Notícias
Minicurso no PPG em Estatística – Prof. Flavio Bambirra Gonçalves (UFMG)
Data: 11, 12 e 13 de novembro
Local: CT da UFRJ – Campus do Fundão. O local exato será confirmado oportunamente.
Horário: a ser confirmado oportunamente
Palestrante: Flavio Bambirra Gonçalves (UFMG)
Title: Stochastic simulation and statistical inference for intractable likelihood problems
Abstract: The complexity of important real-world problems has motivated the proposal of increasingly elaborate statistical models, including models with intractable likelihood functions — that is, likelihoods that cannot be written in closed form or evaluated exactly at finite computational cost. Intractability of this kind is particularly common in infinite-dimensional problems, in which the (augmented) sample space, the parameter space, or both have that feature. The considerable advances in computational power and in stochastic simulation methods over the past decades have permitted the development of statistical methodologies that do not require numerical and/or finite-dimensional approximations to handle intractable likelihood problems. Such methodologies are termed "exact", as the only error they incur is Monte Carlo error, which is controlled by the simulation effort and vanishes as that effort grows. The course is divided into four parts. The first discusses the main stochastic simulation techniques commonly employed in exact inference methodologies: retrospective sampling, simulation of events of unknown probability, and general Monte Carlo methods such as importance sampling, rejection sampling and MCMC. The second part introduces a general formulation of statistical inference problems, including the definitions of statistical model, likelihood-based inference and probabilistic inference. The third part shows how the techniques from the first part are used to build exact inference methodologies for intractable likelihood problems, presenting general MCMC algorithms such as the pseudo-marginal and (divide-and-conquer) Barker's schemes. The fourth and final part treats specific intractable likelihood problems arising in models based on stochastic differential equations and Gaussian processes.