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Simon McGill added section_Bayesian_Inference_One_very__.tex
over 8 years ago
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\section{Bayesian Inference}
One very natural way of representing beliefs $b$ and $\phi$ mathematically is as subjective probability functions. In this case, we may restrict our theories of rationality to those which are consistent with Bayesian inference.
Assume that a belief $b$ actually corresponds to a probability function $\mathbb{B}$ representing a belief about the instantaneous state $Z_t$ of a ``phenomenal world'' variable $Z$, and how the world's next state $Z_{t+1}$ is co-distributed with instantaneous action $a_t$ and sensation $s_{t+1}$.
\[ \mathbb{B} : (Z \times Z \times A \times S) \to \mathbb{R} \]
