Bayesian Parameter Identification for Jump Markov Linear Systems

2020/04/18 by Mark P. Balenzuela, Adrian G. Wills, Balenzuela, Mark P. +6
Computer Science · Engineering · Mathematics · #Algorithm #Applications (stat.AP) #Applied mathematics #Artificial intelligence #Bayesian Methods and Mixture Models #Bayesian probability #Blind Source Separation Techniques #Computer science #Conjugate prior #FOS: Computer and information sciences #FOS: Electrical engineering #Filter (signal processing) #Gibbs sampling #Identification (biology) #Jump #Kalman filter #Markov chain #Mathematical optimization #Mathematics #Methodology (stat.ME) #Particle filter #Physics #Posterior probability #Prior probability #Sampling (signal processing) #Statistics #Systems and Control (eess.SY) #Target Tracking and Data Fusion in Sensor Networks #cs.SY #eess.SY #electronic engineering #information engineering #stat.AP #stat.ME

paper · pdf · doi:10.48550/arxiv.2004.08565

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2020/04/18 · arxiv created 2021/02/10 · arxiv updated 2021/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

This paper presents a Bayesian method for identification of jump Markov linear system parameters. A primary motivation is to provide accurate quantification of parameter uncertainty without relying on asymptotic in data-length arguments. To achieve this, the paper details a particle-Gibbs sampling approach that provides samples from the desired posterior distribution. These samples are produced by utilising a modified discrete particle filter and carefully chosen conjugate priors.

Citations

• Interacting multiple model methods in target tracking: a survey
• The interacting multiple model algorithm for systems with Markovian switching coefficients
• On Gibbs sampling for state space models
• Monte Carlo sampling methods using Markov chains and their applications

Related

• Efficient parameter sampling for Markov jump processes
• Bayesian inference for Markov jump processes with informative observations
• Recursive maximum likelihood identification of jump Markov nonlinear systems
• Particle Gibbs algorithms for Markov jump processes
• Exact Bayesian inference for discretely observed Markov Jump Processes using finite rate matrices