19 Apr


The use of verbal equivalents is itself a contentious issue because of its subjective nature and also because some believe that it is encroaching on the role of the jury. Further, there is no rationale for the boundaries, for example, to discriminate between a likelihood ratio of 99 and one of 101.

The Bayesian approach

The Bayesian approach is favoured by many forensic scientists but has not gained widespread usage in the presentation of DNA evidence. The approach builds upon the likelihood but allows non-scientific data to be introduced in the form of prior odds. The non-scientific data will update the likelihood ratio to produce the final odds either in favour of, or against, the proposition put forward by the prosecution or defence (equation 9.4).

Consider the case against Dennis Adams (R v Adams [1996] Cr. App. R., Part 3) in the UK where he was accused of a rape that occurred in 1991. The trial was in 1994 when the DNA profiling methodology was based upon VNTR analysis that predated STR typing. The DNA evidence put forward by the prosecution was that the DNA profile occurred in 1 in 200 million of the population.

Adams pleaded not guilty; he had an alibi and was not identified at an identity parade. The defence expert produced numerical values for the crime being committed by a local man, for the possibility of not being identified at the parade, and for the alibi. All these prior probabilities were multiplied to determine the prior probability. The defence argued that the evidence (genetic and non-genetic) indicated the innocence of the accused. At the trial the judge allowed this to happen and directed the jury that they could use the Bayesian figure if they wished.

Adams was found guilty. The use of Bayesian evaluation of DNA evidence in the UK legal system has not beenacceptedandhasledtosuccessfulappealsagainstconvictions,includingtheabove example, when the Appeal Court took the view that the use of Bayesian statistics tres- passed on areas exclusively and peculiarly those of the jury. The relationship between different pieces of evidence was for the jury to decide and the mathematical formula might be applied differently by a different set of jurors. Jurors should evaluate the evidence by the joint application of their common sense and knowledge of the world to the material before them. A significant ruling was laid down in the English Courts following another appeal; (R v Doheny and Adams [1996] EWCA Crim 728).

A number of the relevant points can be summarized:

(1) The scientist should give the frequency of the occurrence with which the DNA profile is likely to be found in the population.

(2) It might be appropriate, if the scientist has the necessary data and statistical expertise, to say how many people might be found to have matching profiles in the United Kingdom or in a limited sub-group of individuals (the idea is to give the jury an estimate of how many people in the relevant section of the population are expected to have a matching profile and, therefore, could be the source of the stain).

(3) The jury would then decide, on all the information available, whether the stain originated from the suspect or some other individual with a matching profile.

(4) To help the jury, the judge might direct them along the following lines:

…if you accept the evidence that indicates there are only four or five (or what ever figure) men in the UK population from whom the stain could have originated and the suspect is one of them, are you sure the suspect left the stain or is it pos- sible it was one of the other individuals in the small group who has a matching profile.

Two fallacies
When presenting evidence two errors can be committed if the wording used is not precise — care should be taken to avoid committing the prosecutor’s or defendant’s fallacy.

Prosecutor’s fallacy
This fallacy in describing the strength of the evidence is also called ‘transposed condi- tional’ [8]. If a horse was described as a four legged animal it does not transpose that every four legged animal is a horse. Similarly the statement ‘the probability of gaining this DNA profile IF it came from someone other than the suspect is 1 in 1 million’, does not mean that ‘the probability that the evidence came from someone other than the suspect is 1 in 1 million”. The first statement considers the probability of the evidence given the hypothesis and is correct, but the second statement considers the probability of the hypothesis given the evidence, and is a clear case of the prosecutor’s fallacy. In the case of Andrew Deen (R v Deen [1994] The Times, January 10th, 1994) in the UK, the DNA analyst incorrectly defined match probability as the ‘probability of the semen having originated from someone other than Andrew Deen’. In the examination in chief, the DNA analyst said ‘the likelihood of (the source of the semen) being any other man but Andrew Deen is one in three million’. It is clear that the analyst transposed the condition of the hypothesis and it was one of the reasons that the conviction was quashed by the Court of Appeal. As another example, consider the following dialogue from R v Doheny and Adams (R v Doheny and Adams [1996] EWCA Crim 728):

Q. Is it possible that the semen could have come from a different person from the person who provided the blood samples?

A. It is possible but it is so unlikely as to really not be credible. I can calculate; I can estimate the chances of this semen having come from a man other than the provider of the blood sample. I can work out the chances as being less than 1 in 27 million.

Instead of estimating the probability of semen (crime scene sample) matching blood (of the suspect) if the suspect was innocent, the DNA analyst was estimating the prob- ability of the semen matching suspect’s blood if the suspect left the semen stain. For the population of the UK a match probability of 1 in 27 million means that other per- sons could have a matching profile and without other supporting evidence may not in itself provide sufficient evidence against the defendant. This however is a matter for the court to address and not the scientist. The prosecution expert witness thus inadvertently enhanced and misrepresented the probative value of the evidence [8]. It is therefore imperative that in order to avoid the prosecutor’s fallacy, the scientists write their report carefully and while answering any questions in the court keep their match probability or likelihood statements conditioned on ‘if the defendant was innocent’.

Defendant’s fallacy
If the match probability for a DNA profile was 1 in 27 million as it was in the case against Doheny, the defence could argue, for example, that three people in the UK might match the crime scene profile, the probability of the defendant being the donor of the crime scene sample is therefore only 1/3, which is insufficient for proof beyond reasonable doubt. The issue with this statement is that nothing is known of these three people; whether they exist, where they live, what age they are, what sex they are, and what opportunity they might have to leave their DNA at the scene.

Comparison of three approaches
The high statistical values that are attached to DNA profiles might seem intimidating and can unduly enhance the probative value of DNA evidence. This had led to heated debate over the way in which the evidence should be presented to a court. The frequentist approach is straightforward and understandable by both a jury and a judge. For the reporting officer it is straightforward to state in court and the opportunity for transposing the conditional and stating the prosecutor’s fallacy is less than with the other two approaches. A disadvantage of the approach is that it does not consider two propositions where one is the alternative of the other. The likelihood ratio is a logical approach, it considers an alternative hypothesis. The Bayesian approach is the most

logical way to incorporate all evidence in a case; it considers alternate hypotheses but it is difficult to calculate and conceptualize.

Further reading

Balding, D.J. (2005) Weight-of-evidence for Forensic DNA Profiles. John Wiley & Sons, Ltd, Chichester, pp. 145-156.
Buckelton, J., Triggs, C.M., and Walsh S.J. (2005) Forensic DNA Evidence Interpretation. CRC Press, pp. 27-63.
Evett, I. W., and Weir, B. S. (1998) Interpreting DNA Evidence – Statistical Genetics for Forensic Scientists. Sinauer Associates, pp. 217-246.


1. Cook, R., et al. (1998) A model for case assessment and interpretation. Science and Justice 38,151-156.

2. Evett, I.W., et al. (2000) More on the hierarchy of propositions: exploring the distinction between explanations and propositions. Science and Justice 40, 3-10.

3. Evett, I.W., et al. (2000) The impact of the principles of evidence interpretation on the structure and content of statements. Science and Justice 40, 233-239.

4. Taroni, F., and Aitken, C.G.G. (2000) DNA evidence, probabilistic evaluation and collaborative tests. Forensic Science International 108, 121-143.

5. Meester, R., and Sjerps, M. (2004) Why the effect of prior odds should accompany the likelihood ratio when reporting DNA evidence. Law Probablity and Risk 3, 51-62.

6. DNA Advisory Board(2000) Statistical and population genetic issues affecting the evaluation of the frequency of occurrence of DNA profiles calculated from pertinent population databases. Forensic Science Communications 2.

7. Evett, I.W., and Weir, B.S. (1998) Interpreting DNA Evidence. Sinauer Associates, Inc.

8. Balding, D.J., and Donnelly, P. (1994) The prosecutor’s fallacy and DNA evidence. Criminal Law Review, 711-721.

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