2011/02/27 by Giorgos Sermaidis, Sermaidis, Giorgos, Omiros Papaspiliopoulos +7 · 1 citation
Decision Sciences · Mathematics · #FOS: Computer and information sciences #Markov Chains and Monte Carlo Methods #Methodology (stat.ME) #Probabilistic and Robust Engineering Design #Statistical Methods and Inference #stat.ME
paper · pdf · doi:10.48550/arxiv.1102.5541
23 pages, 6 Figures, 3 Tables
openalex publication_date 2011/02/27 · arxiv created 2012/05/03 · arxiv updated 2012/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop exact Markov chain Monte Carlo methods for discretely-sampled, directly and indirectly observed diffusions. The qualification "exact" refers to the fact that the invariant and limiting distribution of the Markov chains is the posterior distribution of the parameters free of any discretisation error. The class of processes to which our methods directly apply are those which can be simulated using the most general to date exact simulation algorithm. The article introduces various methods to boost the performance of the basic scheme, including reparametrisations and auxiliary Poisson sampling. We contrast both theoretically and empirically how this new approach compares to irreducible high frequency imputation, which is the state-of-the-art alternative for the class of processes we consider, and we uncover intriguing connections. All methods discussed in the article are tested on typical examples.