Variational Inference for the Smoothing Distribution in Dynamic Probit Models

TL;DR

This paper extends variational Bayes methods to dynamic probit models, providing efficient approximation techniques for smoothing distributions and demonstrating their application in finance.

Contribution

It introduces a variational Bayes approach for the smoothing distribution in univariate dynamic probit models, building on previous skew-normal based filtering methods.

Findings

Effective variational approximation for dynamic probit smoothing

Application to financial data demonstrates practical utility

Improved computational efficiency over traditional methods

Abstract

Recently, Fasano, Rebaudo, Durante and Petrone (2019) provided closed-form expressions for the filtering, predictive and smoothing distributions of multivariate dynamic probit models, leveraging on unified skew-normal distribution properties. This allows to develop algorithms to draw independent and identically distributed samples from such distributions, as well as sequential Monte Carlo procedures for the filtering and predictive distributions, allowing to overcome computational bottlenecks that may arise for large sample sizes. In this paper, we briefly review the above-mentioned closed-form expressions, mainly focusing on the smoothing distribution of the univariate dynamic probit. We develop a variational Bayes approach, extending the partially factorized mean-field variational approximation introduced by Fasano, Durante and Zanella (2019) for the static binary probit model to the dynamic setting. Results are shown for a financial application.