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退火式马尔可夫链蒙特卡洛及其祖先推断应用AI 解读

Markov chain Monte Carlo (MCMC; the Metropolis-Hastings algorithm) has been used for many statistical problems, including Bayesian inference, likelihood inference, and tests of significance. Though the method generally works well, doubts about convergence often remain. Here we propose MCMC methods distantly related to simulated annealing. Our samplers mix rapidly enough to be usable for problems in which other methods would require eons of computing time. They simulate…

最优置信集合、生物等效性与帕斯卡蜗线AI 解读

We begin with a decision-theoretic investigation into confidence sets that minimize expected volume at a given parameter value. Such sets are constructed by inverting a family of uniformly most powerful tests, and hence they also enjoy the optimality property of being uniformly most accurate. In addition, these sets possess Bayesian optimal volume properties and represent the first case (to our knowledge) of a frequentist 1 – α confidence set that possesses a Bayesian…

基于 DNA 图谱的法医识别中的参数乘积估计AI 解读

In many areas, such as reliability and forensic identification, it is of interest to estimate a product of unknown parameters, each of which is estimated from test data. The maximum likelihood estimator usually used in both applications is approximately unbiased but has an asymmetric sampling distribution, particularly when the sample size is not large. Consequently, most estimates understate the parameter value, often substantially, and this may be a serious drawback if…

贝叶斯图像分析中的新损失函数AI 解读

Unlike the development of more accurate prior distributions for use in Bayesian imaging, the design of more sensible estimators through loss functions has been neglected in the literature. We discuss the design of loss functions with a local structure that depend only on a binary misclassification vector. The proposed approach is similar to modeling with a Markov random field. The Bayes estimate is calculated in a two-step algorithm using Markov chain Monte Carlo and…

不确定性的诸方面：献给 D. V. LindleyAI 解读

Dennis Lindley: The First 70 Years The Operational Bayesian Approach Pivotal Inference Illustrated on the Darwin Maize Data Bayes Theory in Latent Variable Modelling Bayesian Sampling Schemes for Auditors Optimal Prediction with Hierarchical Models: Bayesian Clustering Inference for a Covariance Matrix The Role of Statistical Theory in Decision Aiding The Signature as a Covariate in Reliability and Biometry Residual Analysis and Outliers in Hierarchical Models The Island…

近似线性检验的功效稳健化AI 解读

We present a general method of improving the power of linear and approximately linear tests when deviations from a translation family of distributions must be taken into account. This method involves the combination of a linear statistic measuring location and a quadratic statistic measuring change of shape of the underlying distribution. The tests (“funnel tests”) are constructed as certain Bayes tests. In general they gain a sizeable amount of power over the linear tests…

一类二项响应混合模型中后验分布存在性的说明AI 解读

Necessary and sufficient conditions are given for the existence of the posterior distribution of the variance components in a class of mixed models for binomial responses. The implications of our results are illustrated through an example.

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贝叶斯模型选择与预测及其实证应用AI 解读

This paper builds on some recent work by the author and Werner Ploberger (1991, 1994) on the development of ‘Bayes models’ for time series and on the authors' model selection criterion ‘PIC’. The PIC criterion is used in this paper to determine the lag order, the trend degree and the presence or absence of a unit root in an autoregression with deterministic trend. A new forecast-encompassing test for Bayes models is developed which allows one Bayes model to be compared with…

任意维度置信集构造的新通用方法及其应用AI 解读

Let $\mathbf{X}$ have a star unimodal distribution $P_0$ on $\mathbb{R}^p$. We describe a general method for constructing a star-shaped set $S$ with the property $P_0(\mathbf{X} \in S) \geq 1 - \alpha$, where $0 < \alpha < 1$ is fixed. This is done by using the Camp-Meidell inequality on the Minkowski functional of an arbitrary star-shaped set $S$ and then minimizing Lebesgue measure in order to obtain size-efficient sets. Conditions are obtained under which this method…

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矩的精确多元贝叶斯Bootstrap分布AI 解读

The common unknown probability law $P$ of a random sample $Y_1,\ldots, Y_n$ is assigned a Dirichlet process prior with index $\alpha$. It is shown that the posterior joint density of several moments of $P$ converges, as $\alpha(\mathbb{R})\rightarrow 0$, to a multivariate B-spline, which is, therefore, the Bayesian bootstrap joint density of the moments. The result provides the basis for possible default nonparametric Bayesian inference on unknown moments.

变量选择的影响：贝叶斯诊断视角AI 解读

Variable selection is ubiquitous in statistical practice. Forward selection, backwards elimination, or a combination thereof are among the most popular techniques. Statistical texts teach direct interpretation of coefficients after variable selection. For scientific purposes, the desired interpretation is unconditional on the variable selection. In this article an influence analysis of variable selection is performed from a Bayesian viewpoint. Variable selection is shown to…

利用广义 Savage–Dickey 密度比计算贝叶斯因子AI 解读

We present a simple method for computing Bayes factors. The method derives from observing that in general, a Bayes factor can be written as the product of a quantity called the Savage-Dickey density ratio and a correction factor; both terms are easily estimated from posterior simulation. In some cases it is possible to do these computations without ever evaluating the likelihood.

稳定分布的贝叶斯推断AI 解读

Very little work on stable distribution parameter estimation and inference appears in the literature due to the nonexistence of the probability density function. This has led in particular to a dearth of Bayesian work in this area. But Bayesian computation via Markov chain Monte Carlo allows us to sample from the distribution of the parameters of the stable distributions, by exploiting a particular mathematical representation involving the stable density.

部分因子实验中删失数据的贝叶斯分析AI 解读

Censored data arise naturally in industrial experiments whose observations are failure times or measurements with mixed continuous-categorical outcomes. When censored data are observed from a fractionated experiment, likelihood-based estimates quite often do not exist, especially when the opportunity for improvement is great. To circumvent this problem, we propose a Bayesian analysis strategy that has a straightforward implementation using the data augmentation and Monte…

贝叶斯因子AI 解读

In a 1935 paper and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null is one-half. Although there has been much discussion of Bayesian hypothesis testing in the context of criticism of P-values, less attention has been given to the Bayes factor as a…

正态均值乘积的参考先验贝叶斯分析AI 解读

Two reference priors for the product of means of n normal distributions with common known variance are developed. One of them induces an improper posterior distribution and therefore is not of much interest. The other is a generalized form of the n = 2 case derived by Berger and Bernardo. The latter is compared with the uniform prior (the Jeffreys prior) in posterior inference and the optimal frequentist coverage criterion. The reference prior is shown to be better than the…

利用混合模型进行贝叶斯密度估计与推断AI 解读

We describe and illustrate Bayesian inference in models for density estimation using mixtures of Dirichlet processes. These models provide natural settings for density estimation and are exemplified by special cases where data are modeled as a sample from mixtures of normal distributions. Efficient simulation methods are used to approximate various prior, posterior, and predictive distributions. This allows for direct inference on a variety of practical issues, including…