Efficient predictive density estimation

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Prediction is at the heart of statistics and vital to many problems of science, engineering, medicine and health sciences, finance and economics, among other fields of study. A predictive density is a density estimate, based on past and current data that can be used as a surrogate density for future or missing observables. Prediction, and more precisely predictive densities, are central in statistical methodology and practice, and arise in linear regression models, non-parametric regression , generalized linear models, time series, stochastic processes; model selection, metrology, and data compression, and others. The main objectives and challenges of this proposal are methodological. They consist in making available and practicable efficient predictive densities for a wide array of situations. The proposed program of research will be concerned with deepening our understanding of statistical methods and foundations as related to the estimation of predictive densities. They will also be motivated by applications, namely by problems with many parameters or more complex structures. In particular, the proposed research is directed towards problems of selective inference or prediction, where methods should arguably take into account a selection mechanism (e.g., of models, of populations to study). Problems with additional information, which are related to restricted parameter space problems will also be investigated. There exists many situations where such prior additional information is available, and for which methods of inference ought to capitalize on such information.