A Particle Filter Method of Inference for Stochastic Differential Equations
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Date
2022-05-31
Authors
Subramani, Pranav
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
Stochastic Differential Equations (SDE) serve as an extremely useful modelling tool
in areas including ecology, finance, population dynamics, and physics. Yet, parameter
inference for SDEs is notoriously difficult due to the intractability of the likelihood function.
A common approach is to approximate the likelihood by way of data augmentation, then
integrate over the latent variables using particle filtering techniques. In the Bayesian
setting, the particle filter is typically combined with various Markov chain Monte Carlo
(MCMC) techniques to sample from the parameter posterior. However, MCMC can be
excessive when this posterior is well-approximated by a normal distribution, in which case
estimating the posterior mean and variance by stochastic optimization presents a much
faster alternative. This thesis explores this latter approach. Specifically, we use a particle
filter tailored to SDE models and consider various methods for approximating the gradient
and hessian of the parameter log-posterior. Empirical results for several SDE models are
presented.
Description
Keywords
Particle Filters, Stochastic Optimization, Stochastic Differential Equations, Bayesian Inference