This paper demonstrates the advantages of sharing information about unknown features of covariates across multiple model components in various nonparametric regression problems including multivariate, heteroscedastic, and semi-continuous responses. In this paper, we present methodology which allows for information to be shared nonparametrically across various model components using Bayesian sum-of-tree models. Our simulation results demonstrate that sharing of information across related model components is often very beneficial, particularly in sparse high-dimensional problems in which variable selection must be conducted. We illustrate our methodology by analyzing medical expenditure data from the Medical Expenditure Panel Survey (MEPS). To facilitate the Bayesian nonparametric regression analysis, we develop two novel models for analyzing the MEPS data using Bayesian additive regression trees - a heteroskedastic log-normal hurdle model with a "shrink-towards-homoskedasticity" prior, and a gamma hurdle model. This article is protected by copyright. All rights reserved.

中文翻译：

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使用共享贝叶斯森林的半参数混合尺度模型

本文展示了在各种非参数回归问题（包括多变量、异方差和半连续响应）中跨多个模型组件共享有关协变量未知特征的信息的优势。在本文中，我们提出了一种方法，该方法允许使用贝叶斯树和树模型在各种模型组件之间以非参数方式共享信息。我们的模拟结果表明，在相关模型组件之间共享信息通常非常有益，尤其是在必须进行变量选择的稀疏高维问题中。我们通过分析医疗支出小组调查 (MEPS) 中的医疗支出数据来说明我们的方法。为了便于贝叶斯非参数回归分析，我们开发了两种使用贝叶斯加性回归树分析 MEPS 数据的新模型 - 一个具有“向同方差收缩”先验的异方差对数正态障碍模型和一个伽玛障碍模型。本文受版权保护。版权所有。