Continuing on how genealogical proof could be made more convincing, beyond the textual reasoning presently employed, by adopting a probabilistic approach.
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 which documents why the evidence now strongly points to Thomas Jefferson (TJ) as being the father of six of the children.
Part 1 looked at the case where we started out believing it was unlikely TJ was the father. This part looks at the case were it is suspected it was either TJ or someone with a direct male line from his grandfather who was the father of Sally Heming's children. The prior probabilities ascribed to TJ and to his make relatives are considered equal at 49% each. The remaining 2% is attributed to some other person or persons. These are the prior probabilities that would be ascribed based on DNA testing which found a good match between a descendant of one of Sally Hemings's children and a descendant to TJ's grandfather but not through TJ. His Y chromosome was of a fairly unusual type, one carried by about only 1% of the British-origin male population.
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 83%, or 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 99.8%, or extremely probable. This is a greater likelihood than the case for a father named on a birth certificate where the probability of that information being false is typically 1-4%.
If only information on the striking similarity was missing the probability that TJ was the father would be 98.8%. While that's not quite up to the 99% standard for extremely probable it is a significant jump from the prior probability of 49%.
The final part in this series will look at the case where the initial belief is high probability that TJ was the father of the six Hemings children.