Inference for a Class of Partially Observed Point Process Models

TL;DR

This paper develops a simulation-based Bayesian framework using sequential Monte Carlo methods for inference in complex, partially observed point process models, addressing challenges in filtering and smoothing.

Contribution

It introduces novel SMC-based approaches for sequential inference in partially observed point processes, with theoretical insights and practical applications in finance.

Findings

Effective SMC methods for filtering and smoothing in complex PP models

Successful application to a doubly stochastic point process in finance

Addresses limitations of existing methods in complex scenarios

Abstract

This paper presents a simulation-based framework for sequential inference from partially and discretely observed point process (PP's) models with static parameters. Taking on a Bayesian perspective for the static parameters, we build upon sequential Monte Carlo (SMC) methods, investigating the problems of performing sequential filtering and smoothing in complex examples, where current methods often fail. We consider various approaches for approximating posterior distributions using SMC. Our approaches, with some theoretical discussion are illustrated on a doubly stochastic point process applied in the context of finance.