Sequential Monte Carlo approach to inference in Bayesian choice models

Monte Carlo methods, such as Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC), have extensive use cases in probabilistic modeling and inference. They usually appear as a way of drawing samples from a distribution of interest, because even for a relatively small model, the target distribution may easily go out of the domain of standard probability distributions, rendering the analytical tools to be almost useless. Sampling methods have been used effectively in such cases. In this thesis, we will be dealing with a probabilistic model that captures the interaction between a recommender system and its users and define a posterior distribution over the user's preferences. The model itself is actually very similar to a Dirichlet-Multinomial model, but it has completely different analytical properties. Although it is not the main purpose of this thesis, this fact also serves as a demonstration of how a slight change in a model may result in a problem which requires drastic changes in the methods of approach. We propose a Sequential Monte Carlo scheme, based on the resample-move algorithm with a Metropolis-within-Gibbs style move kernel, that targets the posterior distribution over the user's preferences. We also provide Stan implementations that target the same posterior distribution and use it for validation purposes. Then we investigate a recommender-user interaction mechanism based on the idea of Thompson sampling by simulating interactions.