I recently stumbled upon a Nature paper from December 2014. Identification of the remains of King Richard III, from Leicester University and a number of international experts, calculates the strength of the non-genetic evidence very much along the lines I suggested here in May 2013. The extracts that follow are from the supplementary information:
In the first such analysis of its kind, we bring together the genetic and genealogical evidence described above with previously-reported non-genetic evidence to come to an overall conclusion about the identity of Skeleton 1.
Indeed the paper refers to this blog and uses my figure for a “conservative” prior.
Taking a conservative approach at each step, we computed a likelihood for each item of observed evidence under each of two opposing hypotheses: Hypothesis 1 (H1): Skeleton 1 is Richard III, and Hypothesis 2 (H2): Skeleton 1 is not Richard III.
As it was reasonable to assume that all the different lines of evidence were independent, the joint likelihood of all the evidence was obtained by multiplication of the individual likelihoods under each hypothesis. The weight of evidence for H1, called the likelihood ratio (LR), was then given by the ratio of the likelihood under H1 to that under H2. We say that an assumption is ‘conservative’ if it reduces the LR.
The LR can be converted into a probability that H1 is true, given a prior probability. We took as starting point the moment that Skeleton 1 was first observed and recognized as a human skeleton, but before any assessments of age, sex, state of health and cause of death were made. At that point, there was substantial evidence that a skeleton found in what is believed to have been the location of Leicester Grey Friars choir could be that of Richard III. All of the information available at the time that Skeleton 1 was unearthed, including its precise location and the nature of the grave, was regarded for this analysis as background information that can inform the prior probability. On the basis of that information, we believe that a sceptical observer could not reasonably have assigned a prior probability less than 1 in 40. This value was proposed in a previous analysis (https://rationalgareth.com/), based on what we judge to be sceptical assessments. The highest probability that could be justified by the prior evidence might be 1 in 2.
The analysis of the genetic evidence takes into account both mitochondrial DNA (mtDNA) transmitted down the female line, and Y-chromosome DNA transmitted down the male line.
While there is a perfect match of the mtDNA with a living relative, the Y-chromosomes do not match. This may be explained as a “false paternity” event in one of the 19 generations separating Richard from his contemporary male relative. Since such events are not all that rare, the failure of the Y-chromosomes to match is only weak evidence against the identification (LR = 0.16, or 6:1 against). The mitochondrial evidence alone gave LR = 478, but with the Y-chromosome evidence this is reduced to 79. Taking into account my skeptical prior we have odds in favour of Richard of only 2:1. A sceptic would have to call the identification probable but hardly convincing.
It is worth noting that the mtDNA evidence was possibly weakened by a paucity of mitochondrial sequences from England with which to compare it. The mitochondrial genome obtained from the skeleton is very rare in Europe, but possibly more common in England, so a more conservative estimate of its frequency was used. When the mitochondrial genetics of the English population is better known it may be possible to improve this figure. At present, however, the genetic evidence is not conclusive but fortunately (and this was the main point of my original blog) it is not needed:
Interestingly, although the “DNA match” reported by the University of Leicester on February 4, 2013 was popularly perceived to have “proved” that Skeleton 1 is Richard III, we find the genetic evidence supports H1 only moderately because the Y DNA evidence points in the other direction. Using our highly conservative approach, with a LR of 79 for mtDNA and Y evidence combined, our sceptic would not be convinced of H1 based on the genetic evidence alone. The non-genetic evidence weight of evidence is over a thousand times stronger than the genetic evidence, under the conservative assumptions outlined above.
The evidence from all sources is summarised in the table reproduced from the LU paper below. The non-genetic evidence comes out as 85,000:1 in favour of Richard.
It is gratifying that the very rough estimates that I made are not too dissimilar to the much more rigorous calculations presented in the paper. I estimated the LR for the non-genetic evidence to be somewhat greater, in the range (0.8-80) million. That is in part because some of the evidence I attempted to use has not been incorporated (e.g. on diet), presumably because a reliable basis for estimating the probabilities could not be found. That is as it should be in a scientific paper. The strength of all the evidence taken into account by the LU team is LR = 6.7 million, giving a probability that the skeleton is Richard of at least 0.999994.
(Weight of evidence is often measured on a logarithmic scale. If we take logs to base 10 we are measuring evidence in ‘bans’, a unit introduced by Alan Turing during his time at Bletchley Park decoding the German enigma messages. On that scale the LU figure for the genetic plus non-genetic evidence is 1.9 + 4.9 = 6.8 bans, compared with my estimate for the non-genetic evidence of 5.9-7.9 bans).
I was also pleased to note that one of the authors of the LU paper is Prof. David J. Balding, author of the text Weight-of-Evidence, that inspired my previous blog. I have collaborated with David on a different matter, that I will blog about here when it is published.