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Logistic函数的上下概率推断AI 解读

A general system of inference which leads to upper and lower posterior distributions based on sample data has been proposed by Dempster (1967). This general theory of inference is applied to the two-parameter logistic function, given the data from independent binomial populations. Inferences are developed for fixed regions about the two parameters and about interesting combinations of these parameters. The resulting upper and lower probabilities are generated by a random…

指数族的共轭先验AI 解读

Let $X$ be a random vector distributed according to an exponential family with natural parameter $\theta \in \Theta$. We characterize conjugate prior measures on $\Theta$ through the property of linear posterior expectation of the mean parameter of $X : E\{E(X|\theta)|X = x\} = ax + b$. We also delineate which hyperparameters permit such conjugate priors to be proper.

面向预测的模型选择方法AI 解读

This article offers a synthesis of Bayesian and sample-reuse approaches to the problem of high structure model selection geared to prediction. Similar methods are used for low structure models. Nested and nonnested paradigms are discussed and examples given.

摘要暂缺

随机过程参数后验分布的渐近正态性AI 解读

Summary Asymptotic normality of the posterior distribution of a parameter in a stochastic process is shown to hold under conditions which do little more than ensure consistency of a maximum likelihood estimator. Much more stringent conditions are required to ensure asymptotic normality of the MLE. This contrast, which has implications of considerable significance, does not emerge in the classical context of independent and identically distributed observations.

用于贝叶斯推断的参考后验分布AI 解读

Summary A procedure is proposed to derive reference posterior distributions which approximately describe the inferential content of the data without incorporating any other information. More explicitly, operational priors, derived from information-theoretical considerations, are used to obtain reference posteriors which may be expected to approximate the posteriors which would have been obtained with the use of proper priors describing vague initial states of knowledge. The…

正态离散矩阵的贝叶斯推断及其在随机多元回归中的应用AI 解读

Summary This paper discusses Bayesian inference procedures for a normal dispersion matrix. Structural information for the prior mean of the dispersion matrix is incorporated into the analysis through a Normal-Wishart prior distribution. Many of the resulting Bayes estimates are invariant, consistent and asymptotically efficient. Using this procedure, a coherent Bayesian argument for stochastic multiple regression analysis is developed, where dependent and independent…

基于删失数据的贝叶斯非参数估计AI 解读

Let $X_1, \cdots, X_n$ be a random sample from an unknown $\operatorname{cdf} F$, let $y_1, \cdots, y_n$ be known real constants, and let $Z_i = \min(X_i, y_i), i = 1, \cdots, n$. It is required to estimate $F$ on the basis of the observations $Z_1, \cdots, Z_n$, when the loss is squared error. We find a Bayes estimate of $F$ when the prior distribution of $F$ is a process neutral to the right. This generalizes results of Susarla and Van Ryzin who use a Dirichlet process…

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非参数贝叶斯区间估计AI 解读

SUMMARY Bayesian confidence bands for a distribution function are converted into confidence intervals for specified population quantiles and also for the mean. Bayesian tolerance limits are similarly constructed.

时间序列中若干异常值问题的贝叶斯分析AI 解读

Two models, the aberrant innovation model and the aberrant observation model, are considered to characterize outliers in time series. The approach adopted here allows for a small probability α that any given observation is ‘bad’ and in this set-up the inference about the parameters of an autoregressive model is considered.

自回归模型拟合中最小 AIC 程序的贝叶斯扩展AI 解读

The proposal of simultaneous use of modified AIC statistics by Bhansali & Downham for the fitting of autoregressive models is reviewed and a Bayesian extension of the minimum AIC procedure is proposed. The practical utility of the procedure is demonstrated by numerical examples.

香农多样性指数的贝叶斯估计AI 解读

SUMMARY This paper is concerned with methods of estimating Shannon's information measure, and with the sampling properties of those estimates. A Bayesian approach is used to suggest two possible classes of estimators, and their properties are compared with those of the usual Shannon measure of diversity. Particular attention is given to comparisons involving the MacArthur model of species abundances.

稀少记录误差的抽样与估计AI 解读

For each individual in a finite population a recorded value is available. A small proportion of the values is in error, all the errors being of the same sign and the maximum fractional error being known. It is required to obtain an upper confidence limit for the total error in the population. Various solutions, including a Bayesian one, are discussed for sampling with probability proportional to the recorded values, and the appropriateness of this form of sampling is…

关于似然、贝叶斯方法与预设值偏好的一则评论AI 解读

As judged by large sample efficiency, one can make use of a preconceived value in a considerably less modest way than Bayes's theorem permits, provided one respects the likelihood function.

二维列联表的经验贝叶斯方法AI 解读

An empirical Bayes method for smoothing two-way tables is presented. It is based on the use of the log linear model and a normal prior distribution. Estimation of the variance component in the prior is discussed, and two approximations are considered, one which utilizes the EM algorithm.

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不依赖偶损失选择的广义贝叶斯估计量AI 解读

Let $x_1, \cdots, x_n$ be i.i.d. random variables with a distribution depending on the real parameter. Under what conditions is a generalized Bayes estimator independent of the choice of the even loss function? The known answer to this question is that this independence holds if the posterior density is symmetric and unimodal. The description of distributions and corresponding generalized prior densities on the real line, for which the posterior density is symmetric and…

摘要暂缺

基于秩序统计量的两样本问题贝叶斯分析AI 解读

Summary A Bayesian analysis of the two-sample, location-shift problem based on the rank order statistic is described. It is assumed that the data available can only at best be considered as being on the ordinal scale. Exact and simplified approximate procedures are suggested. These are not distribution-free since the underlying population distributions need to be specified.

混合概率下的贝叶斯因子AI 解读

Summary A new expression for a Bayes factor as a weighted average of conditional Bayes factors is given, resembling the familiar relation for a marginal probability as a weighted average of conditional probabilities. Interpretations are given for the three contexts of (i) the use of a non-sufficient statistic, (ii) inference for a simple hypothesis versus a vague alternative in terms of inference for a dichotomy and (iii) opinion pooling before sampling.

稳定决策问题AI 解读

A decision problem is characterized by a loss function $V$ and opinion $H$. The pair $(V, H)$ is said to be strongly stable iff for every sequence $F_n \rightarrow_\omega H, G_n \rightarrow_\omega H$ and $L_n\rightarrow V, W_n\rightarrow V$ uniformly, $\lim_{\varepsilon \downarrow 0} \lim \sup_{n\rightarrow \infty} \lbrack \int L_n(\theta, D_n(\varepsilon)) dF_n(\theta) - \inf_D \int L_n(\theta, D) dF_n(\theta)\rbrack = 0$ for every sequence $D_n(\varepsilon)$ satisfying $\int W_n(\theta, D_n(\varepsilon)) dG_n(\theta) \leqq \inf_D \int W_n(\theta, D) dG_n(\theta) + \varepsilon.$…

线性不等式约束下线性模型的贝叶斯分析AI 解读

This article considers the general linear model when the parameter space is subject to linear inequality constraints. A Bayesian analysis of this model is presented using a natural conjugate prior of the mixed type. Expressions are given for the probability that constraints are binding and for the distribution of the parameters. When prior information about the parameters is vague, the Bayesian and sampling methods of model selection are compared. The techniques are applied…

选取包含最佳正态总体子集的新程序AI 解读

A new procedure, called the fiducial procedure, is defined for selecting a subset of a collection of normal populations with common known variance. In the presence of an “indifference zone,” this procedure has probability at least P* of selecting the “best” population. An upper bound is obtained for the smallest indifference zone d* that satisfies the P* condition. Comparisons of relative merit are made between the fiducial procedure, Gupta's (1965) procedure, and an…