Joint meeting with the RSS General Applications Section

An afternoon on statistics and the law

Speakers:

TONY GARDNER-MEDWIN (University College, London)

I shall challenge the conventional view that "beyond reasonable doubt" in criminal trials is a matter of a high threshold on the probability of guilt. This I contend is a necessary but not a sufficient condition for conviction.

A jury will conclude that P(guilt) based on the evidence is high if, in their judgment, such evidence would arise much more frequently in relation to a guilty person than an innocent one. But even when this is true, the evidence may be expected to arise for innocent persons with non-negligible frequency.

My contention is that there is then "reasonable doubt": an innocent defendant could find themselves facing such evidence, even though in nearly all such similar cases the defendant would be guilty. The defendant should be acquitted.

Addressing uncertainties and probabilities conditional on the hypothesis of innocence becomes the most critical issue for a jury to address. Seldom of course is it possible to address these issues with any quantitative precision. But shifting to questions that are conditional on presumption of innocence has immediate implications for the kinds of evidence that are relevant. A criminal record is relevant to P(guilt) but not to P(evidence, if the defendant is innocent of the current allegation).

Statistics for the incidence of infanticide in a population are relevant to one's judgment of P(guilt) given that a person's child has died mysteriously, but they are not relevant to one's judgment of how often such circumstances would arise for an innocent person. If "reasonable doubt" is a question about probabilities conditional on innocence, then clear rational arguments emerge for long standing legal principles about what is and is not admissible evidence, normally justified by rather vague and incomplete reference to concepts such as fairness and morality, prejudicial versus probative impact, or supposed irrelevance or incomprehension of statistical arguments.

Tony's talk

DAVID BALDING (Imperial College, London)

Many legal questions revolve around establishing the relatedness of two or more individuals using DNA profile data.

The use of likelihood ratios to answer such questions is now uncontroversial, and Mendel's laws of inheritance on which the likelihood calculations are based are straightforward.

Yet there nevertheless remain many potential complexities. How does uncertainty about allele proportions, affect the computations? How helpful is it to have genotypes of other individuals whose relatedness to one or more of the parties is not in dispute? What if there are many individuals and many alternative hypotheses to consider?

I will discuss these and related issues while focussing on a specific application to a group of individuals, each the offspring of anonymous donor insemination, who wished to know which, if any, of them had a common natural father.

David's talk

STEPHEN SENN (University of Glasgow)

We live in a litigious age in which the public seems to have extravagant expectations as to what medicine ought to deliver and in which no 'accident' occurs without someone being to blame. What is good news for lawyers is not necessarily good news for the rest of us. I consider some implications of public expectation of proof of non-harm for patients, physicians, investigative journalists, lawyers, drug developers and regulators and statisticians.

Stephen's talk

PATRICK LAYCOCK (Manchester University)

I have interacted with the Law at various levels during my career as a professional statistician. In particular, I have had a part-time post for many years as a Senior Consultant with Capcis, an engineering consultancy. Many of these statistical reports concerned some legal dispute or insurance claim, often involving several parties, over the attachment of blame, or otherwise, to one or more of the parties following some industrial hiccup or catastrophe. Such disputes often drag on for many years and are typically settled 'out of court and on the day'. Except on one occasion, these are my 'second order interactions'- they have not involved an appearance in court. My 'first order interactions' - which involve court appearances - have largely burgeoned since my retirement from teaching and have mostly concerned the statistical significance, or otherwise, of Crown prosecution statements concerning the detection of Class A and Class B drugs on banknotes.

I will discuss some of the statistical problems raised and techniques I have used in these cases and attempt to convey some of the pleasures and frustrations they have brought me. It is both the blessing and the tragedy of our subject area that so many people find it so useful.

Patrick's talk

Meeting Organiser: Richard Boys Telephone: +44 (0)191 2227297

The RSS has established a Statistics and the Law working party chaired by Professor Colin Aitken of Edinburgh University, to address some of the main issues.