Bayesian probability estimation

•Thomas Bayes (1702-1761)

–Minister of the Presbyterian Chapel

at Tunbridge Wells

at Tunbridge Wells

–Amateur mathematician

–*Essay towards solving a problem *

*in the doctrine of
chances*,

published (posthumously) in 1764

published (posthumously) in 1764

•Crucial idea:

background (*prior*)
knowledge

about the plausibility of different theories

can be combined with knowledge about

the relation of theories to evidence

about the plausibility of different theories

can be combined with knowledge about

the relation of theories to evidence

•in a mathematically well-defined way

•even if all knowledge is
uncertain

•to reason about the most likely explanation of the available evidence

•Bayes’ theorem

–“the most important equation in the history of
mathematics” (?)

–a simple consequence of basic definitions, *or
*

–a still-controversial recipe for the probability of
alternative causes for a given event, *or
*

–the implicit foundation of human reasoning

–**a general framework for solving the problems of
perception**