Generalized Bayesian Filtering via Sequential Monte Carlo
This work addresses robust inference for practitioners in fields like object tracking and Gaussian process regression, though it is incremental as it adapts existing methods to a new theoretical setting.
The paper tackles inference in hidden Markov models under model misspecification by introducing a generalized Bayesian filtering framework using sequential Monte Carlo methods, and reports improved performance in object tracking and Gaussian process regression compared to standard and robust filters.
We introduce a framework for inference in general state-space hidden Markov models (HMMs) under likelihood misspecification. In particular, we leverage the loss-theoretic perspective of Generalized Bayesian Inference (GBI) to define generalised filtering recursions in HMMs, that can tackle the problem of inference under model misspecification. In doing so, we arrive at principled procedures for robust inference against observation contamination by utilising the $β$-divergence. Operationalising the proposed framework is made possible via sequential Monte Carlo methods (SMC), where most standard particle methods, and their associated convergence results, are readily adapted to the new setting. We apply our approach to object tracking and Gaussian process regression problems, and observe improved performance over both standard filtering algorithms and other robust filters.