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In R v T [2010] EWCA Crim 2439, [2011] 1 Cr App Rep 85, the Court of Appeal indicated that ‘mathematical formulae’, such as likelihood ratios, should not be used by forensic scientists to analyse data where firm statistical evidence did not exist. Unfortunately, when considering the forensic scientist's evidence, the judgment consistently commits a basic logical error, the ‘transposition of the conditional’ which indicates that the Bayesian argument has not been understood and extends the confusion surrounding it. The judgment also fails to distinguish between the validity of the relationships in a formula and the precision of the data. We explain why the Bayesian method is the correct logical method for analysing forensic scientific evidence, how it works and why ‘mathematical formulae’ can be useful even where firm statistical data is lacking.

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This letter comments on the report "Forensic science in criminal courts: Ensuring scientific validity of feature-comparison methods" recently released by the President's Council of Advisors on Science and Technology (PCAST). The report advocates a procedure for evaluation of forensic evidence that is a two-stage procedure in which the first stage is "match"/"non-match" and the second stage is empirical assessment of sensitivity (correct acceptance) and false alarm (false acceptance) rates. Almost always, quantitative data from feature-comparison methods are continuously-valued and have within-source variability. We explain why a two-stage procedure is not appropriate for this type of data, and recommend use of statistical procedures which are appropriate.