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

Ajay Jasra, Kengo Kamatani, Hiroki Masuda

研究成果: ジャーナルへの寄稿記事

抄録

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.

元の言語英語
ページ(範囲)545-574
ページ数30
ジャーナルScandinavian Journal of Statistics
46
発行部数2
DOI
出版物ステータス出版済み - 6 1 2019

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High-frequency Data
Bayesian inference
Stochastic Equations
Differential equation
Metropolis-Hastings
Quasi-likelihood
Jump Process
Markov Chain Monte Carlo Algorithms
Stable Process
Large Data
Likelihood Function
Regularity Conditions
Unknown Parameters
Verify
Numerical Examples
Zero
Theorem
High-frequency data
Stochastic differential equations
Regularity

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

これを引用

Bayesian inference for stable Lévy–driven stochastic differential equations with high-frequency data. / Jasra, Ajay; Kamatani, Kengo; Masuda, Hiroki.

:: Scandinavian Journal of Statistics, 巻 46, 番号 2, 01.06.2019, p. 545-574.

研究成果: ジャーナルへの寄稿記事

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