Exact Bayesian inference for Markov switching diffusions

• 成果类型: Article; Early Access
• 署名作者: Stumpf-Fetizon, Timothee; Latuszynski, Krzysztof; Palczewski, Jan; Roberts, Gareth
• 署名单位: Bocconi University; University of Warwick; Wroclaw University of Science & Technology
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412; 1467-9868
• DOI: 10.1093/jrsssb/qkag115
• 发表日期: 2026-07-22
• 关键词: Bernoulli MCMC; Intractable Likelihood; Markov Chain Monte Carlo; regime switching; Time Series; MONTE-CARLO METHODS; simulation; MODEL; CONVERGENCE; hastings

摘要

We develop the first exact Bayesian methodology for the problem of inference in discretely observed regime switching diffusions. 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 address the problem through 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. 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.