Bayesian Theory and Medieval History

What was the probability that a medievalist would take part in a panel on Baysean theory as part of the decennial conference for Durham University’s Institute of Advanced Study? Well, a subjective Bayesean analysis would, in all likelihood, have indicated a high probability. If probability is ‘the value at which an expectation depending on the happening of the event ought to be computed, and the value of the thing expected upon its happening’, then the conference and the medievalists attendance was indeed likely. With just such Baysean confidence, Tom McLeish put together a panel for the conference, the theme of which was ‘Evidence on Trial’. He shaped and exploration through the lens of the Baysean prior, the assumptions we make in coming to judgment, of how different disciplines approach different sorts of evidence. Moving between humanities and scientific models enshrined the interdisciplinary focus of the IAS, and the surprising and anticipated benefits of cross-disciplinary dialogue.

The panel consisted of Michael Levine (Philosophy, University of Western Australia), Giles Gasper (History, Durham) and Michael Goldstein (Mathematical Sciences, Durham), chaired by Tom. Michael Levine set off first, with an analysis of David Hume on miracles, and the problems of applying Bayesean analysis to Hume’s position. Hume (1711-1776) and Thomas Bayes (1701-1761) were near contemporaries, although there is no evidence that they knew of each other. Even if they did, Bayes’s work on probability came late in his life and was posthumously presented at the Royal Society by his friend and executor Thomas Price, as An Essay towards solving a Problem in the Doctrine of Chances (1763). Nevertheless, some of the philosophical criticisms of probability theory were brought to the surface.

Giles then followed with a survey of the evidence for the life of Grosseteste, especially in the period from his birth to the later 1220s and the point where his whereabouts and doings are far better documented. As is not uncommon with medieval lives a great deal of contextual information and independent corroboration is lacking, and a great deal of balancing of possible/probable/plausible interpretations for fragmentary, occasionally omnidirectional, evidence. How can we be sure that a charters witness R. Grosseteste was ‘Robert’, and even if so, how are we certain that this Robert Grosseteste was the man who became bishop of Lincoln. We don’t know when Grosseteste was born, we don’t know his age at death (in 1253) save that he had lived a long life. Moreover, there are a lot of prior assumptions at play in the reconstruction of his life: was he ever at the University of Paris, or, before the late 1220s ever at the University of Oxford? was he lecturing in Theology from an earlier point in the 12teens, or was this a later phase in the 1220s? How do we fit in the evidence of his treatises? How are their chronologies to be worked out? Is it plausible to posit intense periods of writing and productivity for Grosseteste? (the answer to that one is almost certainly yes – Tom made a very telling comparison to Robert Schumann, whose compositional output is crammed into a very short space of time). Testing and balancing the evidence, and finding it in the first place, takes time, and rarely produces concrete results. Was Grosseteste married, living in Paris with a wife and children, to return to England after his wife’s death some time before 1224 to take up his first benefice? This is the very neatly argued possibility raised by Nicole Schulman (‘Husband, Father, Bishop: Grosseteste in Paris’, Speculum 72 (1997), 330-46), which is not wholly demonstrable, but, raises all kinds of questions about prior assumptions. Why should family-life be absent from discussions of medieval scholarly achievement and mores?

Finally, after the implicit Bayesean balancing of evidence, Michael Goldstein gave a masterclass in what subjective Baysean statistics consists of, how it can and should be used, and the considerable quantity of uncertainties that have to be included in any analysis. A classic example of probability theory in action: assured that a test for a rare disease is 99% effective, you take the test and test positive. What do you do? Actually you ask for a re-test. If the disease is rare, say 1 in 10,000 people, you have approximately a 0.1 % chance of having the disease. The implications of models, and how these do and don’t apply to the real world were fascinating questions explored, especially with reference to climate change.

A lively and entertaining discussion brought the session to a close, including the question of how Bayesean analysis might, or might not be applicable in historical contexts. Ordered Universe might enjoy taking this on, perhaps! What came out very strongly was the importance of the questions asked, and the care with which any answers are scrutinised. What we don’t know, what we are uncertain about, are in many senses the keys to making sense of the puzzles with which we are faced. The benefit, in this context, of questions from multiple perspectives, of interdisciplinary response to problem solving, is clear. The question least expected can open the the most unexpected avenues to further questions and research.