Stats - created from Mind Map

Seite 1

<ul><li>for when we have a match</li><li> Statistical analysis allows us to focus on the question being asked. For example, If we have a match between evidence ,‘E’ and suspect sample ‘S’ AND the suspect is NOT the donor of the DNA THEN who else could match ‘E’ ? </li><li>What exactly does this question mean? • Quantitative statement that expresses the rarity of the DNA profile</li><li> “What is the estimated frequency of the DNA profile in the population?” </li></ul>

Frequentist<br><br><ul><li> “This DNA profile is expected to occur in approximately 1 in 10 billion individuals in the general unrelated population” </li><li>This DNA profile is expected to occur in approx. 1 in 600 billion individuals in the general unrelated population </li></ul>

LR<br><br><ul><li>It is approximately 10 billion times more likely to obtain this DNA profile if it originated from the defendant than from an unknown unrelated individual in the general population </li></ul>

Match

types of databases<br><br><ul><li>• Offenders / convicted / suspects etc. • Crime scene profiles • “Closed set” database • (Anonymous) population databases </li></ul>

propositions<br><br><ul><li> DNA from bloodstain came from the accused (in which case the probability of the bloodstain having the same profile as the accused = 1). </li><li>DNA from the bloodstain came from a person who by coincidence had the same profile as the suspect  statistical calculation </li></ul>

Bayesian<br><br><ul><li>• Likelihood ratio in context of the entire case

• Prior odds are the odds on Hp before the DNA evidence

• Posterior odds are the odds on Hp after the DNA evidence; posterior odds relates to probability of guilt

• Posterior odds= LR x prior odds </li><li>It is approx. 600 billion times more likely to obtain this DNA profile if it originated from the defendant than from an unknown unrelated individual in the general population </li></ul>

reliability of database

subpopulation issue

international<br><br><ul><li>STRs</li></ul>

Calculating profile frequency<br><br><ul><li>but issues:

The allele frequencies are ‘accurate’ &amp;amp; relevant • The population that they’re from is in HardyWeinberg equilibrium. • The loci are in linkage equilibrium • The population that the data is from mates at random (what does this mean? - “linkage”…)… • The alternate ‘true offender’ is unrelated to the nominated suspect. </li></ul>

random match probability<br><br><ul><li> Estimating the frequency of the DNA profile in the population  Product rule  Simplest population genetic model  First order approximation </li></ul>

conditional probability<br><br><ul><li> Estimating the probability that a 2nd person has the DNA profile given that the suspect has it  Subpopulation formulae  Robust population model </li></ul>

Identity<br><br><ul><li>The DNA originated from the suspect </li></ul>

Coincidence<br><br><ul><li>The DNA originates from someone other than the suspect. The suspect and the true donor share the same DNA profile by chance (identical twins aside) </li></ul>

problem with simplistic approach<br><br><ul><li>• The allele frequencies are ‘accurate’ &amp;amp; relevant • The population that they’re from is in Hardy-Weinberg equilibrium. • The loci are in linkage equilibrium • The population that the data is from, mates at random (what does this mean? - “linkage”…)… • The alternate ‘true offender’ is unrelated to the nominated suspect. </li></ul>

the court wants<br><br><ul><li>The Court is trying to assess the probability of guilt given the evidence: </li></ul>

the scientist can give them<br><br><ul><li>The scientist can only provide information on the probability of the evidence:

– Let E = the DNA evidence that Mr Citizen’s DNA profile matches the crime profile </li></ul>

theorem<br><br><ul><li>• The Crown and defense advance conflicting hypotheses to explain the evidence (E)

• The scientist must evaluate the strength of the DNA evidence Pr(E) given each of the alternate hypotheses: </li><li>the probability that Mr Citizen’s DNA profile matches the crime profile given Mr Citizen is the source of the crime profile

Pr( HpE</li><li>)Pr( HdE

the probability that Mr Citizen’s DNA profile matches the crime profile given that Mr Citizen is not the source of the crime profile and that it has originated from an unrelated individual </li></ul>

size of database<br><br><ul><li>200 unrelated individuals sufficient for estimation of allele frequencies

• Need to include sampling error estimates </li></ul>

sampling variation