Bayesian Analysis for Neural Data

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)

Abstract

Phase coherence is an approach to measuring entrainment of the brain to stimuli. Often, this is
calculated using the inter-trial phase coherence (ITPC). However, there is scope for improving upon this measure. The ITPC discards information by averaging across trials, but with
a Bayesian approach a per-item analysis is possible. Circular data needs to be carefully approached when using Hamiltonian Monte Carlo to sample from the posterior. If the periodicity
is ignored, then sampling will be inefficient. To solve this problem a custom prior distribution
is developed. The model is applied to two experimental datasets and simulated data. The
Bayesian approach provides a better false-positive rate alongside a discovery of novel results.
One approach of neuroscientists to record brain activity is through gene expression. Activity is
quantified by counting the number of cells that are identified as expressing this gene using a
visual marker. A particular trait of this kind of data is that the sample size is small. Yet, statistical
analysis is approached with methods such as t-tests or ANOVA’s. It is natural to model the
grouped structure of these data using a hierarchical Bayesian model. The Bayesian approach
models uncertainty explicitly which is an invaluable for small datasets such as these. A model
is developed and applied to two experimental datasets. The Bayesian construction offers new
results where previously statistical significance was not present.
Correlation matrices can be difficult to estimate. In a Bayesian analysis the use of prior distributions over the space of correlation matrices solves this problem. However, such distributions
are scarce: due to this lack of flexibility it is important to understand how a particular choice of
a correlation matrix prior may be restrictive in representing domain knowledge. For example,
the LKJ is a useful prior distribution for correlation matrices, but it can be regularising. The geometry of correlation matrices is reviewed, and it is shown how to encourage certain properties
such as sparsity, in distributions over this space.
Date of Award19 Mar 2024
Original languageEnglish
Awarding Institution
  • The University of Bristol
SupervisorConor Houghton (Supervisor), Cian O'Donnell (Supervisor) & Clea Warburton (Supervisor)

Keywords

  • Bayesian modelling
  • Neuroscience
  • Applied statistics
  • Hierarchical modelling

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