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季节性时间序列建模与预测的另一种方法AI 解读

This article proposes an alternative methodology for modeling and forecasting seasonal series. The approach is in the Bayesian autoregression tradition pioneered by Doan, Litterman, and Sims and builds seasonality directly into the prior of the coefficients of the model by means of a set of uncertain linear restrictions. As an illustration, the method is applied to 10 U.S. quarterly macroeconomic series. For each series, the author compares the forecasting performance of a…

非实验数据下独立性公理的后验概率AI 解读

This article addresses the issues associated with the construction of posterior probabilities for violation of the independence axiom of expected utility from nonexperimental data. To illustrate the methodology of analyzing nonexperimental evidence, the authors consider seat-belt-usage-data. They find a posterior probability close to one of an Allais-type paradox in these data. In addition, the evidence is not inconsistent with Machina's Hypothesis II but is inconsistent…

《非实验数据下独立性公理的后验概率（或：系紧安全带并扇形展开）》评论AI 解读

Steven Garber, Mark Kamlet, [Posterior Probabilities of the Independence Axiom with Nonexperimental Data (Or Buckle up and Fan out)]: Comment, Journal of Business & Economic Statistics, Vol. 10, No. 1 (Jan., 1992), pp. 44-48

对《非实验数据下独立性公理的后验概率》的回复AI 解读

Robert C. Marshall, Jean-Francois Richard, Gary A. Zarkin, [Posterior Probabilities of the Independence Axiom with Nonexperimental Data (Or Buckle up and Fan out)]: Reply, Journal of Business & Economic Statistics, Vol. 10, No. 1 (Jan., 1992), pp. 48-49

“客观”贝叶斯单位根检验AI 解读

Abstract Due to weaknesses in traditional tests, a Bayesian approach is developed to investigate whether unit roots exist in macroeconomic time‐series. Bayesian posterior odds comparing unit root models to stationary and trend‐stationary alternatives are calculated using informative priors. Two classes of reference priors which are informative but require minimal subjective prior input are used. In this sense the Bayesian unit root tests developed here are objective.…

利用 Gibbs 抽样进行捕获—再捕获估计AI 解读

Capture-recapture models are widely used in the estimation of population sizes. Based on data augmentation considerations, we show how Gibbs sampling can be applied to calculate Bayes estimates in this setting. As a result, formulations which were previously avoided because of analytical and numerical intractability can now be easily considered for practical application. We illustrate this potential by using Gibbs sampling to calculate Bayes estimates for a hierarchical…

非线性假设的贝叶斯因子与似然分布AI 解读

New methods are proposed which allow Bayes factors to be computed for hypotheses which impose nonlinear restrictions on the parameters. Projection methods are used to induce the prior distribution over the restricted parameter space which is required for computation of the Bayes factor. Various distance metrics are introduced to define the projection, including a utility-based metric which gives Kullback-Leibler divergence as a special case. Draws from the restricted and…

二元响应筛查的稳健设计AI 解读

Optimal screening procedures are derived using Bayesian decision theory. A simple heuristic solution is determined using an asymptotic posterior distribution for the parameters in a linear probit model. The solution is shown to be optimal within a class of possible procedures and robust to departures from model assumptions.

合并规则不确定时整合不同实验结果的贝叶斯方法AI 解读

Given data from several experiments or observational studies initially believed to be similar, it is desired to estimate the means corresponding to one or more experiments of particular interest. To illustrate the proposed methodology we consider a simple specification where there are no covariates. A class of prior distributions for the set, μ = (μ1,…, μL), of experiment means is specified to reflect the beliefs that (a) there are subsets of μ such that the μ1's within each…

贝叶斯分析中适当的似然函数AI 解读

The validity of posterior probability statements follows from probability calculus when the likelihood is the density of the observations. To investigate other cases, a second, more intuitive definition of validity is introduced, based on coverage of posterior sets. This notion of validity suggests that the likelihood must be the density of a statistic, not necessarily sufficient, for posterior probability statements to be valid. A convenient numerical method is proposed to…

参数非线性函数后验密度的拉普拉斯展开AI 解读

SUMMARY An asymptotic expansion for marginal posterior densities of nonlinear functions of parameters is derived. The density in question is proportional to an integral over a lower dimensional manifold with the integrand including an appropriate change-in-volume term, Laplace's method is applied to obtain the expansion. Avoiding the difficult step of the explicit parameterization of the manifold, we carry out the expansion via an implicit and local parameterization, and the…

存在大量干扰参数时的经验贝叶斯与条件推断AI 解读

This paper concerns the use of empirical Bayes methods to improve the efficiency of a parameter of interest, θ, in the presence of many nuisance parameters, {øi}, one from each data stratum. A class of distributions is introduced such that for fixed θ, the minimal sufficient statistic ti(θ) for øi is from an exponential family and hence complete. By imposing the assumption that the øi's are generated from an unspecified distribution function Q, we show that for this class of…

柯西模型中的条件推断AI 解读

Many computations associated with the two-parameter Cauchy model are shown to be greatly simplified if the parameter space is represented by the complex plane rather than the real plane. With this convention we show that the family is closed under Mö bius transformation of the sample space: there is a similar induced transformation on the parameter space. The chief raison d'être of the paper, however, is that the two-parameter Cauchy model provides an example of a nonunique…

评估后验影响的图形化个案统计量AI 解读

A single number summary of the influence of an observation on the posterior of the parameter of interest is useful, but does not convey all aspects of the effect of deleting the observation. We propose a plot that does convey all the effects of an observation on the posterior.

点过程统计分析的动态方法AI 解读

An approach to the analysis of point processes based on sequential analysis of successive intervals assuming a piecewise constant intensity rate is presented. Bayesian inference for processes with explanatory variables is derived in terms of on-line estimation, filtering and prediction. Limiting equations for the time-continuous intensity rate are obtained and solved for the no-covariates case. Examples are provided and the approach is applied in a numerical example.

非贝叶斯分类规则的误分类率与Fisher线性判别的稳健性AI 解读

We call a classification procedure non-Bayes if it does not converge to the Bayes classification procedure. An asymptotic expansion is found for the expected error rate of such a classification rule. This is used to compare the estimates of Fisher's linear discriminant rule, F, and the quadratic discriminant rule, Q, under departures from the equal variance matrices assumption. It is found that F is quite robust to departures from the equal variances assumption.

有限状态马尔可夫链的经验贝叶斯估计量AI 解读

Using results of Anderson & Goodman (1957), we develop empirical Bayes estimates for the transition probabilities of a finite stationary Markov chain. Some asymptotic properties of these estimators are also derived.

线性回归模型的贝叶斯最优设计AI 解读

A Bayesian version of Elfving's theorem is given for the $\mathbf{c}$-optimality criterion with emphasis on the inherent geometry. Conditions under which a one-point design is Bayesian $\mathbf{c}$-optimum are described. The class of prior precision matrices $R$ for which the Bayesian $\mathbf{c}$-optimal designs are supported by the points of the classical $\mathbf{c}$-optimal design is characterized. It is proved that the Bayesian $\mathbf{c}$-optimal design, for large $n,$…

正态方差的改进不变置信区间AI 解读

Confidence intervals for the variance of a normal distribution with unknown mean are constructed which improve upon the usual shortest interval based on the sample variance alone. These intervals have guaranteed coverage probability uniformly greater than a predetermined value $1-\alpha$ and have uniformly shorter length. Using information relating the size of the samples mean to that of the sample variance, we smoothly shift the usual minimum length interval closer to zero,…

非参数回归中的极小极大贝叶斯估计AI 解读

One observes $n$ data points, $(\mathbf{t}_i, Y_i),$ with the mean of $Y_i$, conditional on the regression function $f,$ equal to $f(\mathbf{t}_i).$ The prior distribution of the vector $\mathbf{f} = (f(\mathbf{t}_1), \ldots, f(\mathbf{t}_n))^t$ is unknown, but lies in a known class $\Omega.$ An estimator, $\hat{\mathbf{f}},$ of $\mathbf{f}$ is found which minimizes the maximum $E\|\hat{\mathbf{f}} - \mathbf{f}\|^2.$ The maximum is taken over all priors in $\Omega$ and the…

带协变量的单臂老虎机问题AI 解读

As does Woodroofe, we consider a Bayesian sequential allocation between two treatments that incorporates a covariate. The goal is to maximize the total discounted expected reward from an infinite population of patients. Although our model is more general than Woodroofe's, we are able to duplicate his main result: The myopic rule is asymptotically optimal.

线性模型中的贝叶斯预测：小区域估计应用AI 解读

This paper introduces a hierarchical Bayes (HB) approach for prediction in general mixed linear models. The results find application in small area estimation. Our model unifies and extends a number of models previously considered in this area. Computational formulas for obtaining the Bayes predictors and their standard errors are given in the general case. The methods are applied to two actual data sets. Also, in a special case, the HB predictors are shown to possess some…

可忽略性与粗化数据AI 解读

We present a general statistical model for data coarsening, which includes as special cases rounded, heaped, censored, partially categorized and missing data. Formally, with coarse data, observations are made not in the sample space of the random variable of interest, but rather in its power set. Grouping is a special case in which the degree of coarsening is known and nonstochastic. We establish simple conditions under which the possible stochastic nature of the coarsening…