Exact Bayesian inference for Markov switching diffusions

2025-02-13

AI Summary

This work addresses the challenge of Bayesian inference for Markov-switching diffusion processes under discrete-time observations. Existing approaches rely on time-discretization approximations, inducing systematic bias in parameter estimation—particularly at drift and volatility jumps—and risking model misspecification. We propose the first exact algorithm rigorously grounded in the continuous-time posterior distribution. Our method introduces a joint modeling framework that integrates a latent Markov jump process with continuous-time diffusion dynamics, and develops an exact sampling algorithm combining Markov chain Monte Carlo (MCMC) and Monte Carlo expectation–maximization (MCEM) to jointly infer diffusion parameters and latent state trajectories. Numerical experiments and empirical analysis demonstrate that our approach achieves substantially higher estimation accuracy and scalability than discretization-based methods, with comparable computational cost, while entirely eliminating discretization-induced bias.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Bayesian Learning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Content-based information diffusion
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

We give the first exact Bayesian methodology for the problem of inference in discretely observed regime switching diffusions. We design an MCMC and an MCEM algorithm that target the exact posterior of diffusion parameters and the latent regime process. The algorithms are exact in the sense that they target the correct posterior distribution of the continuous model, so that the errors are due to Monte Carlo only. Switching diffusion models extend ordinary diffusions by allowing for jumps in instantaneous drift and volatility. The jumps are driven by a latent, continuous time Markov switching process. We illustrate the method on numerical examples, including an empirical analysis of the method's scalability in the length of the time series, and find that it is comparable in computational cost with discrete approximations while avoiding their shortcomings.

Problem

• Exact Bayesian inference for Markov switching diffusions
• MCMC and MCEM algorithms targeting exact posterior distributions
• Avoiding approximation shortcomings in regime switching diffusion models

Innovation

• Exact Bayesian inference for Markov switching diffusions
• MCMC and MCEM algorithms target exact posterior
• Avoids discrete approximations' shortcomings with comparable cost