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加权抽样的贝叶斯方法AI 解读

Bayesian statistical inference for sampling from weighted distribution models is studied. Small-sample Bayesian bootstrap clone (BBC) approximations to the posterior distribution are discussed. A second-order property for the BBC in unweighted i.i.d. sampling is given. A consequence is that BBC approximations to a posterior distribution of the mean and to the sampling distribution of the sample average, can be made asymptotically accurate by a proper choice of the random…

删失数据的贝叶斯自助法AI 解读

A Bayesian bootstrap for a censored data model is introduced. Its small sample distributional properties are discussed and found to be similar to Efron's bootstrap for censored data. In the absence of censoring, the Bayesian bootstrap for censored data reduces to Rubin's Bayesian bootstrap for complete data. A first-order large-sample theory is developed. This theory shows that both censored data bootstraps are consistent bootstraps for approximating the sampling…

基于部分信息的一致且稳健的位置参数贝叶斯程序AI 解读

We consider Bayes procedures for a location parameter $\theta$ that are robust with respect to the shape of the distribution $F$ of the data. The case where $F$ is fixed (nonrandom) and the case where $F$ has a Dirichlet distribution are both treated. The procedures are based on the posterior distributions of the location parameter given the partial information contained in a robust estimate of location. We show consistency and asymptotic normality of the procedures and give…

对称单峰密度及其众数的贝叶斯方法AI 解读

Bayes solutions for i.i.d. sampling from a decreasing density on the half line and for i.i.d. sampling from a symmetric unimodal density with an unknown mode are given. Posterior quantities are obtained as finite sums; Monte Carlo methods based on sampling finite Markov chains are developed for their evaluation.

有限总体的贝叶斯自助法AI 解读

A Bayesian bootstrap for a finite population is introduced; its small-sample distributional properties are discussed and compared with those of the frequentist bootstrap for a finite population. It is also shown that the two are first-order asymptotically equivalent.

贝叶斯 bootstrap 的大样本研究AI 解读

An asymptotic justification of the Bayesian bootstrap is given. Large-sample Bayesian bootstrap probability intervals for the mean, the variance and bands for the distribution, the smoothed density and smoothed rate function are also provided.

有限总体抽样的贝叶斯统计推断AI 解读

Bayesian statistical inference for sampling a finite population is studied by using the Dirichlet-multinomial process as prior. It is shown that if the finite population variables have a Dirichlet-multinomial prior, then the posterior distribution of the inobserved variables given a sample is also Dirichlet-multinomial. If the population size tends to infinity (the sample size is fixed), sampling without replacement from a Dirichlet multinomial process is equivalent to the…

一类贝叶斯非参数估计：第一部分，密度估计AI 解读

Given a positive, normalized kernel and a finite measure on an Euclidean space, we construct a random density by convoluting the kernel with the Dirichlet random probability indexed by the finite measure. The posterior distribution of the random density given a sample is classified. The Bayes estimator of the density function is given.

泊松强度函数极小极大估计札记AI 解读

The empirical intensity function of the Poisson point process is shown to be a nonparametric minimax estimator for a weighted quadratic loss function.