Aitchison, L.D; (2021) Bayesian inference in neural circuits and synapses. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Bayesian inference describes how to reason optimally under uncertainty. As the brain faces considerable uncertainty, it may be possible to understand aspects of neural computation using Bayesian inference. In this thesis, I address several questions within this broad theme. First, I show that con dence reports may, in some circumstances be Bayes optimal, by taking a \doubly Bayesian" strategy: computing the Bayesian model evidence for several di erent models of participant's behaviour, one of which is itself Bayesian. Second, I address a related question concerning features of the probability distributions realised by neural activity. In particular, it has been show that neural activity obeys Zipf's law, as do many other statistical distributions. We show the emergence of Zipf's law is in fact unsurprising, as it emerges from the existence of an underlying latent variable: ring rate. Third, I show that synaptic plasticity can be formulated as a Bayesian inference problem, and I give neural evidence in support of this proposition, based on the hypothesis that neurons sample from the resulting posterior distributions. Fourth, I consider how oscillatory excitatory-inhibitory circuits might perform inference by relating these circuits to a highly effective method for probabilistic inference: Hamiltonian Monte Carlo.

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