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给定样本均值的后验收敛AI 解读

For various applications one wants to know the asymptotic behavior of $w(\theta | \overline{X})$, the posterior density of a parameter $\theta$ given the mean $\overline{X}$ of the data rather than the full data set. Here we show that $w(\theta | \overline{X})$ is asymptotically normal in an $L^1$ sense, and we identify the mean of the limiting normal and its asymptotic variance. The main results are first proved assuming that $X_1, \dots, X_n, \dots$ are independent and…

随机缺失观测下马尔可夫依赖二元序列的经验贝叶斯模型AI 解读

We develop an improved empirical Bayes estimation methodology for the analysis of two-state Markov chains observed from heterogeneous individuals. First, the two transition probabilities corresponding to each chain are assumed to be drawn from a common, bivariate distribution that has beta marginals. Second, randomly missing observations are incorporated into the likelihood for the hyperparameters by efficiently summing over all possible values for the missing observations.…

关于无信息先验的若干讨论AI 解读

This article focuses primarily on a comparison between the reference priors of Berger and Bernardo and the reverse reference priors suggested by J. K. Ghosh. Sufficient conditions are given that provide agreement between the two classes of priors. Several examples are given showing the agreement or disagreement between the two. In addition, these priors are compared under a criterion that requires the frequentist coverage probability of the posterior region of a real-valued…

通过蒙特卡洛实验的曲线拟合实现最优设计AI 解读

This article explores numerical methods for stochastic optimization, with special attention to Bayesian design problems. A common and challenging situation occurs when the objective function (in Bayesian applications, the expected utility) is very expensive to evaluate, perhaps because it requires integration over a space of very large dimensionality. Our goal is to explore a class of optimization algorithms designed to gain efficiency in such situations, by exploiting…

多重局部序列比对的贝叶斯模型与 Gibbs 抽样策略AI 解读

A wealth of data concerning life's basic molecules, proteins and nucleic acids, has emerged from the biotechnology revolution. The human genome project has accelerated the growth of these data. Multiple observations of homologous protein or nucleic acid sequences from different organisms are often available. But because mutations and sequence errors misalign these data, multiple sequence alignment has become an essential and valuable tool for understanding structures and…

信息与条件推断AI 解读

Consider non-Bayesian inference about a parameter of interest β in the presence of a nuisance parameter λ based on a statistic S = (T, A). If the conditional distribution of T given A does not depend on λ and if A contains no information about β in the presence of λ, then A is said to be ancillary for θ in the presence of λ, and inference about θ is to be based on the conditional distribution of T given A. This approach has been the basis for several definitions of…

利用 Gibbs 抽样输出计算边际似然AI 解读

In the context of Bayes estimation via Gibbs sampling, with or without data augmentation, a simple approach is developed for computing the marginal density of the sample data (marginal likelihood) given parameter draws from the posterior distribution. Consequently, Bayes factors for model comparisons can be routinely computed as a by-product of the simulation. Hitherto, this calculation has proved extremely challenging. Our approach exploits the fact that the marginal…

周期成分动态线性模型的贝叶斯推断AI 解读

Dynamic linear models (DLM's) with time-varying cyclical components are developed for the analysis of time series with persistent though time-varying cyclical behavior. The development covers inference on wavelengths of possibly several persistent cycles in nonstationary time series, permitting explicit time variation in amplitudes and phases of component waveforms, decomposition of stochastic inputs into purely observational noise and innovations that impact on the waveform…

信息与条件推断AI 解读

Consider non-Bayesian inference about a parameter of interest β in the presence of a nuisance parameter λ based on a statistic S = (T, A). If the conditional distribution of T given A does not depend on λ and if A contains no information about β in the presence of λ, then A is said to be ancillary for θ in the presence of λ, and inference about θ is to be based on the conditional distribution of T given A. This approach has been the basis for several definitions of…

周期成分动态线性模型中的贝叶斯推断AI 解读

Dynamic linear models (DLM's) with time-varying cyclical components are developed for the analysis of time series with persistent though time-varying cyclical behavior. The development covers inference on wavelengths of possibly several persistent cycles in nonstationary time series, permitting explicit time variation in amplitudes and phases of component waveforms, decomposition of stochastic inputs into purely observational noise and innovations that impact on the waveform…

计量经济学的方法论AI 解读

The methodology of econometrics is concerned with rules governing the building of statistical models in economics. These two volumes draw together 62 previously published studies in economics and statistics. The volumes are divided into 12 sections covering controversial topics ranging from the earliest days of econometrics to the present. Sections include policy analysis, exogeneity, causality, Bayesian perspective and British econometrics.

随机缺失的马尔可夫依赖二元序列的经验贝叶斯模型AI 解读

We develop an improved empirical Bayes estimation methodology for the analysis of two-state Markov chains observed from heterogeneous individuals. First, the two transition probabilities corresponding to each chain are assumed to be drawn from a common, bivariate distribution that has beta marginals. Second, randomly missing observations are incorporated into the likelihood for the hyperparameters by efficiently summing over all possible values for the missing observations.…

摘要暂缺

具有近似频率学有效性的扰动椭球与最高后验密度区域AI 解读

SUMMARY This paper considers, in the multiparameter case, perturbed ellipsoidal and highest posterior density regions with both Bayesian and frequentist validity up to o(n −1).

最优探索的一类贝叶斯模型AI 解读

SUMMARY Each of several locations contains an unknown number of objects of value. A single search of a location will discover some of these objects which are then removed. Discoveries yield rewards. A ‘distribution of effort’ problem is posed concerning how to explore the locations optimally—i.e. to maximize the expected return from discoveries made. This is formulated as a Bayes sequential decision problem for which index policies are optimal. A natural simple case is one…

利用不等式约束估计量改进特征价格估计AI 解读

Economists commonly estimate the value of characteristics not traded in explicit markets by hedonic pricing. Unfortunately, these nonexplicitly traded characteristics often display a lack of independent variation or multicollinearity. Often some prior information on the value of these characteristics is available from submarkets. This paper utilizes this type of prior information to circumvent multicollinearity problems in hedonic pricing models using an inequality…

数据驱动平滑拟合优度检验的一致性与蒙特卡洛模拟AI 解读

The data driven method of selecting the number of components in Neyman's smooth test for uniformity, introduced by Ledwina, is extended. The resulting tests consist of a combination of Schwarz's Bayesian information criterion (BIC) procedure and smooth tests. The upper bound of the dimension of the exponential families in applying Schwarz's rule is allowed to grow with the number of observations to infinity. Simulation results show that the data driven version of Neyman's…

无限可分分布的近似随机数生成及其贝叶斯推断应用AI 解读

SUMMARY Stochastic processes with independent increments play a central role in Bayesian nonparametric inference. The distributions of the increments of these processes, aside from fixed points of discontinuity, are infinitely divisible and their Laplace and/or Fourier transforms in the Lévy representation are usually known. Conventional Bayesian inference in this context has been limited largely to providing point estimates of the random quantities of interest, although…

多元判别分析与最大惩罚似然密度估计AI 解读

SUMMARY A new theoretical point of view is discussed in the framework of density estimation. The multivariate true density, viewed as a prior or penalizing factor in a Bayesian framework, is modelled by a Gibbs potential. Estimating the density consists in maximizing the posterior. For efficiency of time, we are interested in an approximate estimator f̂ = Bπ of the true density f, where B is a stochastic operator and π is the raw histogram. Then, we investigate the…

通过马尔可夫链蒙特卡洛方法进行贝叶斯模型选择AI 解读

SUMMARY Markov chain Monte Carlo (MCMC) integration methods enable the fitting of models of virtually unlimited complexity, and as such have revolutionized the practice of Bayesian data analysis. However, comparison across models may not proceed in a completely analogous fashion, owing to violations of the conditions sufficient to ensure convergence of the Markov chain. In this paper we present a framework for Bayesian model choice, along with an MCMC algorithm that does not…

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…

摘要暂缺

嵌套假设的参考贝叶斯检验及其与 Schwarz 准则的关系AI 解读

To compute a Bayes factor for testing H 0: ψ = ψ0 in the presence of a nuisance parameter β, priors under the null and alternative hypotheses must be chosen. As in Bayesian estimation, an important problem has been to define automatic, or “reference,” methods for determining priors based only on the structure of the model. In this article we apply the heuristic device of taking the amount of information in the prior on ψ equal to the amount of information in a single…

贝叶斯图像处理中的新损失函数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…