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AR(1) 模型分析中的平坦先验与无知先验AI 解读

Abstract The paper compares, by a Monte‐Carlo study based on an AR(1) model, the performance of the flat prior and the ignorance prior suggested by Phillips. It argues that the ignorance prior gives heavy weight to values of the autoregressive parameter p higher than 1, and hence distorts the sample evidence as summarized in the likelihood function. It yields bimodal posterior distributions, with the second mode at p higher than 1, even when the true value of p is…

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批评批评者：随机趋势的客观贝叶斯分析AI 解读

Abstract In two recent articles, Sims (1988) and Sims and Uhlig (1988/1991) question the value of much of the ongoing literature on unit roots and stochastic trends. They characterize the seeds of this literature as ‘sterile ideas’, the application of nonstationary limit theory as ‘wrongheaded and unenlightening’, and the use of classical methods of inference as ‘unreasonable’ and ‘logically unsound’. They advocate in place of classical methods an explicit Bayesian approach…

单位根贝叶斯推断的不同路径AI 解读

Abstract This paper is a comment on P. C. B. Phillips, ‘To criticise the critics: an objective Bayesian analysis of stochastic trends’ [Phillips, (1991)]. Departing from the likelihood of an univariate autoregressive model different routes that lead to a posterior odds analysis of the unit root hypothesis are explored, where the differences in routes are due to the different choices of the prior. Improper priors like the uniform and the Jeffreys prior are less suited for…

构造准确参数经验贝叶斯置信区间的样本再利用方法AI 解读

SUMMARY Parametric empirical Bayes (EB) methods of point estimation for a vector of unknown parameters date to the landmark paper of James and Stein (1961). The usual approach is to use the mean of the estimated posterior distribution of each parameter, where the estimation of the prior parameters (‘hyperparameters’) is accomplished through the marginal distribution of the data. While point estimates computed this way usually perform well, interval estimates based on the…

污染分布部分已知时的 ε 污染稳健贝叶斯分析AI 解读

SUMMARY Prior distributions of the form π=(1−ϵ)π0+ϵq,π0 being the base elicited prior, q being contamination and ϵ reflecting the amount of error in π0 that is deemed possible, are considered. It is assumed that π0 is completely specified and that only some quantiles of q are known. As π varies over this class, the ranges of the posterior mean and of the posterior probabilities of an arbitrary set are determined. Some examples including hypotheses testing related to a…

后验贝叶斯因子AI 解读

SUMMARY A general procedure for computing Bayes factors for the comparison of arbitrary models is described, based on the use of the posterior mean of the likelihood under each model rather than the usual prior mean. The use of the posterior mean has several advantages, including reduced sensitivity to variations in the prior and the avoidance of the Lindley paradox in testing point null hypotheses. The frequency properties of the new procedure are evaluated in standard…

贝叶斯与经典问题中直径和体积最小的置信集合AI 解读

If $X \sim P_\theta, \theta \in \Omega$ and $\theta \sim G \ll \mu$, where $dG/d\mu$ belongs to the convex family $\Gamma_{L, U} = \{g: L \leq \operatorname{cg} \leq U$, for some $c > 0\}$, then the sets minimizing $\lambda(S)$ subject to $\inf_{G \in \Gamma_{L,U}} P_G(S\mid X) \geq p$ are derived, where $P_G(S\mid X)$ is the posterior probability of $S$ under the prior $G$, and $\lambda$ is any nonnegative measure on $\Omega$ such that $\mu \ll \lambda \ll \mu$.…

Certain orthogonal polynomials are employed to estimate the prior distribution of the parameter of natural exponential families with quadratic variance functions in an approach which combines Bayesian and nonparametric empirical Bayesian methods. These estimates are based on samples from the marginal distribution rather than the conditional distribution.

某些贝叶斯估计量的变分形式AI 解读

A general representation is obtained for the formal Bayes estimator of a parameter matrix. We assume that the prior distribution is symmetric in some sense, but it is not specified otherwise. The formal Bayes risk is minimized subject to order constraints by a variational technique; hence our representation is called "the variational form of the Bayes estimator" (VFBE). The VFBE is used to obtain estimators that have good frequency properties relative to the usual…

比较实验与小区域估计中的贝叶斯及非贝叶斯程序：计算、频率学性质与联系AI 解读

The estimation of a treatment contrast from experimental data and the estimation of a small-area mean are special cases of the prediction of the realization of a linear combination of fixed and random effects in a possibly unbalanced two-part mixed linear model. In this article a Bayesian approach to point and interval prediction is presented and its computational requirements are examined. Differences between the Bayesian approach and the traditional (classical) approach…

回归参数稳定性的贝叶斯显著性检验AI 解读

This paper presents a Bayesian significance test for stationarity of a regression equation using the highest posterior density credible set. In addition, a solution to the Behrens-Fisher problem is provided. From a Monte Carlo simulation study, it has been shown that the Bayesian significance test has stronger power than the Cusum and the Cusum of squares tests. The Bayesian significance test may be useful in detecting individual parameter nonstationarity.

存在删失时的贝叶斯残差分析AI 解读

Use of the posterior distribution of the realized error terms for residual analysis in a linear model was advocated by Zellner (1975) and Zellner & Moulton (1985). The same idea was used by Chaloner & Brant (1988) to define outliers and calculate posterior probabilities of observations being outliers. This paper extends the same concept to other models, including regression models for lifetime data, by using an approach similar to that of Cox & Snell (1968). Residual plots…

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指数回归模型推断的无信息先验AI 解读

In the exponential regression model, inference concerning the regression parameter is notoriously difficult, even when using the Bayesian noninformative prior approach. The reference prior approach (Bernardo, 1979; Berger & Bernardo, 1989) is considered, and argued to yield very satisfactory inferences. Estimation and credible sets are considered in a specific example.

贝叶斯与非贝叶斯区间估计之间的关系AI 解读

SUMMARY Let Y 1, ..., Y n denote independent observations each distributed according to a density depending on a scalar parameter θ. Suppose that we are interested in constructing an interval estimate for 0. One approach is to construct a confidence region with a specified coverage probability based on the likelihood ratio test statistic. Another approach is to construct a highest posterior density region with a specified posterior probability. The goal of this paper is to…

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现值关系中的协整检验AI 解读

A Bayesian methodology is used to examine the bivariate time series properties of stock prices and dividends. The hypothesis that stock prices and dividends are cointegrated is emphasized. Exact small sample results are calculated using a specific parameterization for the bivariate model. Some commonly encountered problems in conventional cointegration tests based on asymptotic theory are thereby eliminated. We consider three hypotheses whose nonlinear form entails the need…

实际产出的跨期性质：贝叶斯分析AI 解读

This paper analyzes the univariate properties of real output and extends traditional analyzes in three ways: (1) a Bayesian approach is taken; (2) extensive cross-country comparisons are performed; and (3) a model is developed which allows for the possibility that real output may be fractionally integrated. In addition, standard comparisons between ARIMA and deterministic trend models are made. The class of fractionally integrated processes, while possessing certain…