Fast Estimation of Bayesian State Space Models Using Amortized Simulation-Based Inference

TL;DR

This paper introduces a rapid amortized simulation-based inference algorithm for Bayesian state space models, enabling quick estimation of hidden states with high accuracy after initial training.

Contribution

It proposes a novel training approach focusing on specific posterior characteristics, significantly speeding up state estimation in complex models.

Findings

Pretraining takes several hours, but posterior inference for new data is very fast.

The method achieves sufficient accuracy in stochastic volatility, DSGE, and seasonal models.

It outperforms traditional methods in speed while maintaining accuracy.

Abstract

This paper presents a fast algorithm for estimating hidden states of Bayesian state space models. The algorithm is a variation of amortized simulation-based inference algorithms, where a large number of artificial datasets are generated at the first stage, and then a flexible model is trained to predict the variables of interest. In contrast to those proposed earlier, the procedure described in this paper makes it possible to train estimators for hidden states by concentrating only on certain characteristics of the marginal posterior distributions and introducing inductive bias. Illustrations using the examples of the stochastic volatility model, nonlinear dynamic stochastic general equilibrium model, and seasonal adjustment procedure with breaks in seasonality show that the algorithm has sufficient accuracy for practical use. Moreover, after pretraining, which takes several hours, finding the posterior distribution for any dataset takes from hundredths to tenths of a second.