Sequential Monte Carlo

Stochastic Volatility (SV) models are a popular class of models to analyze the dependency structure between stocks and their volatility. In this paper, we develop a new class of SV models by incorporating carefully selected copula structures to reconstruct stylised empirical behaviours that cannot be captured by symmetric Gaussian innovations.

In this paper, we propose an epidemic model with the transmission rate between susceptible and infected individuals, β, being time varying and piecewise constant. At any point in time, β is linked to a latent variable that follows a Hidden Semi-Markov Model (HSMM). This HSMM-driven epidemic Model (HSMM-EM) structures the data into multiple regimes, which greatly enhances decision-making capabilities, while the limited number of continuous model parameter guarantees straightforward model interpretation.

In this paper, we explore the class of the Hidden Semi-Markov Model (HSMM), a flexible extension of the popular Hidden Markov Model (HMM) that allows the underlying stochastic process to be a semi-Markov chain. A major motivation of this paper is to provide methods to estimate HSMMs (1) in a computationally feasible time, (2) in an exact manner, i.e. only subject to Monte Carlo error, and (3) in a sequential setting.

My doctoral research evolves around the topic of Sequential Bayesian Learning for State Space Models. More generally, I am working on estimating model parameters in a batch as well as in a times series setting, with a focus on latent variable models. This thesis includes projects with Hidden Semi-Markov Models, Copulae, and Epidemic Models that have latent factors attached.