Efficient predictive density estimation

预测是统计学的核心，对科学、工程、医学和健康科学、金融和经济等研究领域的许多问题至关重要。预测密度是基于过去和当前数据的密度估计，可用作未来或丢失可观测对象的替代密度。预测，以及更精确的预测密度，在统计方法和实践中是核心的，并出现在线性回归模型、非参数回归、广义线性模型、时间序列、随机过程、模型选择、计量和数据压缩等中。这项提案的主要目标和挑战是方法论的。它们包括为广泛的情况提供可用的和实际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。它们也会受到应用的驱动，即受具有许多参数或更复杂结构的问题的驱动。特别是，拟议的研究针对的是选择性推理或预测的问题，其中的方法可以说应该考虑到一种选择机制(例如，对模型的选择，对要研究的人群的选择)。还将研究与受限参数空间问题有关的具有附加信息的问题。在许多情况下，可以获得这种先前的补充信息，对于这些情况，推理方法应当利用这种信息。

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.