Local consistency of Markov chain Monte Carlo methods

Kamatani, Kengo

doi:10.1007/s10463-013-0403-3

Cited by 10 publications

(34 citation statements)

References 36 publications

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“…Equation (8) becomes ‖ ‖̄N (· | x N ) − (· | s N ) ‖ ‖TV → 0 in P. By lemmas 2 and 3 in the work of Kamatani (2014), the following convergence is sufficient for local consistency:…”

Section: Appendix B Proof For the Local Consistency Of The Metropolismentioning

confidence: 99%

Bayesian inference for stable Lévy–driven stochastic differential equations with high‐frequency data

Jasra

Kamatani

Masuda

2018

Scandinavian J Statistics

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In this paper, we consider parametric Bayesian inference for stochastic differential equations driven by a pure‐jump stable Lévy process, which is observed at high frequency. In most cases of practical interest, the likelihood function is not available; hence, we use a quasi‐likelihood and place an associated prior on the unknown parameters. It is shown under regularity conditions that there is a Bernstein–von Mises theorem associated to the posterior. We then develop a Markov chain Monte Carlo algorithm for Bayesian inference, and assisted with theoretical results, we show how to scale Metropolis–Hastings proposals when the frequency of the data grows, in order to prevent the acceptance ratio from going to zero in the large data limit. Our algorithm is presented on numerical examples that help verify our theoretical findings.

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Section: Appendix B Proof For the Local Consistency Of The Metropolismentioning

confidence: 99%

Bayesian inference for stable Lévy–driven stochastic differential equations with high‐frequency data

Jasra

Kamatani

Masuda

2018

Scandinavian J Statistics

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“…See Kamatani [2014a]) when d is the sample size of the data. However this is not always the case as described in the last part of Kamatani [2014a]. In our case, (2.2) is not satisfied in two respects: the state space is not the same for d ∈ N, and M = M (d) should satisfy a certain rate.…”

Section: Consistency For High Dimensional Mcmcmentioning

confidence: 99%

Random walk Metropolis algorithm in high dimension with non-Gaussian target distributions

Kamatani

2020

Stochastic Processes and their Applications

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“…In this section, we review consistency of MCMC studied in Kamatani (2014a). Set a sequence of Markov (2014a)) when d is the sample size of the data.…”

Section: Consistencymentioning

confidence: 99%

Efficient strategy for the Markov chain Monte Carlo in high-dimension with heavy-tailed target probability distribution

Kamatani¹

2018

Bernoulli

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The purpose of this paper is to introduce a new Markov chain Monte Carlo method and exhibit its efficiency by simulation and high-dimensional asymptotic theory. Key fact is that our algorithm has a reversible proposal transition kernel, which is designed to have a heavy-tailed invariant probability distribution. The high-dimensional asymptotic theory is studied for a class of heavy-tailed target probability distribution. As the number of dimension of the state space goes to infinity, we will show that our algorithm has a much better convergence rate than that of the preconditioned Crank Nicolson (pCN) algorithm and the random-walk Metropolis (RWM) algorithm. We also show that our algorithm is at least as good as the pCN algorithm and better than the RWM algorithm for light-tailed target probability distribution.

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Local consistency of Markov chain Monte Carlo methods

Cited by 10 publications

References 36 publications

Bayesian inference for stable Lévy–driven stochastic differential equations with high‐frequency data

Bayesian inference for stable Lévy–driven stochastic differential equations with high‐frequency data

Random walk Metropolis algorithm in high dimension with non-Gaussian target distributions

Efficient strategy for the Markov chain Monte Carlo in high-dimension with heavy-tailed target probability distribution

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