# Variational Inference for the Smoothing Distribution in Dynamic Probit Models

arXiv: https://arxiv.org/abs/2104.07537 · HTML: https://mlsanity.com/paper/2104.07537/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Apr 2021.

## Built on by (most cited first, 3 of 3)

- [Bayesian Inference for the Multinomial Probit Model under Gaussian Prior Distribution](https://mlsanity.com/paper/2206.00720/) (2022)
- [Efficient expectation propagation for posterior approximation in high-dimensional probit models](https://mlsanity.com/paper/2309.01619/) (2023)
- [Expectation propagation for the smoothing distribution in dynamic probit](https://mlsanity.com/paper/2309.01641/) (2023)

## Abstract (arXiv)

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.