Introduction: The Bayesian View of Probability and Statistics

The Bayesian perspective involves using probabilities to represent degrees of belief. It implements both inductive and deductive reasoning through Bayes' theorem

$$P(T\vert E)=\frac{P(E\vert T)P(T)}{P(E)}\textrm{,}$$ (2)

which generates the posterior probability $P(T\vert E)$, representing the degree of belief in a theory $T$, in the light of observational or experimental evidence $E$, from the likelihood $P(E\vert T)$, which is the probability that $T$ assigns to the occurrence of $E$, the prior probability $P(T)$, representing the degree of belief in $T$, before the occurrence of $E$, and the marginal likelihood $P(E)$, which is the average $\sum_{T\in{}S}P(E\vert T)P(T)$, over the set $S$ of available theories, of the likelihood.

This report aims to use Bayesian methods to provide a mathematical re-statement of certain recent epistemological arguments, in particular those associated with standpoint epistemology, which have previously been expressed in natural-language terms. It is then hoped to apply Bayesian arguments to current directions in the physical sciences.