25/2015Logical Framework for Updating UncertaintyOdds form of Bayes’ theorem:Pr(𝐻𝑝 𝐼)Pr(𝐻𝑑 𝐼)prior oddsfactfinderCedar Crest CollegeForensic Science Training Institute Pr(𝐸 𝐻𝑝 ,𝐼)Pr(𝐸 𝐻𝑑 ,𝐼) Pr(𝐻𝑝 𝐸,𝐼)Pr(𝐻𝑑 𝐸,𝐼)Likelihood Ratioposterior oddsexpert witnessfactfinder43

Forensic Science Training Institute 12 5. What is the probability that a person drawn randomly from this population has blond hair and blue eyes? A. 0.013 B. 0.0936 C. 0.2054 D. 0.26 E. 1.05 3 64 9 5 brown blue hazel green 0% 0% 0% 0% 0% 0% 0.05 0.79 0.06 0.10 eye color of blond haired people: black brown r