Nonparametric Binary Regression: A Bayesian Approach

The performance of Bayes estimates are studied, under an assumption of conditional exchangeability. More exactly, for each subject in a data set, let $\xi$ be a vector of binary covariates and let $\eta$ be a binary response variable, with $P\{\eta = 1\mid \xi\} = f(\xi)$ . Here, $f$ is an unknown function to be estimated from the data; the subjects are independent, and satisfy a natural "balance" condition. Define a prior distribution on $f$ as $\sum_kw_k\pi_k/\sum_kw_k$ , where $\pi_k$ is uniform on the set of $f$ which only depend on the first $k$ covariates and $w_k > 0$ for infinitely many $k$ . Bayes estimates are consistent at all $f$ if $w_k$ decreases rapidly as $k$ increase. Otherwise, the estimates are inconsistent at $f \equiv 1/2$ .The performance of Bayes estimates are studied, under an assumption of conditional exchangeability. More exactly, for each subject in a data set, let $\xi$ be a vector of binary covariates and let $\eta$ be a binary response variable, with $P\{\eta = 1\mid \xi\} = f(\xi)$. Here, $f$ is an unknown function to be estimated from the data; the subjects are independent, and satisfy a natural "balance" condition. Define a prior distribution on $f$ as $\sum_kw_k\pi_k/\sum_kw_k$, where $\pi_k$ is uniform on the set of $f$ which only depend on the first $k$ covariates and $w_k > 0$ for infinitely many $k$. Bayes estimates are consistent at all $f$ if $w_k$ decreases rapidly as $k$ increase. Otherwise, the estimates are inconsistent at $f \equiv 1/2$.

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笔记与分组

分类依据与纠错

Nonparametric Binary Regression: A Bayesian Approach

代码、数据与补充材料

非参数二元回归：贝叶斯方法

原文摘要

同方向的基础文献

同方向的基础文献