CREST：スクール（Prof. Omiros Papaspiliopoulos）

Part Ia: brief introduction to SDEs
(Ito lemma, linear SDEs, generator)

Part Ib: Statistical inference for SDEs
(observation schemes, probabilistic inference, approaches in the literature)

Part II: Statistical inference for the fully observed case
(quadratic variation, Girsanov's theorem for likelihood inference)

Part I and II would be covered in at most 2 hours.Part II is essential for what follows

Part III: discrete-time dynamics of diffusions and discrete-time likelihood
(discretization schemes, local linearization, pseudo-likelihood, exact simulation of diffusions)

Part III should be about 1.5 hour.

Part IV: Monte Carlo inference for discretely observed diffusions with known diffusivity
(missing data and a formal data augmentation, data augmentation for diffusions, simulation of diffusion bridges, MCMC for parameter estimation)

Part IV should be about 1.5 hour.

Part V: MCMC for general reducible diffusions
(Lamperti transformation and reducible diffusions, lack of convergence of basic MCMC algorithms, transformations of diffusion paths and efficient MCMC)

Part V should be about 1 hour.

Part VI: MCMC for irreducible partially observed multivariate diffusions
(Durham and Gallant approach, general diffusion bridges, path transformations, unobserved components)
Part VI should be about an 1 hour.

□2010.6.23 - 7.7,16:20-18:30開催

Monte Carlo Likelihood-based Inference for Diffusions (モンテ・カルロによる尤度に基づいた拡散過程の推測)

講演者：Prof. Dr. Omiros PAPASPILIOPOULOS, Asst. Professor in the Dept. of Economics and Business and Ramon y Cajal Research Fellow at the Universitat Pompeu Fabra