Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
121 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Bayesian Parameter Inference for Partially Observed Stopped Processes (1201.3767v1)

Published 18 Jan 2012 in stat.CO and stat.ME

Abstract: In this article we consider Bayesian parameter inference associated to partially-observed stochastic processes that start from a set B0 and are stopped or killed at the first hitting time of a known set A. Such processes occur naturally within the context of a wide variety of applications. The associated posterior distributions are highly complex and posterior parameter inference requires the use of advanced Markov chain Monte Carlo (MCMC) techniques. Our approach uses a recently introduced simulation methodology, particle Markov chain Monte Carlo (PMCMC) (Andrieu et. al. 2010 [1]), where sequential Monte Carlo (SMC) approximations (see Doucet et. al. 2001 [18] and Liu 2001 [27]) are embedded within MCMC. However, when the parameter of interest is fixed, standard SMC algorithms are not always appropriate for many stopped processes. In Chen et. al. [11] and Del Moral 2004 [15] the authors introduce SMC approximations of multi-level Feynman-Kac formulae, which can lead to more efficient algorithms. This is achieved by devising a sequence of nested sets from B0 to A and then perform the resampling step only when the samples of the process reach intermediate level sets in the sequence. Naturally, the choice of the intermediate level sets is critical to the performance of such a scheme. In this paper, we demonstrate that multi-level SMC algorithms can be used as a proposal in PMCMC. In addition, we propose a flexible strategy that adapts the level sets for different parameter proposals. Our methodology is illustrated on the coalescent model with migration.

Citations (20)

Summary

We haven't generated a summary for this paper yet.