标题： 对多项逻辑回归和计数回归模型的对数线性贝叶斯自适应回归树 显示英文标题

标题： Log-Linear Bayesian Additive Regression Trees for Multinomial Logistic and Count Regression Models

摘要： 我们介绍了贝叶斯加性回归树（BART）用于对数线性模型，包括多项逻辑回归和具有零膨胀和过离散的计数回归。 BART 已经被应用于各种设定下的非参数均值回归和二元分类问题。 然而，现有 BART 的应用仅限于高斯“数据”模型，无论是观测到的还是潜在的。 这主要是因为高斯似然函数有高效的马尔可夫链蒙特卡洛（MCMC）算法可用。 但是，尽管许多有用的模型自然可以用潜在高斯变量来表述，也有许多模型并非如此——包括本文讨论的模型。 我们为这些新模型开发了新的数据增强策略和仔细指定的先验分布。 与原始 BART 先验一样，新的先验分布经过精心构建和校准，以保持灵活性同时防止过拟合。 新先验和数据增强方案结合在一起，使我们能够在非高斯模型的背景下实现高效的 MCMC 抽样器。 这些新方法的有效性通过示例和对之前发表的数据集的应用进行了说明。 显示英文摘要

摘要： We introduce Bayesian additive regression trees (BART) for log-linear models including multinomial logistic regression and count regression with zero-inflation and overdispersion. BART has been applied to nonparametric mean regression and binary classification problems in a range of settings. However, existing applications of BART have been limited to models for Gaussian "data", either observed or latent. This is primarily because efficient MCMC algorithms are available for Gaussian likelihoods. But while many useful models are naturally cast in terms of latent Gaussian variables, many others are not -- including models considered in this paper. We develop new data augmentation strategies and carefully specified prior distributions for these new models. Like the original BART prior, the new prior distributions are carefully constructed and calibrated to be flexible while guarding against overfitting. Together the new priors and data augmentation schemes allow us to implement an efficient MCMC sampler outside the context of Gaussian models. The utility of these new methods is illustrated with examples and an application to a previously published dataset.