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。

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.