Biased Online Parameter Inference for State-Space Models

TL;DR

This paper introduces a modified SMC2 algorithm for Bayesian online static parameter estimation in state-space models that maintains constant computational cost over time, with theoretical analysis of bias and empirical validation.

Contribution

It presents a computationally efficient version of SMC2 with fixed cost over time and analyzes its bias properties under certain assumptions.

Findings

The algorithm has constant computational cost over time.

Bias does not accumulate as the time parameter increases.

Empirical results validate the algorithm on Bayesian models.

Abstract

We consider Bayesian online static parameter estimation for state-space models. This is a very important problem, but is very computationally challenging as the state- of-the art methods that are exact, often have a computational cost that grows with the time parameter; perhaps the most successful algorithm is that of SMC2 [9]. We present a version of the SMC2 algorithm which has computational cost that does not grow with the time parameter. In addition, under assumptions, the algorithm is shown to provide consistent estimates of expectations w.r.t. the posterior. However, the cost to achieve this consistency can be exponential in the dimension of the parameter space; if this exponential cost is avoided, typically the algorithm is biased. The bias is investigated from a theoretical perspective and, under assumptions, we find that the bias does not accumulate as the time parameter grows. The algorithm is implemented on several Bayesian statistical models.