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通过密度估计开展贝叶斯非参数函数型数据分析AI 解读

In many modern experimental settings, observations are obtained in the form of functions, and interest focuses on inferences on a collection of such functions. We propose a hierarchical model that allows us to simultaneously estimate multiple curves nonparametrically by using dependent Dirichlet Process mixtures of Gaussians to characterize the joint distribution of predictors and outcomes. Function estimates are then induced through the conditional distribution of the…

广义空间狄利克雷过程模型AI 解读

In many applications, spatial data are assumed to be point referenced, e.g., ob-served at geo-coded locations. Modelling for this kind of data usually introduces spatial structure in the form of spatial random effects where a term capturing residual spatial association is explicitly introduced. This pure spatial effect is customarily modelled as a mean-zero stationary Gaussian process (GP). The SDP introduced by Gelfand et al. (2005) produces a random spatial process which…

贝叶斯模型选择：渐近分析与精确计算AI 解读

SUMMARY Model determination is a fundamental data analytic task. Here we consider the problem of choosing among a finite (without loss of generality we assume two) set of models. After briefly reviewing classical and Bayesian model choice strategies we present a general predictive density which includes all proposed Bayesian approaches that we are aware of. Using Laplace approximations we can conveniently assess and compare the asymptotic behaviour of these approaches.…