Statistics in DNA Matching ST. PAUL’S SCHOOL 12/03/15

Prepared by:Kee Wen Ng & Adam Burchfield

Overview

Used throughout the world in criminal courts to assess guilt.

The evidence that often closes criminal cases is a DNA match.

Our DNA is almost always unique.

Statistical thinking is required to understand exactly what a match is.

Juries need to carefully consider how a match forms part of the evidence in a trial.

Background Information

Denis Adams Rape trial of 1996:

A DNA match was the only evidence heard by the jury.

All the other evidence pointed towards innocence.

Victim described her attacker to be in his 20’s.

Victim didn’t pick out Adams at identity parade.

She also said Adams didn’t fit the description, saying he looked 40.

Adams was 37.

He had an alibi for the night in question, his girlfriend saying he had spent the night with her.

Imagine you’re the jury

From what you know, is he:

Prosecutor’s Fallacy

Misinterpreting the probability:

If a random person’s profile matches the crime sample, is it not equal the probability this particular person is innocent on the basis of the evidence.

The statistical mistake:

Assuming the match probability is 1 in 2 million:

How DNA Profiling Works

DNA sequence made up by: G-guanine, C-cytosine, A-adenine,T-thymine.

Part of DNA Compound: GTAAAAGAATTCATGATAGATAGATAGATAGATAGATAGATAGCGTCCATCGTATGGTTTAAAGGGACCAAGGGGTACGATCGAGTAGGATA

99.9% of the sequence is the same in every person

Variable Number Tandem Repeats:In Non-coding regions, prone to mutations

Short Tandem Repeats (STR),e.g.: GATA

Longer repeats are heavier, thus moves slower

Likelihood Ratio

Likelihood Ratio (LR) =

LR measures the impact of the evidence

Adam’s case:LR = 2000000

Other factors:- Population- Alibi- Victim’s identifying test

Taking into account population

Town population of 150000 + people from outside town 50000

Without considering any other factors, prior odds of guilt:P(Adam is guilty) = P(any other person is guilty) = 1/200000

Posterior odds of guilt = LR x prior odds = 10

New likelihood of guilt is 10:1

P(Adam is guilty after taking DNA and population into account)= ≈ 91%

Victim fails to recognise AdamsWe want to numerically approximate the other evidence

If Adams was guilty:

10% chance that the victim cannot identify Adams

If Adams was innocent:

90% chance the victim cannot identify Adams in this case

This leads to the likelihood ratio of the impact of the victim not identifying Adams as:

LRvictim = 0.1/0.9 = 1/9

Girlfriend as an Alibi

If Adams was guilty:

25% chance that Adam’s girlfriend lies

If Adams was innocent:

50% chance that they spent the night together

This leads to the likelihood ratio of the impact of having his girlfriend as an alibi as:

LRalibi = 0.25/0.5 = 1/2

Taking all of these into accountAnd comparing with other values

Posterior odds = LRvictim x LRalibi x prior odds = 1/9 x 1/2 x 10 = 5/9

Adam is guilty: innocent = 5/9: 1

P(Adam is guilty) = = 35%

Is this ridiculous?Relatives with similar DNA & Biased perspectives

More values:

-What if the DNA match probability is improved by 10, 100 times?-What if the victim successfully pointed Adam out?-What if the crime was committed in London with 8m population?-What if there was a mistake made in the DNA lab?

Wider ImpactCourt of Appeal Ruling:

Post-Adams trial, the court ousted the use of explicit Bayesian statistics from the reasoning admissible before a jury in DNA cases.

Royal Statistical Society reports:

The court argues ‘common sense’ must be applied to statistics.

RSS push for basic training in probability and statistics as an integral component of legal education.

Busy practitioners lack the time and opportunities to fill in persistent gaps in their professional training.

Others may be unaware of their lack of knowledge, or believe that they understand enough already, but do so only imperfectly

Something to think about..

How do you think the criminal system should make use of statistics in DNA matching?