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信息度量与贝叶斯层级模型AI 解读

We consider the Bayesian statistical models in which the prior distribution of the parameter vector θ1 in the distribution of an observable random vector X is to be specified in a hierarchical fashion and one wants to learn about the hyperparameters at each level of this prior distribution. It is shown that for a wide class of information measures, based on the so-called f divergence, the information decreases as one moves to higher levels of hyperparameters. This result…

时间序列模型的后验赔率AI 解读

This paper is concerned with model selection in time series analysis. A Bayesian approach is adopted to investigate various decision criteria previously advocated. The discussion is conducted in the context of a class of nonlinear time series models of sufficient generality to encompass a wide range of processes currently of interest.

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衡量统计成本分摊的精度AI 解读

This article examines the use of regression analysis for allocating indirect costs. When multiple regression is used to estimate the weights of several allocation factors, conventional standard errors and correlation coefficients can be misleading with respect to the statistical precision of the cost allocations. This article develops alternative allocation approaches and measures of precision that use linear prediction theory and Bayesian inference. The proposed methods are…

回归中一步变量选择的最优性质AI 解读

We consider the selection of the best subset of independent variables of a fixed size for possible inclusion in a regression model. The classical procedures (largest $\mathbb{R}^2$ to enter) are shown to be uniformly invariant Bayes in the sense of Paulson (1952) and Kudo (1956).

融贯且连续的推断AI 解读

If the sampling model is a continuous function of the parameter and if either the parameter space or the observation space is compact, then a coherent inference which is a continuous function of the observation must be the posterior of a proper, countably additive prior.

二元数据的实验设计AI 解读

Models for binary data are usually such that the information matrix depends on the unknown parameters. Thus the standard criteria for optimality in regression experiments cannot be applied without modification. Methods of going around this difficulty include the use of initial point estimates, sequential methods, and Bayesian analysis. This article is mainly concerned with the robustness and the number of design points for methods involving initial estimates, and for…

参数经验贝叶斯推断：理论与应用AI 解读

This article reviews the state of multiparameter shrinkage estimators with emphasis on the empirical Bayes viewpoint, particularly in the case of parametric prior distributions. Some successful applications of major importance are considered. Recent results concerning estimates of error and confidence intervals are described and illustrated with data.

利用符号秩对匹配对进行似然推断AI 解读

SUMMARY Exact and approximate inference based on the marginal likelihood which results from the signed ranks of the within pair differences of independent matched pairs is considered. Inference is made using Bayesian ideas. A quickly computed approximate analysis is introduced and this is shown to be extremely good when the within pair differences are assumed to have a normal distribution. Numerical comparisons are also made when the differences have a logistic distribution,…

贝叶斯非线性回归及酶动力学实例AI 解读

A nonlinear regression model is applied to several sets of enzyme kinetics data, treating the entire regression vector as the parameter of interest. The resulting marginal posterior distributions are presented alongside the usual Student's t posterior distributions implicit in the usual linearized regression. The prior distribution used is that which is minimally informative about the regression vector. In the special case of the linear model this procedure leads to the…

时间序列模型的后验赔率AI 解读

This paper is concerned with model selection in time series analysis. A Bayesian approach is adopted to investigate various decision criteria previously advocated. The discussion is conducted in the context of a class of nonlinear time series models of sufficient generality to encompass a wide range of processes currently of interest.

Since Robbins (1956), a large literature has evolved treating the empirical Bayes formulation of a sequence of decision problems. In this paper we look at the formulation and the asymptotic optimality criterion as a classical iid problem and a consistency property. With this point of view and the finite state component problem, we evoke classical results on Bayes procedures to prove a complete class theorem and to establish the asymptotic optimality of Bayes empirical Bayes…

狄利克雷分布混合与列联表估计AI 解读

Assuming a multinomial sampling model, prior distributions are developed which can accept prior information about symmetry and independence in a two-way contingency table. Bayesian estimates for the cell probabilities are obtained from the posterior distributions which are attractive alternatives to the usual classical estimates when vague prior information about symmetry or independence is available.

模型选择中的样本量选择与可区分性评估AI 解读

In this article we present a general Bayesian approach to discrimination. We describe how the difference between two separate families of distributions can be assessed in terms of differences between two binomial models. Two examples that illustrate the methodology are included. Specifically, we investigate the extent to which it is possible to discriminate between the von Mises and the wrapped normal distributions and also between the normal and a family of t distributions.

鱼类种群年龄构成估计的贝叶斯优化AI 解读

To estimate the age distribution of a fish population, a two-phase stratified sample design is proposed. Bayesian methods are employed to determine (a) optimal estimators of the desired population proportions; and (b) the optimal choice of second-phase sample sizes subject to a fixed budget. A summary of the results of some numerical examples is presented. These examples demonstrate typical expected gains obtained by using the Bayesian optima as compared to alternative…

多项分布与列联表检验的功效及加权功效AI 解读

The strength of a significance test is defined as a weighted average of the power especially if the weights are a prior density. The concept is a compromise between Neyman-Pearsonian and Bayesian methods and is applied to tests for multinomial equiprobability and for no association in contingency tables. The differences of the power functions of two criteria, X 2 and G, are illustrated for the trinomial, where G arose earlier from a partially Bayesian approach. Other methods…

模型选择中的样本量选择与可区分性评估AI 解读

In this article we present a general Bayesian approach to discrimination. We describe how the difference between two separate families of distributions can be assessed in terms of differences between two binomial models. Two examples that illustrate the methodology are included. Specifically, we investigate the extent to which it is possible to discriminate between the von Mises and the wrapped normal distributions and also between the normal and a family of t distributions.

鱼类种群年龄构成估计的贝叶斯优化AI 解读

To estimate the age distribution of a fish population, a two-phase stratified sample design is proposed. Bayesian methods are employed to determine (a) optimal estimators of the desired population proportions; and (b) the optimal choice of second-phase sample sizes subject to a fixed budget. A summary of the results of some numerical examples is presented. These examples demonstrate typical expected gains obtained by using the Bayesian optima as compared to alternative…

多项分布与列联表检验的功效和强度AI 解读

The strength of a significance test is defined as a weighted average of the power especially if the weights are a prior density. The concept is a compromise between Neyman-Pearsonian and Bayesian methods and is applied to tests for multinomial equiprobability and for no association in contingency tables. The differences of the power functions of two criteria, X 2 and G, are illustrated for the trinomial, where G arose earlier from a partially Bayesian approach. Other methods…

策略性信息传递AI 解读

This paper develops a model of strategic communication, in which a better-informed Sender (S) sends a possibly noisy signal to a Receiver (R), who then takes an action that determines the welfare of both. We characterize the set of Bayesian Nash equilibria under standard assumptions, and show that equilibrium signaling always takes a strikingly simple form, in which S partitions the support of the (scalar) variable that represents his private information and introduces noise…

一个具有贝叶斯充分性但不具有经典充分性的统计量AI 解读

In a Borel setting, every classically sufficient statistic is Bayes sufficient, but not vice versa. The example is a hypothesis testing problem in which Bayesians, but not classicists, can achieve zero error probabilities.

控制问题中估计量可容许性与不可容许性的一般结果AI 解读

Let $\mathbf{X} = (X_1, \cdots, X_p)^t$ be an observation from a $p$-variate normal distribution with unknown mean $\mathbf{\theta} = (\theta_1, \cdots, \theta_p)^t$ and identity covariance matrix. We consider a control problem which, in canonical form, is the problem of estimating $\mathbf{\theta}$ under the loss $L(\mathbf{\theta, \delta}) = (\mathbf{\theta}^t \mathbf{\delta} - 1)^2$, where $\mathbf{\delta(x)} = (\delta_1(\mathbf{x}), \cdots, \delta_p(\mathbf{x}))^t$ is…

一种简单的预测密度函数AI 解读

An easily computable predictive density is considered. Although involving a plain maximum likelihood technique, it coincides with the posterior predictive density with a noninformative prior. For standard situations achievements are comparable with classical inference.