大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

Computational statistics for stochastic differential equations - diffusion bridge methods

Michael Sørensen (University of Copenhagen)

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4. Computational statistics for stochastic differential equations - diffusion bridge methods

大阪大学 数理・データ科学セミナー データ科学セミナーシリーズ 第50回

Computational statistics for stochastic differential equations - diffusion bridge methods

Michael Sørensen (University of Copenhagen)

Statistical inference for discrete time data from a stochastic differential equation model is considered with focus on diffusion bridge methods. The likelihood function is only very rarely explicitly known, but likelihood as well Bayesian inference can be performed by means of computational methods based on simulation of diffusion bridges. First it will be explained, how inference for discretely observed diffusion models is possible by using diffusion bridge simulation within the EM-algorithm or the Gibbs sampler. Then we present two methods for diffusion bridge simulation, the retrospective method proposed by Beskos, Papaspiliopoulos and Roberts and the simple method proposed by Bladt, Finch and Sørensen. We consider applications to discrete time observations of diffusions and integrated diffusion as well as diffusion models with random effects. Finally we present a new simulation methods, called the confluent diffusion method, proposed by Mider, Jenkins, Pollock, Roberts and Sørensen. The new method combines the retrospective and the simple method.

本発表はJST CREST JPMJCR14D7によってサポートされています．