# Bayesian Inference for the Multinomial Probit Model under Gaussian Prior Distribution

arXiv: https://arxiv.org/abs/2206.00720 · HTML: https://mlsanity.com/paper/2206.00720/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 11 references that are in the map.
- First posted on arXiv 1 Jun 2022.

## Builds on (most cited first, 6 of 6)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Conjugate Bayes for probit regression via unified skew-normal distributions](https://mlsanity.com/paper/1802.09565/) (2018)
- [Scalable and Accurate Variational Bayes for High-Dimensional Binary Regression Models](https://mlsanity.com/paper/1911.06743/) (2019)
- [A closed-form filter for binary time series](https://mlsanity.com/paper/1902.06994/) (2019)
- [A Class of Conjugate Priors for Multinomial Probit Models which Includes the Multivariate Normal One](https://mlsanity.com/paper/2007.06944/) (2020)
- [Variational Inference for the Smoothing Distribution in Dynamic Probit Models](https://mlsanity.com/paper/2104.07537/) (2021)

## Built on by (most cited first, 1 of 1)

- [Efficient expectation propagation for posterior approximation in high-dimensional probit models](https://mlsanity.com/paper/2309.01619/) (2023)

## Abstract (arXiv)

Multinomial probit (mnp) models are fundamental and widely-applied regression models for categorical data. Fasano and Durante (2022) proved that the class of unified skew-normal distributions is conjugate to several mnp sampling models. This allows to develop Monte Carlo samplers and accurate variational methods to perform Bayesian inference. In this paper, we adapt the abovementioned results for a popular special case: the discrete-choice mnp model under zero mean and independent Gaussian priors. This allows to obtain simplified expressions for the parameters of the posterior distribution and an alternative derivation for the variational algorithm that gives a novel understanding of the fundamental results in Fasano and Durante (2022) as well as computational advantages in our special settings.