stories and statistics: what can the sally clark case tell us about the psychology of evidential...

Stories and statistics: What can the Sally Clark case tell us about the psychology of evidential reasoning?

David LagnadoDavid Lagnado

Division of Psychology and Division of Psychology and Language SciencesLanguage Sciences

University College LondonUniversity College London

Evidential reasoning

How do people assess and combine How do people assess and combine evidence to make decisions? evidence to make decisions? – Legal, Medical, Financial, Social …Legal, Medical, Financial, Social …

Cognitive science approachCognitive science approach– What kinds of representations?What kinds of representations?– What kinds of inference patterns?What kinds of inference patterns?

How do these compare with normative or How do these compare with normative or formal methods of evidential reasoning?formal methods of evidential reasoning?– Bayesian networks now used to model Bayesian networks now used to model

complex forensic evidence (Taroni et al, 2006)complex forensic evidence (Taroni et al, 2006)

Reasoning with legal Reasoning with legal evidenceevidence

Legal domainLegal domain– E.g. juror, judge, investigator, mediaE.g. juror, judge, investigator, media

Complex bodies of interrelated Complex bodies of interrelated evidenceevidence– Forensic evidence; witness testimony; Forensic evidence; witness testimony;

alibis; confessions etcalibis; confessions etcNeed to integrate wide variety of Need to integrate wide variety of

evidence to reach singular conclusion evidence to reach singular conclusion (e.g. guilt of suspect)(e.g. guilt of suspect)

Story model (Pennington & Hastie, 1986, 1991, 1992)

Evidence evaluated through story Evidence evaluated through story construction construction – ‘‘Stories involve human action sequences in Stories involve human action sequences in

which relationships of physical causality and which relationships of physical causality and intentional causality between events are intentional causality between events are central’central’

Jurors use prior causal knowledge and Jurors use prior causal knowledge and expectations about story structure to fill in expectations about story structure to fill in gaps in evidencegaps in evidence

Active ‘sense-making’ process to construct Active ‘sense-making’ process to construct an account of what happenedan account of what happened

Evidential Reasoning

Reasoning Reasoning fromfrom evidenceevidence– Use the evidence to Use the evidence to

construct ‘most construct ‘most plausible’ account plausible’ account of what happenedof what happened

– Generate a causal Generate a causal story based on the story based on the evidenceevidence

Reasoning Reasoning aboutabout evidenceevidence– Assessing the Assessing the

strength/reliability/vstrength/reliability/validity of the alidity of the evidenceevidence

– How well does the How well does the evidence support the evidence support the putative putative hypotheses/stories?hypotheses/stories?

think-aloud protocols from jurors in simulated trials suggest that they predominantly engage in former

Continuum? Individual variability in competence at juror Individual variability in competence at juror

reasoning (Kuhn et al., 1994) and evidential reasoning (Kuhn et al., 1994) and evidential reasoning in general (Kuhn, 1991)reasoning in general (Kuhn, 1991)

SATISFICING

Construct single story

using evidence

SATISFICING

Construct single story

using evidence

THEORY-EVIDENCE CO-ORDINATION

Construct multiple storiesEvaluate against evidence

and alternatives

THEORY-EVIDENCE CO-ORDINATION

Construct multiple storiesEvaluate against evidence

and alternatives

Group deliberation helps shift --->

Requires ability to reflect on one’s own reasoning?

Stories: blessing or curse?

Story is concrete and categoricalStory is concrete and categorical Describes a singular causal processDescribes a singular causal process

Hard to simultaneously Hard to simultaneously compare/evaluate multiple compare/evaluate multiple stories (cf Wigmore)stories (cf Wigmore)

Danger of neglecting Danger of neglecting alternative accountsalternative accounts

Evidence often Evidence often gathered/interpreted for a gathered/interpreted for a single story (confirmation single story (confirmation bias)bias)

The ‘truth’ might not make The ‘truth’ might not make a good storya good story

Economy of representationEconomy of representation Easy to communicateEasy to communicate Clear-cut basis for decision Clear-cut basis for decision

and actionand action Identify key variables to Identify key variables to

blameblame

Binocular rivalry

Switch between two coherent percepts (green vs red)

Even when inputs are mixed

Switch between two coherent stories(prosecution vs defence)

Even when evidence is mixed

Sally Clark case

Sally & Stephen Clark married, both solicitorsSally & Stephen Clark married, both solicitors Son Christopher born in 1996Son Christopher born in 1996

– Died suddenly at home aged 11 weeksDied suddenly at home aged 11 weeks– Sally alone with child; noticed he was unwell; Sally alone with child; noticed he was unwell;

ambulance called, but he could not be ambulance called, but he could not be resuscitatedresuscitated

Postmortem (Dr Williams): Postmortem (Dr Williams): – Death from natural causes - lung infection Death from natural causes - lung infection

(and bruises consistent with resuscitation (and bruises consistent with resuscitation attempts) attempts)

– Body was crematedBody was cremated

Sally Clark case

Harry born in 1997Harry born in 1997– Died suddenly at home aged 8 weeksDied suddenly at home aged 8 weeks– Stephen at home with Sally; but Sally alone with child Stephen at home with Sally; but Sally alone with child

when discovered unwell; ambulance called, but he could when discovered unwell; ambulance called, but he could not be resuscitatednot be resuscitated

Postmortem (Dr Williams): Postmortem (Dr Williams): – Suspicious - death from shaking? Suspicious - death from shaking? – Re-examined death of Christopher Re-examined death of Christopher – Concluded it too was unnatural, with evidence of Concluded it too was unnatural, with evidence of

smothering smothering

Sally Clark charged with murder of both children Sally Clark charged with murder of both children

Prosecution case

Christopher & Harry were smotheredChristopher & Harry were smothered– Nb change from Dr Williams’ initial claims of Nb change from Dr Williams’ initial claims of

shaking for Harry (error in diagnosis of retinal shaking for Harry (error in diagnosis of retinal haemorrhages)haemorrhages)

Neither died from SIDS because there were Neither died from SIDS because there were unexplained injuries unexplained injuries

Numerous similarities between the two Numerous similarities between the two deaths deaths – ‘‘which would make it an affront to commonsense which would make it an affront to commonsense

to conclude that either death was natural, and it to conclude that either death was natural, and it was beyond coincidence for history to so repeat was beyond coincidence for history to so repeat itself’ itself’

Prosecution case

‘‘SimilaritiesSimilarities’’– Babies died at similar agesBabies died at similar ages– Both found unconscious in same room; at same Both found unconscious in same room; at same

time; shortly after feedtime; shortly after feed– Mother alone with child when found unwellMother alone with child when found unwell– Father either away or due to go awayFather either away or due to go away– (Medical evidence of previous abuse & (Medical evidence of previous abuse &

deliberate injury)deliberate injury)

How unlikely are these given that mother How unlikely are these given that mother is innocent? (beyond coincidence?) is innocent? (beyond coincidence?)

Prosecution case: Injuries to Christopher

Blood in lungs

Blood in lungs

Torn frenulum

Torn frenulum BruisesBruises

SmotheringSmothering

nosebleednosebleed

Prior smothering

Prior smothering

Both fresh & older blood

Between lip and jaw

Small marks on arms and legs

Prosecution case:Injuries to Harry

Old fracture & dislocation

Hypoxic damage to

brain

Hypoxic damage to

brain

Haemorrhages in eyelids

Haemorrhages in eyelids

Haemorrhages to eyes


SmotheringSmothering Shaking/ prior abuse

Shaking/ prior abuse

Rib injuriesRib injuries Spinal injuriesSpinal injuries

Spinal bleeding & swollen cord

Prosecution case:Credibility of witnesses

Sally Clark states she found Harry slumped in bouncy chair

Sally Clark states she found Harry slumped in bouncy chair

Harry slumped in bouncy chair?

Harry slumped in bouncy chair?

Police surgeon says impossible for baby of 8 weeks to slump in bouncy chair

Police surgeon says impossible for baby of 8 weeks to slump in bouncy chair

Sally Clark reliabilitySally Clark reliability

Sally’s testimony in doubt

Sally Clark alone with Harry


Stephen Clark states he returned home at 5.30/5.45pm


Taxi records show Stephen Clark returned home at 8.10pm


Opportunity/ Motive

Sally Clark smothered Harry


Stephen Clark reliability


Stephen lying to protect wife

Stephen’s testimony in doubt

Professor Sir Roy Meadow (Paediatrics)Professor Sir Roy Meadow (Paediatrics) Report – Report – ‘‘Sudden unexpected deaths in Sudden unexpected deaths in

infancyinfancy’’ Risk factors – age of mother (<26), smoker in Risk factors – age of mother (<26), smoker in

household, no wage earnerhousehold, no wage earner None applied to Clark family None applied to Clark family

Chance of one SIDS in family= 1 in 8,543Chance of one SIDS in family= 1 in 8,543 Chance of two SIDS = 1/8543 x 1/8543 Chance of two SIDS = 1/8543 x 1/8543

= 1/73 million= 1/73 million ‘‘……by chance that happening will occur by chance that happening will occur

about once every hundred yearsabout once every hundred years’’

Prosecution case:Statistical evidence

Defence case

Sally Clark did not kill her childrenSally Clark did not kill her children– They died of natural but unexplained causesThey died of natural but unexplained causes– Medical evidence amounts only to suspicionMedical evidence amounts only to suspicion

Two of prosecution experts said cause of Two of prosecution experts said cause of deaths deaths ‘‘unascertainedunascertained’’

Case hinges upon Dr WilliamCase hinges upon Dr William’’s reliability s reliability and competence and competence

Blood in lungs

Blood in lungs

Torn frenulum

Torn frenulum BruisesBruises

Resuscitationattempts

Resuscitationattempts

Reliability of Dr WilliamsReliability of Dr Williams

Postmortem effects

Postmortem effects

Report of Torn

frenulum

Report of Torn

frenulum

Report of Bruises

Report of Bruises

HaemoderosisHaemoderosis

Report from police & hospital

Report from police & hospital

Change of opinionPoor conduct of postmortemLow quality photos etc

Change of opinionPoor conduct of postmortemLow quality photos etc

Defence case: Injuries to Christopher

NB distinguish event from reports of event

Defence case: Injuries to Harry

Hypoxic damage to

brain

Hypoxic damage to

brain

Haemorrhages to eyelids

Haemorrhages to eyelids



Natural causes

post-death

Natural causes

post-death

PostmortemPostmortem



Change of opinionPrior error with slidesChange of opinionPrior error with slides









Opportunity/ Motive


Sally Clark smothered HarryStephen very

unlikely to lie to protect wife if she killed their children

Stephen admitted lack of knowledge, and mentioned taxi records

Stephen admitted lack of knowledge, and mentioned taxi records

Explain Stephen testimony mistake

Defence case: Statistical evidence

2 SIDS death = significantly greater than 1/73 million

Mother >26No smokersWage earner

Mother >26No smokersWage earner

SIDS death1SIDS death1 SIDS death2SIDS death2

genetic or environmental

factors

genetic or environmental

factors

Calculation Calculation for two for two deaths deaths ignores ignores possible possible genetic & genetic & environmentaenvironmental factors l factors

Estimate for Estimate for probability of probability of one SIDS one SIDS death death questionablequestionable

Known risk factors

UNKNOWN risk factors

Deaths are not independent (so cannot simply square)

Verdict

Sally Clark found guilty by 10-2 Sally Clark found guilty by 10-2 majoritymajority

Imprisoned for lifeImprisoned for life

First Appeal:Statistical evidence Statistical evidence

misleadingmisleading Non independenceNon independence

– 1/73 million figure flawed1/73 million figure flawed– Probabilities are not independent Probabilities are not independent

RelevanceRelevance– Probability of two SIDS deaths insufficientProbability of two SIDS deaths insufficient– needs to be compared against probability that mother needs to be compared against probability that mother

murders both her children murders both her children – Estimated incidence of this is much lower than of two SIDS Estimated incidence of this is much lower than of two SIDS

deathsdeaths

‘it is clearly inadequate to concentrate on a single cause of death. If we make an assessment of the probability of two babies in one family both dying from SIDS, we must equally make a similar assessment of the probability of two babies in one family both being murdered (and so on, for any other causes that may be under consideration)…’ Dawid (2002)

EvidenceEvidence

SIDSSIDS MurderMurder

Two alternative causes of the deathsTwo alternative causes of the deaths

(exclusive but not exhaustive – other causes possible, also possible that one SIDS, one murdered etc)(exclusive but not exhaustive – other causes possible, also possible that one SIDS, one murdered etc)

Prior probability of SIDS is low

Prior probability of murder is even lower

Prior to other/medical evidence, probability of double SIDS greater than probability of double murder

Evidence of 2 deaths

Appeal dismissed

Court of appeal judgmentCourt of appeal judgment– No need for expert statisticians to give oral testimony No need for expert statisticians to give oral testimony

––““it was hardly rocket scienceit was hardly rocket science””– Defence already pointed out flaws in statisticsDefence already pointed out flaws in statistics– What matters is that probability of two SIDS deaths is What matters is that probability of two SIDS deaths is

very low, not exact figurevery low, not exact figure– Statistic might have had larger impact on jury than it Statistic might have had larger impact on jury than it

should have, but case against Sally Clark was should have, but case against Sally Clark was nevertheless overwhelmingnevertheless overwhelming

"In the context of the trial as a whole, the point on statistics "In the context of the trial as a whole, the point on statistics was of minimal significance and there is no possibility of the was of minimal significance and there is no possibility of the jury having been misled so as to reach verdicts that they jury having been misled so as to reach verdicts that they might not otherwise have reached."might not otherwise have reached."

Second appeal

Discovery of new evidenceDiscovery of new evidence– Harry had bacterial infection Harry had bacterial infection – Known by Dr Williams but not disclosed at trial!Known by Dr Williams but not disclosed at trial!– (When jury asked about blood tests for Harry, (When jury asked about blood tests for Harry,

Williams said Williams said nono relevantrelevant test results) test results)

Plausible cause of Harry’s death Plausible cause of Harry’s death – according to 11 independent expertsaccording to 11 independent experts– Also casts doubt on ChristopherAlso casts doubt on Christopher’’s death due to s death due to

unreliability of Dr Williamsunreliability of Dr Williams

Harry’s death

Hypoxic damage to

brain

Hypoxic damage to

brain

Hemorrhages to eyelids

Hemorrhages to eyelids

Hemorrhages to eyes

Hemorrhages to eyes

Natural causes

post-death

Natural causes

post-death

PostmortemPostmortem



Failure to disclose

etc

Failure to disclose

etc

Bacterial infectionBacterial infection

Micro-biological

tests

Micro-biological

tests

Conclusions about Christopher

Second appeal

Conviction declared unsafeConviction declared unsafe– Sally Clark released 2003Sally Clark released 2003

PostscriptPostscript– Several other similar convictions involving Several other similar convictions involving

Meadow subsequently overturnedMeadow subsequently overturned– Meadow struck off medical register 2005; Meadow struck off medical register 2005;

reinstated on appeal 2006reinstated on appeal 2006– Williams guilty of serious misconduct 2005Williams guilty of serious misconduct 2005

Sally dies 2007Sally dies 2007

Lessons

Various repercussions for legal domainVarious repercussions for legal domain– Expert witnesses Expert witnesses – (expert in child health not an expert in statistics)(expert in child health not an expert in statistics)– Interpretation and presentation of statistical Interpretation and presentation of statistical

evidence evidence

For evidential reasoningFor evidential reasoning– Understanding statistical evidenceUnderstanding statistical evidence– Role of causal networksRole of causal networks– Reliability of evidence (and experts)Reliability of evidence (and experts)– Stories and blameStories and blame

Statistical evidence

Well-documented problems when people reason Well-documented problems when people reason with probabilities (Kahneman, 2012)with probabilities (Kahneman, 2012)– Base rate neglect; prosecutor's fallacy; conjunction Base rate neglect; prosecutor's fallacy; conjunction

errorserrors

In contrast people are good at qualitative causal In contrast people are good at qualitative causal reasoningreasoning

One approach that reconciles these findingsOne approach that reconciles these findings– People need suitable causal models for appropriate People need suitable causal models for appropriate

probabilistic reasoning (Krynski & Tenenbaum, 2007; probabilistic reasoning (Krynski & Tenenbaum, 2007; Sloman, 2005; Lagnado, 2011)Sloman, 2005; Lagnado, 2011)

Classic probability problems facilitated with Classic probability problems facilitated with causal modelscausal models

Medical diagnosis problem(Krynski & Tenenbaum, 2007)

Given +test people grossly Given +test people grossly overestimate probability of canceroverestimate probability of cancer

(Neglect low base rate) (Neglect low base rate) Mistaken use of false positive Mistaken use of false positive

probabilityprobability Low false + Low false + high probability of high probability of

cancer cancer

+ TEST+ TEST

CancerCancer CystCyst

+ TEST+ TEST

CancerCancer

Alternative cause of +test made Alternative cause of +test made explicit explicit

People give better estimates of People give better estimates of probability of cancer probability of cancer

Improved probabilistic reasoning Improved probabilistic reasoning given suitable causal model given suitable causal model

shown for several classic problems shown for several classic problems

Statistical evidence

To avoid errors in Sally Clark caseTo avoid errors in Sally Clark case– Need suitable (causal) model to Need suitable (causal) model to

understand probabilities understand probabilities – Need to consider (probability) of Need to consider (probability) of

alternative causesalternative causes– Need to combine via Bayes ruleNeed to combine via Bayes rule

Misleading categories

Case framed as murder vs SIDSCase framed as murder vs SIDS Exclusive but not exhaustive Exclusive but not exhaustive Tempting to reason: not-SIDS -> murderTempting to reason: not-SIDS -> murder But other natural explanations possible (eg But other natural explanations possible (eg

infections etc)infections etc) Key to represent alternative causes …Key to represent alternative causes …

EvidenceEvidence

NaturalNatural UnnaturalUnnatural

EvidenceEvidence

other naturalother natural smothersmother

Other …Other …SIDSSIDS

Non-independence

Main focus on flawed assumption of Main focus on flawed assumption of independence of SIDS deathsindependence of SIDS deaths– Judges, lawyers, media, etc Judges, lawyers, media, etc

People understand independence/non-People understand independence/non-independence when framed causallyindependence when framed causally– Possible unobserved common causes of SIDS deathsPossible unobserved common causes of SIDS deaths– Eg genetic or environmental factorsEg genetic or environmental factors

SIDS1SIDS1

Genetic or environmental

Genetic or environmental

SIDS2SIDS2

Understanding/using probability

Second error –Second error –– How is probability of SIDS relevant to How is probability of SIDS relevant to

probability that Sally is guilty of murder?probability that Sally is guilty of murder?– Need to use Bayes rule Need to use Bayes rule – Requires comparison with prior probability of Requires comparison with prior probability of

child murder child murder

Danger of prosecutor's fallacyDanger of prosecutor's fallacy– Assume that 1 in 73 million figure applies to Assume that 1 in 73 million figure applies to

probability that Sally Clark is innocentprobability that Sally Clark is innocent– Eg P(2deaths|not guilty) = P(not guilty|Eg P(2deaths|not guilty) = P(not guilty|

2deaths)2deaths)

Statistical evidence Probabilistic reasoning improved by explicit Probabilistic reasoning improved by explicit

causal models (Krynski &Tenenbaum,2007)causal models (Krynski &Tenenbaum,2007) Avoid MeadowAvoid Meadow’’s second error by explicitly s second error by explicitly

representing probability of double murder?representing probability of double murder?

EvidenceEvidence

SIDSSIDS MurderMurderPrior of double SIDS is low

Prior for double murder is even lower

Ongoing empirical work on improving Bayesian reasoning using causal models

Representing alternative cause and its prior probability should improve probabilistic judgments

Causal networks

Key role of causal reasoning borne out by Key role of causal reasoning borne out by Sally Clark caseSally Clark case

But story model needs to be developedBut story model needs to be developed Formal means for representing causal models Formal means for representing causal models

and inferenceand inference Include representation of evidence and Include representation of evidence and

reliability (and their interrelations)reliability (and their interrelations) Move closer to theory-evidence co-ordinationMove closer to theory-evidence co-ordination Even if people don’t always do this- they can!Even if people don’t always do this- they can!

Legal idioms Evidential reasoning in terms of Evidential reasoning in terms of

causal building blockscausal building blocks– Capture generic inference patternsCapture generic inference patterns– Reusable and combinableReusable and combinable– Qualitative causal structureQualitative causal structure– Based on Bayesian networksBased on Bayesian networks– Akin to schema/scriptsAkin to schema/scripts

Fenton, Lagnado & Neil, 2012Fenton, Lagnado & Neil, 2012

Legal idioms

Evidence idiomEvidence idiom Evidence Evidence depends on depends on HypothesisHypothesis Evidence is more likely if hypothesis is trueEvidence is more likely if hypothesis is true Observed evidence raises the probability of Observed evidence raises the probability of

hypothesishypothesis

BruisesBruises

Smother Smother

EvidenceEvidence

Hypothesis Hypothesis Smothering causes bruises(probabilistically)

Explaining away Explaining away – EEvidence is often rebuttedvidence is often rebutted

Legal idioms

BruisesBruises

Smother Smother ResuscitationResuscitation

Stephen reportStephen report

Evidence for alternative cause of bruises

Legal idioms

Distinguish event from reportDistinguish event from report

EventEvent

HypothesisHypothesis

ReportReport

BruisesBruises

Christopher smotheredChristopher smothered

Williams report of bruises

Williams report of bruises

Police / hospital report of NO

bruises

Police / hospital report of NO

bruises

Legal idioms Evidence – Reliability idiomEvidence – Reliability idiom

Evidence EEvidence E

Hypothesis HHypothesis H ReliabilityReliability

Williams reportWilliams report

BruisesBruises Reliability of Williams

Reliability of Williams

Impact of evidence on hypothesis is modulated by its reliability

Williams slide errors

Williams slide errors

Legal idioms

Reliability of witness reports Reliability of witness reports – Separate factors for reliabilitySeparate factors for reliability

Williams reportWilliams report

BruisesBruises Reliability of Williams

Reliability of Williams

VeracityVeracity

Is Williams honest?

ObjectivityObjectivity

Is Williams biased?

CompetenceCompetence

Is Williams mistaken?

From Schum (2001)

Legal idioms

Opportunity idiomOpportunity idiom

Sally smothers Harry

Sally smothers Harry

Sally alone with HarrySally alone with Harry

Stephen reportStephen report

ReliabilityReliability

Opportunity is often a pre-condition of guilt

Legal idioms

Motive idiomMotive idiom

Motive is typically a pre-condition of guilt

Sally murders baby

Sally murders baby

Sally career driven

Sally career driven

Sally resentfulSally resentful

Letters to parents

Letters to parents

evidence

Use of ironyUse of irony

rebuttal

Combining idioms – alibi evidence

Stephen lying to protect wife?

Stephen memory error?

ReliabilityReliability

Sally smothered Harry

Sally smothered Harry

Sally alone with HarrySally alone with Harry

Opportunity

Taxi record 8.10Taxi record 8.10Stephen report 5.30

Stephen report 5.30

Conflicting Evidence reports

Status of framework

NormativeNormative– Formal model to capture appropriate probabilistic Formal model to capture appropriate probabilistic

inference (and support theory-evidence co-ordination) inference (and support theory-evidence co-ordination)

DescriptiveDescriptive– Do people’s inferences conform to the model?Do people’s inferences conform to the model?– Qualitatively? Quantitatively?Qualitatively? Quantitatively?– Empirical studies suggest good fit to qualitative Empirical studies suggest good fit to qualitative

patternspatterns

PrescriptivePrescriptive– Guide to interpreting complex evidence and improving Guide to interpreting complex evidence and improving

inference (shift towards TEC)inference (shift towards TEC)

The big picture

Combining network fragments into a Combining network fragments into a large-scale modellarge-scale model

Key factors at trial

Prosecution case

Defence case

Cognitive Economy?

How do people do this?How do people do this?– Lab-based studies support the claim that they Lab-based studies support the claim that they

use idioms for small-scale problems (Lagnado, use idioms for small-scale problems (Lagnado, 2011; Lagnado et al., 2012)2011; Lagnado et al., 2012)

– But how does this scale-up?But how does this scale-up? Story-tellingStory-telling

– Use of narrative to simplify?Use of narrative to simplify?– Reasoning Reasoning from from but not but not aboutabout evidence evidence

Stories and BlameStories and Blame

Stories constructed from causal networksStories constructed from causal networks Cohesive narrative to explain eventsCohesive narrative to explain events To attribute blame for negative outcomesTo attribute blame for negative outcomes But focus of stories can compromise But focus of stories can compromise

proper theory-evidence co-ordination proper theory-evidence co-ordination


At trialAt trial Prosecution presented one cohesive Prosecution presented one cohesive

story – story – Sally smothered both babiesSally smothered both babies Explains most of the medical evidenceExplains most of the medical evidence Explains unreliability of Stephen & Sally testimonyExplains unreliability of Stephen & Sally testimony ‘‘SupportedSupported’’ by statistical evidence by statistical evidence

Defence did not present one single Defence did not present one single story, but numerous disconnected story, but numerous disconnected pieces to explain the different injuries pieces to explain the different injuries etcetc

Possible line of juror reasoning?

Jurors reject SIDS due to extreme rarityJurors reject SIDS due to extreme rarity Neglect low base-rate of smothering Neglect low base-rate of smothering

because this was never raised at trial because this was never raised at trial Accept smothering because:Accept smothering because:

– it gives it gives ‘‘simplesimple’’ explanation of injuries explanation of injuries– (and explains inconsistent testimonies)(and explains inconsistent testimonies)– Assigns blame to someone Assigns blame to someone

A A ‘‘plausibleplausible’’ story? story?

Importance of causal story that Importance of causal story that assigns blame?assigns blame?

At second appealAt second appeal– New New ‘‘storystory’’ in which Harry died from in which Harry died from

infection and Dr Williams & Meadow infection and Dr Williams & Meadow were blamedwere blamed

Aftermath & MediaAftermath & Media– Professor MeadowProfessor Meadow’’s statistical errors are s statistical errors are

highlighted highlighted


Importance of clarity in evidential Importance of clarity in evidential reasoningreasoning– For jurors, lawyers, judges, experts, media …For jurors, lawyers, judges, experts, media …

How can this be improved?How can this be improved?– Shift from single casual story to theory-Shift from single casual story to theory-

evidence co-ordinationevidence co-ordination– Use peopleUse people’’s capacity for causal reasoning to s capacity for causal reasoning to

support better probabilistic inference? support better probabilistic inference? – Introduce formal methods eg Bayesian networks Introduce formal methods eg Bayesian networks

etc to help model and evaluate evidence? etc to help model and evaluate evidence? – Ongoing research! Ongoing research!

Lessons for evidential reasoning

Thank you!

Collaborators Collaborators – Norman Fenton (QMUL)Norman Fenton (QMUL)– Martin Neil (QMUL)Martin Neil (QMUL)

Evidence projectEvidence project– Philip DawidPhilip Dawid– William TwiningWilliam Twining

BAYES RULE (odds version)

P(2deaths|guilty) = 1P(2deaths|~guilty) =1/73million (ignoring error of non-independence)

P(guilty) = 1/84million (based on stats for double child murders – but perhaps should just consider guilty = at least one murder)

P(guilty|2deaths) = 0.009

Nbp/1-p = odds

P = odds/(1+odds)

stories and statistics: what can the sally clark case tell us about the psychology of evidential...

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