The third and final part in this series looks at the situation where the initial belief is high probability that Thomas Jefferson (TJ) was the father of the six children of Sally Hemings. Remember, the objective is to add a quantitative probabilistic overlay to the Genealogical Proof Standard so making it more transparent and convincing, beyond the textual reasoning presently employed.
This example draws on some of the evidence presented in the article "Sally Hemings's Children: A Genealogical Analysis of the Evidence" by Helen Leary published in the NGS Quarterly in September 2001.
Part 1 looked at the case where we started out believing it was unlikely TJ was the father. Part 2 was a middle probability case consistent with DNA findings. This part looks at the case were there is already a strong belief that TJ was the father of Sally Heming's children. The evidence for that might include the statement against Eston Hemings' entry on the 1870 census that "This is the son of Thomas Jefferson"
The prior probabilities ascribed to TJ is 95%, that of his relatives 3% and others 2%.
All the conditional probabilities from part 1 are retained.
In this case the posterior probability, after accounting for the striking similarity between TJ and Eston Hemings, is 99.37%, or extremely probable.
Adding in the coincidence between the times of Sally Heming's conceptions and TJ residence at Montecello increases the probability of TJ being the father to 99.99%, still extremely probable but verging on virtually certain.
Even this 99.99% does not meet the Genealogical Proof Standard. To do so would require looking at each element of the evidence covered in Leary's article. That's quite viable, although assessing the conditional probabilities may lead to healthy debate. You may wish to continue the analysis on this third case adding on the relative's and supporter's opinions (recognizing these may have been expressed with the aim of protecting TJ's reputation) and DNA evidence used as the basis for prior probabilities in the first two parts as conditional probabilities. If you do so, you'll find the probability that TJ was the father decreases a few 100ths of a percentage point.
It takes some slam dunk evidence against TJ being the father to reverse the odds. There is little point in going to the effort to examine additional evidence that does not have the potential to do so, even if that would be necessary for the GPS.