Statistics and Computational Methods Seminar Series - 2024/25

Speaker: Augusto Fasano (University of Torino)

Title: Filtering procedures for dynamic multinomial probit models

Abstract

The multinomial probit constitutes a widely-used model for categorical data in many applications, especially in the econometrics and discrete-choice literature. The computational challenges encountered when fitting this model still motivate ongoing research both from the frequentist and Bayesian viewpoints. In this contribution, we consider a dynamic formulation based on a state-space model where at each time one observes a sample from a multinomial probit with time-specific parameter value. Dependence across time is then induced by the Markovian dynamics of the latent parameter. We show that the filtering and predictive distribution of the latent parameter belong to the unified skew-normal family, developing an associated i.i.d. sampler to approximate quantities of interest via Monte Carlo. Motivated by the computational bottlenecks of the sampler encountered already for moderate sample sizes, we also develop approximate methods for online inference based on assumed density filtering and expectation propagation. This gives more scalable, yet accurate, algorithms for online inference about the latent state and prediction of future observations. Results are shown over simulated data and a real dataset regarding reservations made from a list of results from an online booking platform.