bayes s theorem and the weighing of evidence by juries n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Bayes’s Theorem and the Weighing of Evidence by Juries PowerPoint Presentation
Download Presentation
Bayes’s Theorem and the Weighing of Evidence by Juries

Loading in 2 Seconds...

play fullscreen
1 / 23

Bayes’s Theorem and the Weighing of Evidence by Juries - PowerPoint PPT Presentation


  • 70 Views
  • Uploaded on

Bayes’s Theorem and the Weighing of Evidence by Juries. Philip Dawid University College London. STATISTICS = LAW. Interpretation of evidence. Hypothesis testing. Decision-making under uncertainty. Prosecution Hypothesis. INGREDIENTS. Defence Hypothesis. Evidence. BAYESIAN APPROACH.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Bayes’s Theorem and the Weighing of Evidence by Juries' - stash


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
statistics law
STATISTICS = LAW
  • Interpretation of evidence
  • Hypothesis testing
  • Decision-making under uncertainty
ingredients
Prosecution HypothesisINGREDIENTS
  • Defence Hypothesis
  • Evidence
slide4

BAYESIAN APPROACH

Find posterior probability of guilt:

– or posterior odds:

  • FREQUENTIST APPROACH

Look at

& effect on decision rules

– and possibly

sally clark
SALLY CLARK

Sally Clark murdered them

Sally Clark’s two babies died unexpectedly

Cot deaths (SIDS)

possible decision rule
POSSIBLE DECISION RULE
  • CONVICT whenever

OCCURS

Can we discount possibility of error?

— if so, right to convict

alternatively
Alternatively…
  • P(2 babies die of SIDS = 1/73 million) (?)
  • P(2 babies die of murder = 1/2000 million) (??)

BOTH figures are equally relevant to the decision between the two possible causes

bayes
BAYES:

POSTERIOR

ODDS

LIKELIHOOD RATIO

PRIOR ODDS

=

73m

??

If prior odds = 1/2000 million,

Posterior odds = 0.0365

impact of evidence
IMPACT OF EVIDENCE

By BAYES, this is carried by the

LIKELIHOODRATIO

  • Appropriate subject of expert testimony?
  • Instruct jury on how to combine LR with prior odds?
impact of a lr of 100
IMPACT OF A LR OF 100

Probability

of Guilt

identification evidence
IDENTIFICATION EVIDENCE

M = DNA match

B = other background evidence

Assume

– “match probability”

MP

prosecutor s argument
PROSECUTOR’S ARGUMENT

The probability of a match having arisen by innocent means is 1/10 million.

So

= 1/10 million

– i.e.

is overwhelmingly close to 1.

–CONVICT

defence argument
DEFENCE ARGUMENT
  • Absent other evidence, there are 30 million potential culprits
  • 1 is GUILTY (and matches)
  • ~3 are INNOCENT and match
  • Knowing only that the suspect matches, he could be any one of these 4 individuals
  • So

–ACQUIT

bayes1
BAYES
  • POSTERIOR ODDS = (10 MILLION)  “PRIOR” ODDS
  • PROSECUTOR’S argument OK if
  • DEFENCE argument OK if

Only BAYES allows for explicit incorporation of B

denis adams
DENIS ADAMS
  • Sexual assault
  • DNA match
  • Match probability = 1/200 million

1/20 million

1/2 million

  • Doesn’t fit description
  • Victim: “not him”
  • Unshaken alibi
  • No other evidence to link to crime
court presented with
Court presented with
  • LR for match
  • Instruction in Bayes’s theorem
  • Suggested LR’s for defence evidence
  • Suggested priors before any evidence
prior
PRIOR
  • 150,000 males 18-60 in local area

DEFENCE EVIDENCE B=D&A

  • D: Doesn’t fit description/victim does not recognise
  • A: Alibi
trial appeal retrial appeal
Trial –Appeal – Retrial – Appeal

BAYES rejected

  • “usurps function of jury”
  • “jury must apply its common sense”

– HOW?

SALVAGE?

  • Use “Defence argument”
  • Apply other evidence
database search
DATABASE SEARCH
  • Rape, DNA sample
  • No suspect
  • Search police database, size 10,000
  • Find single “match”, arrest
  • Match probability1/1 million

EFFECT OF SEARCH??

defence
DEFENCE

– (significantly) weakens impact of evidence

PROSECUTION

We have eliminated 9,999 potential culprits

– (slightly) strengthens impact of evidence

bayes prosecutor correct
BAYES  Prosecutor correct

Defence switches hypotheses

  • Suspect is guilty
  • Some one in database is guilty

– equivalent AFTER search

– but NOT BEFORE

Different priors

Different likelihood ratio

– EFFECTS CANCEL!

conclusions
CONCLUSIONS
  • Interpretation of evidence raises deep and subtle logical issues
  • STATISTICS and PROBABILITY can address these
  • BAYES’S THEOREM is the cornerstone

Need much greater interaction between lawyers and statisticians