Many statistical applications use models that incorporate latent variables. For example, random effect panel data models, use latent variables to account for dependence between observations. State space models whose latent variables follow a Markov process, are used in economics, finance, and engineering.
Inference about the model parameters in those latent variable models can be challenging because the likelihood is an integral over the latent variables. This integral is analytically intractable and can be computationally challenging to evaluate when the dimension of the latent variables is high.
The aim of this project is to develop flexible Bayesian approach for both random effect panel data and state space models, that is based on recent advances in Particle Markov chain Monte Carlo methods. The research will aim to apply the methods in a number of areas including health research, financial applications.