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

Variational Inference for the Smoothing Distribution in Dynamic Probit Models