Efficient predictive density estimation

预测是统计学的核心，对于科学、工程、医学和健康科学、金融和经济以及其他研究领域的许多问题都至关重要。预测密度是基于过去和当前数据的密度估计，可以用作未来或缺失可观测值的替代密度。预测，更准确地说是预测密度，是统计方法和实践的中心，在线性回归模型、非参数回归、广义线性模型、时间序列、随机过程中出现；模型选择，计量，数据压缩等。该提案的主要目标和挑战是方法论。它们包括为各种各样的情况提供可用和可行的有效预测密度。拟议的研究计划将涉及加深我们对与预测密度估计有关的统计方法和基础的理解。它们也会受到应用程序的激励，即具有许多参数或更复杂结构的问题。特别是，拟议的研究是针对选择性推断或预测的问题，其中的方法应该考虑到选择机制（例如，模型，要研究的人口）。与受限参数空间问题相关的附加信息问题也将被研究。在许多情况下，这些先验的附加信息是可用的，因此推理方法应该利用这些信息。

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.