Generative Bayesian Filtering and Parameter Learning

TL;DR

This paper introduces Generative Bayesian Filtering (GBF), a flexible, simulation-based inference framework for complex nonlinear, non-Gaussian models that does not require explicit density evaluation, and demonstrates its effectiveness in hierarchical and intractable models.

Contribution

It extends Generative Bayesian Computation to dynamic models and introduces the Generative-Gibbs sampler for parameter learning without explicit density calculations.

Findings

GBF outperforms existing likelihood-free methods in accuracy.

GBF is effective in hierarchical models with intractable densities.

Empirical studies include estimation of $eta$-stable stochastic volatility models.

Abstract

Generative Bayesian Filtering (GBF) provides a powerful and flexible framework for performing posterior inference in complex nonlinear and non-Gaussian state-space models. Our approach extends Generative Bayesian Computation (GBC) to dynamic settings, enabling recursive posterior inference using simulation-based methods powered by deep neural networks. GBF does not require explicit density evaluations, making it particularly effective when observation or transition distributions are analytically intractable. To address parameter learning, we introduce the Generative-Gibbs sampler, which bypasses explicit density evaluation by iteratively sampling each variable from its implicit full conditional distribution. Such technique is broadly applicable and enables inference in hierarchical Bayesian models with intractable densities, including state-space models. We assess the performance of the proposed methodologies through both simulated and empirical studies, including the estimation of $\alpha$-stable stochastic volatility models. Our findings indicate that GBF significantly outperforms existing likelihood-free approaches in accuracy and robustness when dealing with intractable state-space models.