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通过贝叶斯抽样估计有限混合分布AI 解读

SUMMARY A formal Bayesian analysis of a mixture model usually leads to intractable calculations, since the posterior distribution takes into account all the partitions of the sample. We present approximation methods which evaluate the posterior distribution and Bayes estimators by Gibbs sampling, relying on the missing data structure of the mixture model. The data augmentation method is shown to converge geometrically, since a duality principle transfers properties from the…

灵活函数形式下的贝叶斯效率分析：AIM 成本函数AI 解读

In this article, the authors describe the use of Gibbs sampling methods for drawing posterior inferences in a cost frontier model with an asymptotically ideal price aggregator, nonconstant returns to scale, and composed error. An empirical example illustrates the sensitivity of efficiency measures to assumptions made about the functional form of the frontier. The authors also examine the consequences of imposing regularity through parametric restrictions alone.

In this article, a model of single variable sampling plan with type I censoring is studied. Under the assumption that the variable is exponentially distributed and the loss function is a polynomial, an explicit expression of the Bayes risk is derived. Then, a simple and finite algorithm to determine an optimal sampling plan for minimizing the Bayes risk is suggested. Furthermore, a discretization method is proposed so that one can easily obtain an approximately optimal…

最大似然估计与后验分布非正态性的若干诊断AI 解读

Standard large-sample maximum likelihood and Bayesian inference, based on limiting multivariate normal distributions, may be dubious when applied with small or moderate sample sizes. We define and discuss several measures of nonnormality of MLE and posterior distributions that may be used as diagnostics and can indicate whether reparameterization will be effective in improving inferences. We begin by showing how the nonlinearity measures introduced by Beale and Bates and…

非参数响应面设计的渐近贝叶斯准则AI 解读

This paper deals with Bayesian design for response surface prediction when the prior may be finite or infinite dimensional, the design space arbitrary. In order that the resulting problems be manageable, we resort to asymptotic versions of D-, G- and A-optimality. Here the asymptotics stem from allowing the error variance to be large. The problems thus elicited have strong game-like characteristics. Examples of theoretical solutions are brought forward, especially when the…

卫星影像贝叶斯分类中的信息性先验AI 解读

In the Bayesian classification of satellite images, a prior distribution is used that aims to model the belief of spatial homogeneity of the underlying region. We extend this prior distribution to model certain topographical features of the area such as the position of the roads, the slopes, and the aspects. We demonstrate the effectiveness of this prior distribution in a reconstruction algorithm by means of a simulation study in which the quality of the result is assessed…

混沌系统中的估计函数方法AI 解读

Berliner considered Bayesian and likelihood-based approaches for estimation and prediction in a chaotic system with measurement error. This article proposes the use of estimating functions for this problem. Logistic and exponential maps are analyzed. Estimators are shown to be consistent and asymptotically normal. Small-sample behavior is studied with simulations.

频率先验信念的实证检验：方法与先天性心脏病案例AI 解读

We consider the problem of critiquing prior beliefs concerning the distribution of a discrete random variable in the light of a sequentially obtained sample. A topical application concerns a probabilistic expert system for the diagnosis of congenital heart disease, which requires specification of a large number of conditional probabilities that are initially imprecisely estimated by a suitable “expert.” These prior beliefs may be formally updated as data become available,…

气象场的统计时空建模方法AI 解读

In this article we develop a random field model for the mean temperature over the region in the northern United States covering eastern Montana through the Dakotas and northern Nebraska up to the Canadian border. The readings are temperatures at the stations in the U.S. historical climatological network. The stochastic structure is modeled by a stationary spatial-temporal Gaussian random field. For this region, we find little evidence of temporal dependence while the spatial…

皮特曼接近性度量：统计估计量的比较AI 解读

Preface Part I. Introduction 1. Evolution of Estimation Theory Least Squares Method of Moments Maximum Likelihood Uniformly Minimum Variance Unbiased Estimation Biased Estimation Bayes and Empirical Bayes Influence Functions and Resampling Techniques Future Directions 2. PMC Comes of Age PMC: A Product of Controversy PMC as an Intuitive Criterion 3. The Scope of the Book History, Motivation, and Controversy of PMC A Unified Development of PMC Part II. Development of Pitman's…

频率先验信念的经验评估：方法与先天性心脏病案例AI 解读

We consider the problem of critiquing prior beliefs concerning the distribution of a discrete random variable in the light of a sequentially obtained sample. A topical application concerns a probabilistic expert system for the diagnosis of congenital heart disease, which requires specification of a large number of conditional probabilities that are initially imprecisely estimated by a suitable “expert.” These prior beliefs may be formally updated as data become available,…

气象场时空统计建模方法：评论AI 解读

Abstract In this article we develop a random field model for the mean temperature over the region in the northern United States covering eastern Montana through the Dakotas and northern Nebraska up to the Canadian border. The readings are temperatures at the stations in the U.S. historical climatological network. The stochastic structure is modeled by a stationary spatial-temporal Gaussian random field. For this region, we find little evidence of temporal dependence while…

卫星图像贝叶斯分类中的信息先验AI 解读

In the Bayesian classification of satellite images, a prior distribution is used that aims to model the belief of spatial homogeneity of the underlying region. We extend this prior distribution to model certain topographical features of the area such as the position of the roads, the slopes, and the aspects. We demonstrate the effectiveness of this prior distribution in a reconstruction algorithm by means of a simulation study in which the quality of the result is assessed…

椭圆轮廓误差下的贝叶斯卡尔曼滤波AI 解读

The basic recursive equations of the Kalman filter, for independent normally distributed error sources in both the observation and the system equations, are shown to hold for a larger class of distributions. It is shown that, for error sources following jointly a general elliptical distribution, the conditional posterior distribution of the parameters and the one-step ahead predictive distribution at every stage t are also elliptical. This generalizes some recent results of…

This paper describes a dynamic or state-space approach for analyzing discrete time or grouped survival data. Simultaneous estimation of baseline hazard functions and of time-varying covariate effects is based on maximization of posterior densities or, equivalently, a penalized likelihood, leading to Kalman-type smoothing algorithms. Data-driven choice of unknown smoothing parameters is possible via an EM-type procedure. The methods are illustrated by applications to real…

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自回归模型的近似中位数无偏估计AI 解读

This paper introduces approximately median-unbiased estimators and confidence intervals for univariate AR(p) models with time trends. The methods are applied to the Nelson-Plosser macroeconomic data series, the extended Nelson-Plosser series, and some annual stock dividend and price series. The results show that most of the series exhibit substantially greater persistence than least squares estimates and some Bayesian estimates suggest. For example, for the extended…

Equity 估计量的统计性质AI 解读

The equity estimator, proposed by L. Krishnamurthi and A. Rangaswamy (1987), is shown to be inconsistent and to not necessarily improve upon the mean square error of the least squares estimator. A Monte Carlo experiment, based on the price-promotion model marketing research, with marketing data, is performed. The mean square error of the equity estimator is compared to that of two empirical Bayes estimators and the least square estimator. The empirical Bayes estimators have…

扩散过程离散观测的贝叶斯因子AI 解读

We present an approach to model selection for a time series of data on a fine time scale. The underlying process generating the data is modelled as a continuous time stochastic process. The underlying continuous processes are assumed to be diffusions with time varying drift and diffusion coefficient. Several approaches to modelling the diffusion coefficient are described. To perform model selection, we propose an approximation to the Bayes factor that uses only the discrete…

Gibbs 抽样器的协方差结构：估计量与增广方案比较AI 解读

We study the covariance structure of a Markov chain generated by the Gibbs sampler, with emphasis on data augmentation. When applied to a Bayesian missing data problem, the Gibbs sampler produces two natural approximations for the posterior distribution of the parameter vector: the empirical distribution based on the sampled values of the parameter vector, and a mixture of complete data posteriors. We prove that Rao-Blackwellization causes a one-lag delay for the…

奇异 Wishart 分布与奇异多元 Beta 分布AI 解读

This paper extends the study of Wishart and multivariate beta distributions to the singular case, where the rank is below the dimensionality. The usual conjugacy is extended to this case. A volume element on the space of positive semidefinite $m \times m$ matrices of rank $n < m$ is introduced and some transformation properties established. The density function is found for all rank-$n$ Wishart distributions as well as the rank-1 multivariate beta distribution. To do that,…

设计实验分析的预测方法AI 解读

Viewing the analysis of designed experiments as a model selection problem, we introduce the use of a predictive Bayesian criterion in this context based on the predictive density of a replicate experiment (PDRE). A calibration of the criterion is provided to assist in the model choice. The relationships of the proposed criterion to other prevalent criteria, such as AIC, BIC, and Mallows's C p , are given. An information theoretic criterion based on the PDRE's of two…

使用狄利克雷过程先验估计正态均值AI 解读

In this article, the Dirichlet process prior is used to provide a nonparametric Bayesian estimate of a vector of normal means. In the past there have been computational difficulties with this model. This article solves the computational difficulties by developing a “Gibbs sampler” algorithm. The estimator developed in this article is then compared to parametric empirical Bayes estimators (PEB) and nonparametric empirical Bayes estimators (NPEB) in a Monte Carlo study. The…

近似贝叶斯推断AI 解读

Consider statistical inference about a scalar parameter and suppose that information about that parameter is to be summarized by a system of interval estimates. It is well known that methods of interval estimation that do not correspond to Bayesian inference with respect to some prior distribution have some logical difficulties. This article proposes a measure of how close a system of interval estimates is to being of Bayesian form. Using this measure, several non-Bayesian…