Generalized Bayesian Filtering via Sequential Monte Carlo

Understand

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 $\beta$-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.