Expectation propagation for the smoothing distribution in dynamic probit

TL;DR

This paper develops an efficient expectation propagation algorithm for the smoothing distribution in high-dimensional dynamic probit models, improving accuracy over existing methods in financial applications.

Contribution

It introduces a novel EP-based inference routine for the skew-normal smoothing distribution in dynamic probit models, enhancing computational efficiency and accuracy.

Findings

The EP algorithm outperforms existing approximations in accuracy.

Application to financial data demonstrates practical effectiveness.

The method scales better to higher dimensions.

Abstract

The smoothing distribution of dynamic probit models with Gaussian state dynamics was recently proved to belong to the unified skew-normal family. Although this is computationally tractable in small-to-moderate settings, it may become computationally impractical in higher dimensions. In this work, adapting a recent more general class of expectation propagation (EP) algorithms, we derive an efficient EP routine to perform inference for such a distribution. We show that the proposed approximation leads to accuracy gains over available approximate algorithms in a financial illustration.