Sequential Monte Carlo for Applications in Structural Biology, Financial Time Series and Epidemiology

Abstract

Sequential Monte Carlo (SMC) methods are widely used to draw samples from intractable target distributions. Moreover, they have also been adopted to other computational methods for inference such as the particle Markov chain Monte Carlo methods and the SMC$^2$ methods. In practice, some difficulties arise and are hindering the use of SMC-based methods; examples are the degeneracy of the particles in SMC and the intractability of the target distribution. This thesis addresses these challenges across various domains and proposes effective solutions.

This thesis introduces SMC and SMC-based methods with specific challenges in three diverse fields. Firstly, we propose an SMC method for sampling protein structures from the Boltzmann distribution which is highly constrained, crucial for studying the Boltzmann distribution of protein structures and estimating atomic contacts in viral proteins such as SARS-CoV-2. Secondly, we present a particle Gibbs sampler incorporating the approximate Bayesian computation strategy for stochastic volatility models with intractable likelihoods, offering a solution for parameter inference in financial data analysis by fitting stochastic volatility models to S\&P 500 Index time-series data during the 2008 financial crisis. Finally, we introduce a compartmental model with stochastic transmission dynamics and covariates, facilitating better alignment with real-world data for modeling the spread of COVID-19 in Ontario, for which we employ an SMC$^2$ algorithm incorporating the approximate Bayesian computation strategy.