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Activity Number: 396 - Savage Awards Session
Type: Topic Contributed
Date/Time: Tuesday, July 30, 2019 : 2:00 PM to 3:50 PM
Sponsor: International Society for Bayesian Analysis (ISBA)
Abstract #302961 Presentation
Title: Geometric Bayes
Author(s): Andrew Holbrook*
Companies: UCLA Department of Human Genetics
Keywords: Differential geometry; Geodesic Monte Carlo; Spectral inference; Time series; Dimension reduction; Neural decoding

I provide a very brief synopsis of my investigations into the intersections between differential geometry and Bayesian analysis. My thesis combines these two disciplines with the hope that a synergy might emerge and facilitate the useful application of Bayesian inference to real-world science. In particular, dynamic and high-dimensional neural data provides a challenging litmus test for the proposed methods.

A major component of my work is the development and application of probabilistic models defined over smooth manifolds: dependencies between time series are modeled using the manifold of Hermitian positive definite matrices; probability density functions are modeled using the infinite sphere; and high-dimensional data are modeled using the Stiefel manifold. Whereas formulating a manifold-based model is not difficult—in a certain sense, the geometry occurs a priori in each of the cases considered—the non-trivial geometry presents computational challenges for model-based inference. Hence, my dissertation contributes two new algorithms for Bayesian inference on Riemannian manifolds. In turn, these algorithms power Bayesian neural decoding and spectral inference.

Authors who are presenting talks have a * after their name.

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