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使用依赖 Bernstein 多项式的有界数据全非参数回归AI 解读

We propose a novel class of probability models for sets of predictor-dependent probability distributions with bounded domain. The proposal extends the Dirichlet–Bernstein prior for single density estimation, by using dependent stick-breaking processes. A general model class and two simplified versions are discussed in detail. Appealing theoretical properties such as continuity, association structure, marginal distribution, large support, and consistency of the posterior…

贝叶斯非参数纵向数据分析AI 解读

Fernando A. Quintanaa*, Wesley O. Johnsonb, L. Elaine Waetjenc & Ellen B. Goldca Departamento de Estadística, Pontificia Universidad Católica de Chile Santiago, Chileb Department of Statistics, University of California Irvine, Irvine, CA, USAc Department of Obstetrics and Gynecology, and Department of Public Health Sciences, Division of Epidemiology, University of California Davis, Davis, CA, USACONTACT Fernando A. Quintana quintana@mat.uc.cl Departamento de Estadística,…

贝叶斯聚类与乘积分割模型AI 解读

Summary We present a decision theoretic formulation of product partition models (PPMs) that allows a formal treatment of different decision problems such as estimation or hypothesis testing and clustering methods simultaneously. A key observation in our construction is the fact that PPMs can be formulated in the context of model selection. The underlying partition structure in these models is closely related to that arising in connection with Dirichlet processes. This allows…

固定行边际总数的 k×l 列联表同质性非参数贝叶斯分析AI 解读

In this work I postulate a nonparametric Bayesian model for data that can be accommodated in a contingency table with fixed right margin totals. This data structure usually arises when comparing different groups regarding classification probabilities for a number of categories. I assume that cell count vectors for each group are conditionally independent, with multinomial distribution given vectors of classification probabilities. In turn, these vectors of probabilities are…

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部分可交换二元数据的依赖阶数评估AI 解读

The problem we consider is how to assess the order of serial dependence within partially exchangeable binary sequences. We obtain exact conditional tests comparing any two orders by finding the conditional distribution of data given certain transition counts. These tests are facilitated with a new Monte Carlo scheme. Asymptotic tests are also discussed. In particular, we show that the likelihood ratio tests have an asymptotic chi-squared distribution, thus generalizing the…