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Title: Bayesian inference for stable L\'{e}vy driven stochastic differential equations with high-frequency data Authors:  Kengo Kamatani - Osaka University (Japan) [presenting]
Ajay Jasra - National University of Singapore (Singapore)
Hiroki Masuda - Kyushu University (Japan)
Abstract: The focus is on parametric Bayesian inference for stochastic differential equations (SDE) driven by a pure-jump stable L\'{e}vy process, which is observed at high frequency. In most cases of practical interest, the likelihood function is not available, so we use a quasi-likelihood and place an associated prior to 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 (MCMC) algorithm for Bayesian inference and assisted by our theoretical results, we show how to scale Metropolis-Hastings proposals when the frequency of the data grows, in order to prevent the acceptance ratio going to zero in the large data limit. Our algorithm is presented on numerical examples that help to verify our theoretical findings.