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基于随机生成树的非平稳软分区高斯过程模型AI 解读

There has been a long-standing challenge in developing locally stationary Gaussian process models concerning how to obtain flexible partitions and make predictions near boundaries. In this work, we develop a new class of locally stationary stochastic processes, where local partitions are modeled by a soft partition process via predictive random spanning trees that leads to highly flexible spatially contiguous subregion shapes. This valid nonstationary process model knits…

偏微分方程模型的参数估计AI 解读

Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown, and need to be estimated from the measurements of the dynamic system in the present of…

结果依赖型随访的纵向研究AI 解读

We propose Bayesian parametric and semiparametric partially linear regression methods to analyze the outcome-dependent follow-up data when the random time of a follow-up measurement of an individual depends on the history of both observed longitudinal outcomes and previous measurement times. We begin with the investigation of the simplifying assumptions of Lipsitz, Fitzmaurice, Ibrahim, Gelber, and Lipshultz, and present a new model for analyzing such data by allowing…

基于贝叶斯小波方法的函数型数据聚类AI 解读

Summary We propose a nonparametric Bayes wavelet model for clustering of functional data. The wavelet-based methodology is aimed at the resolution of generic global and local features during clustering and is suitable for clustering high dimensional data. Based on the Dirichlet process, the nonparametric Bayes model extends the scope of traditional Bayes wavelet methods to functional clustering and allows the elicitation of prior belief about the regularity of the functions…