Bayesian Computation: From Posterior Densities to Bayes Factors, Marginal Likelihoods, and Posterior Model Probabilities

Chen, Ming‐Hui

doi:10.1016/s0169-7161(05)25015-0

Cited by 6 publications

(2 citation statements)

References 17 publications

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“…However, direct implementation of Bayesian filtering (3)-( 4) is computationally expensive. Practical implementation of these algorithms, in their most general form, is achieved using particle filtering (Pearl 1988, Arulampalam et al 2002 and Bayesian programming (Lebeltel et al 2004, Chen 2005.…”

Section: Bayesian Filtering Algorithmmentioning

confidence: 99%

Distributed Bayesian filtering using logarithmic opinion pool for dynamic sensor networks

Bandyopadhyay

Chung

2018

Automatica

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The discrete-time Distributed Bayesian Filtering (DBF) algorithm is presented for the problem of tracking a target dynamic model using a time-varying network of heterogeneous sensing agents. In the DBF algorithm, the sensing agents combine their normalized likelihood functions in a distributed manner using the logarithmic opinion pool and the dynamic average consensus algorithm. We show that each agent's estimated likelihood function globally exponentially converges to an error ball centered on the joint likelihood function of the centralized multi-sensor Bayesian filtering algorithm. We rigorously characterize the convergence, stability, and robustness properties of the DBF algorithm. Moreover, we provide an explicit bound on the time step size of the DBF algorithm that depends on the time-scale of the target dynamics, the desired convergence error bound, and the modeling and communication error bounds. Furthermore, the DBF algorithm for linear-Gaussian models is cast into a modified form of the Kalman information filter. The performance and robust properties of the DBF algorithm are validated using numerical simulations.

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Section: Bayesian Filtering Algorithmmentioning

confidence: 99%

Distributed Bayesian filtering using logarithmic opinion pool for dynamic sensor networks

Bandyopadhyay

Chung

2018

Automatica

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“…Advances in computational capability have facilitated the implementation of Bayesian filters for robotic localization and mapping [29]- [32] as well as planning and control [33]- [35]. Practical implementation of these algorithms, in their most general form, is achieved using particle filtering [26], [36] and Bayesian programming [37], [38]. This paper focuses on developing a consensus framework for distributed Bayesian filters.…”

Section: Introductionmentioning

confidence: 99%

Distributed estimation using Bayesian consensus filtering

Bandyopadhyay

Chung

2014

2014 American Control Conference

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Abstract-We present the Bayesian consensus filter (BCF) for tracking a moving target using a networked group of sensing agents and achieving consensus on the best estimate of the probability distributions of the target's states. Our BCF framework can incorporate nonlinear target dynamic models, heterogeneous nonlinear measurement models, non-Gaussian uncertainties, and higher-order moments of the locally estimated posterior probability distribution of the target's states obtained using Bayesian filters. If the agents combine their estimated posterior probability distributions using a logarithmic opinion pool, then the sum of Kullback-Leibler divergences between the consensual probability distribution and the local posterior probability distributions is minimized. Rigorous stability and convergence results for the proposed BCF algorithm with single or multiple consensus loops are presented. Communication of probability distributions and computational methods for implementing the BCF algorithm are discussed along with a numerical example.

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Integrated likelihood computation methods

Zhao

Severini

2016

Comput Stat

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Bayesian Computation: From Posterior Densities to Bayes Factors, Marginal Likelihoods, and Posterior Model Probabilities

Cited by 6 publications

References 17 publications

Distributed Bayesian filtering using logarithmic opinion pool for dynamic sensor networks

Distributed Bayesian filtering using logarithmic opinion pool for dynamic sensor networks

Distributed estimation using Bayesian consensus filtering

Integrated likelihood computation methods

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