After the 1998 DNA study in Nature indicted Thomas Jefferson apropos of the paternity of Eston Hemings and the rest of Sally Hemings’ children, the Thomas Jefferson Memorial Foundation (hereafter, TJMF)—now merely the Thomas Jefferson Foundation—formed a committee to examine the DNA study and strands of historical evidence. In 2000, the foundation declared, “The DNA study, combined with multiple strands of currently available documentary and statistical evidence, indicates a high probability that Thomas Jefferson fathered Eston Hemings, and that he most likely was the father of all six of Sally Hemings’s children appearing in Jefferson’s records.” How did the committee come up with such a bold pronouncement? White McKenzie Wallenborn, a member of the committee, catalogs some of the suspicious activities of the committee, while the Jefferson-Hemings liaison was under investigation, in his essay, “A Committee Insider’s Viewpoint.” His view is that the verdict was the result of a kangaroo court, intent “to force [committee members] to accept something that was politically correct and not historically accurate.”
Dr. Wallenborn, the sole dissenting member of the committee, noted that its members seemed intent on finding evidence that showed Jefferson’s involvement with Hemings instead of investigating the issue with an open mind. Writes Wallenborn of the actions of archeologist Fraser Neiman:
When the committee was assembling for one of its meetings in February 1999, the head of the Archeology Department at Monticello dropped a packet of papers on the table next to me and said (and this is exactly how another member of the committee and I recollect it): “I’ve got him!” He repeated this statement again and then explained his ‘Monte Carlo Simulation.’ This just seemed to be an inappropriately enthusiastic remark for someone who is working at Thomas Jefferson’s home.
The packet of papers was published by Neiman as “Coincidence or Causal Connection?” in the William and Mary Quarterly. The argument driving the paper, which proved to be of considerable consequence in the decision of the TJMF’s committee report to implicate Jefferson in the paternity of Eston Hemings and the other children of Sally Hemings, is fallacious.
The Monte-Carlo argument of Neiman uses Bayesian induction and proposes to show that there is only a one-in-one-hundred chance that Thomas Jefferson and only Thomas Jefferson was not the father of Eston Hemings, but also all of Sally Hemings’s children. That is prima facie a very dicey claim, given that the DNA evidence shows only that Jefferson is a candidate for paternity in the case of Eston Hemings—viz., Eston has the Jefferson Y-chromosome. Prior to considering his argument, anyone with even a tyro’s appreciation for logic would grasp beforehand that there must be some prodigiously compelling historical evidence that drives it.
What is the evidence that drives the Bayesian argument? It is the suspicion that Jefferson was at Monticello nine months prior to the birth of each of Sally Hemings’s children. Following that coincidence, Neiman establishes “a quantitative means of combining that estimate with other evidence to produce an overall assessment of the probability that Jefferson fathered all of Hemings’ children.”
Neiman begins: If someone other than Jefferson should be the father, what would be the probability that each of Hemings’s conception dates would be within a period when Jefferson was at Monticello, not elsewhere?
The Monte-Carlo statistical method Neiman employs is a method of simulation-based inference, usually used for highly complex systems for which deterministic algorithms are unsuited, because there is considerable uncertainty about the inputs. In that regard, it uses a relative frequency, not an a priori, approach to probability to determine outcomes. Repeated random samplings take the place of a priori calculation. Computers are generally employed to expedite the number of random tries.
Let me illustrate with a non-complex example: a flip of a coin. Consider the probability of a head coming up in one flip of the coin. Using the a priori approach, which assumes the equal probability of all outcomes prior to the flip, one places the expected outcome (head) over all possible outcomes (head or tail) to arrive at the probability assessment of 1/2 or 0.5. Nonetheless, one might object that such a method, though convenient and practical, is not sufficiently precise, for no coin is so perfectly manufactured such that the likelihood of a head prior to any flip is exactly 0.5. Thus, a better measure of likelihood would be to flip a particular coin a very large number of times—the more flips, the better the consequence—and draw out the probability from experience. In such a manner, experience would determine the bias of the coin.
The Monte-Carlo method is similar, only that the flips of the coin (or whatever outcome for which one desires a probability assessment) are done by a computer in an effort to generate quickly large amounts of data—here concerning Jefferson’s paternity. Neiman constructs four models, with slightly different parameters, and comes up with the following distribution-schemes, given the record of Jefferson’s stays at Monticello and the birthdays of Hemings’s children. The table he titles “Relative Frequency Distributions for the Number of Conceptions that Fall during or Three Days before a Jefferson Visit, for the Four Monte Carlo Models.”
Model 1 0.0 3.6 19.1 37.3 29.2 9.7 1.2
Model 2 0.0 0.0 13.8 37.7 34.3 12.7 1.5
Model 3 0.1 6.3 24.6 36.8 24.2 7.2 0.8
Model 4 0.0 4.3 18.3 34.3 30.6 11.1 1.3
0 1 2 3 4 5 6
Given these distribution schemes, Neiman then uses Bayes’s theorem to derive a probability assessment for Jefferson being the father of all six children.
p(J/e) = p(J) x p(e/J)
p(J) x p(e/J) + p(~J) x p(e/~J)
Given an extremely low a priori probability of 0.05 that Jefferson was the father of all six children [(J), assumed arbitrarily, just to get the ball rolling] and given a very low probability of 0.012 that Jefferson was not the father of all six children though he was present each time at conception (e/~J), Neiman arrives at an 84 percent a posteriori likelihood that Jefferson was the father of all six—a probability that increases commensurate with an increase in the a priori probability (e.g., an a priori probability of 0.10 generates an a posteriori probability of 92 percent and an even a priori probability generates near certainty). On assumption of a very low prior probability of Jefferson being the father of all six children, we ultimately arrive at an extremely high probability that he was, given the coincidence of him being present at Monticello nine months prior to the birth of each child. Note how that coincidence drives the argument.
Furthermore, Neiman has us note that the low a priori probability of Jefferson being the father of all six children that was given at the start does not take into consideration any other evidence that might also implicate Jefferson—the DNA evidence and other historically relevant data. Once we factor in all such evidence, the prior probability increases commensurately. At some point, it becomes ridiculous to consider Jefferson’s stays at Monticello and Hemings’s conception dates as independent. Coincidence becomes causal concatenation. Jefferson fathered all six children. Q.E.D.
Nieman ends his paper with gasconade which concerns doubting doubt. “Serious doubt about the existence and duration of the relationship and about Jefferson’s paternity of Hemings’s six children can no longer be reasonably doubted.”
It is a clever argument, but let us get outside of the “proof” to disclose the inveiglement. First, the argument assumes that Sally Hemings was at Monticello with Jefferson every time she became pregnant, but there is no record of her whereabouts for any of the times. We cannot merely assume that as a matter of fact. Second, Jefferson was at Monticello 16 other times between the conceptions of Sally Hemings’s first and last child, and Hemings did not get pregnant. That is evidence that Neiman’s argument does not accommodate. One might remonstrate that no one cares about the times Hemings did not get pregnant, only her pregnancies. Yet that invites discussion, if Jefferson was potent and could not, as the story-tellers at Monticello assert, could not keep out his hand from Hemings. Third, Neiman assumes that Sally Hemings was not promiscuous—i.e., that there was one and only one father for all of Hemings’ children. That is gratuitous, given that her mother had several paramours: two white and two black. Finally, on assumption that Sally Hemings had only one paramour, Neiman presumes that other possible Jefferson-chromosome paternity candidates were not present at each conception. Could brother Randolph Jefferson have been present on each occasion? He lived only 20 miles south of Monticello, though it was an arduous 20 miles. There are other difficulties with the argument that have been addressed in the secondary literature. They need not concern us here.
In sum, Neiman’s argument is not only misleading, but also scandalously fallacious. Statistical arguments are only as good as the data that go into them. When you contaminate the data, even slightly, by selectively culling data that will secure the sought-out conclusion and by ignoring relevant evidence that creates difficulties for the thesis, then the results can become massively skewed—hence, the 0.99 percent probability that Jefferson fathered all of Sally Hemings’s children.
The difficulties underscore problems with arguments based on computer-based simulations. The results are reliable only insofar as all the relevant data have been entered. Here we come to the issue, which we can see best by returning to the example of ascertaining the probability of a head from a particular coin. Assuming that the coin has some bias, however slight, for no coin can be perfectly struck, one cannot ascertain that bias through computer simulation unless one first enters the defects of the coin into the computer. That, of course, presupposes knowledge of the biases, which would obviate the need of the computer in the first place.
It is astonishing that Neiman’s model had such an influence on the TJMF’s committee report in 2000. The conclusion that there is a 0.99 probability that Jefferson fathered not only Eston Hemings, but all of Sally Hemings’ children, given the gross state of historical uncertainty, should have been cause for alarm for any rational person.