British Academy: The UK's National Academy for the Humanities and Social Sciences
'PHILOSOPHICAL LECTURES' SYMPOSIUM
Bayes's Theorem
Saturday 10 March 2001
The British Academy, 10 Carlton House Terrace, London, SW1Y 5AH
Bayes's Theorem is a powerful but controversial tool for assessing how probable specified evidence makes some hypothesis. It claims that the probability of a hypothesis h on evidence e and background knowledge k (the posterior probability of h) is equal to the probability of e given h and k (the predictive power of h), multiplied by the probability of h given only k (the prior probability of h), divided by the probability of e given only k (the prior probability of e). The prior probability of e is its probability if h is true is multiplied by the prior probability that h is true, plus its probability if h is false is multiplied by the prior probability that h is false.
Representing by P(h/e & k) the posterior probability of h, by P(e/h & k) the predictive power of h, by P(h/k) the prior probability of h, and by (e/k) the prior probability of e, Bayes's Theorem then reads
P (h/e & k) = | P(e/h & k) P(h/k) |
| P(e/k) |
Thus suppose that we have background knowledge k that a certain coin has with equal probability either a bias of 2/3 in favour of landing heads, or a bias of 2/3 in favour of landing tails. Let h be the hypothesis that it has a bias of 2/3 in favour of landing heads. Suppose we toss it four times and all these tosses are heads (e). Bayes's Theorem then tells us that this evidence gives a probability of 16/17 to the hypothesis h.
We may not be able to give exact numerical values to the terms on the right-hand side of Bayes's Theorem, but so long as we can give rough values, we can give a rough value to the left-hand side. So perhaps we can use it to assess (roughly) the probabilities, not merely of simple statistical hypotheses, but of scientific theories, historical claims and world-views. Yet to apply it at all, we need to be able to ascribe prior probabilities to hypotheses. But can we do that in an objective way, even when we are dealing with simple statistical hypotheses and have some substantial relevant background knowledge from observation? And what about when all our observational evidence is included in e - are there a priori criteria for ascribing prior probabilities? Or must the prior probability of a hypothesis measure merely a given person`s initial degree of confidence in that hypothesis? This symposium will investigate whether Bayes's Theorem has any philosophical justification at all, whether it has application in statistical science, in the law-courts, and in assessing the probability of world-views such as theism. There will be opportunity for discussion following each paper.
Attendance at the conference is free, and all those interested are welcome to attend, but it is essential to register in advance. In order to register, please complete the attached form and return it to Angela Pusey at the British Academy, 10 Carlton House Terrace, London SW1Y 5AH (telephone: 020 7969 5200; email: a.pusey@britac.ac.uk). If you would like to have buffet lunch at the Academy at a cost of £12 per person please indicate this on the form, and enclose a cheque made payable to the British Academy.
PROGRAMME
Sat 10 March |
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| 10.00 | Coffee and registration |
Session I | 10.30 | Introduction |
| 11.00 | Bayes's Theorem: The Philosophical Issues |
| 12.15 | Lunch |
Session II: | 13.30 | Bayes's Theorem and Statistical Science |
Session III: | 14.45 | Bayes's Theorem and Weighing Evidence by Juries |
| 16.00 | Tea |
Session IV: | 16.30 | Bayes's Theorem, Miracles and Theism |
Publication
Papers from this symposium were published in 2002 as
Bayes's Theorem, edited by Richard Swinburne (Proceedings of the British Academy, 113)