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未识别测量误差模型中由非正规先验得到正规后验AI 解读

The problem considered is inference in a simple errors-in-variables model where consistent estimation is impossible without introducing additional exact prior information. The probabilistic prior information required for Bayesian analysis is found to be surprisingly light: despite the model's lack of identification, a proper posterior is guaranteed for any bounded prior density, including those representing improper priors. This result is illustrated with the improper…

似然区域的稳健贝叶斯解释AI 解读

Likelihood regions are shown to be robust in the sense that their posterior probability content is relatively insensitive to contaminations of the prior. This provides a Bayesian interpretation of regions that are commonly used by frequentists to construct confidence intervals and whose use are also advocated by the pure likelihood approach.

序贯点估计中局部极小极大遗憾的渐近下界AI 解读

Let $\Omega$ be an interval and let $F_\omega, \omega \in \Omega,$ denote a one-parameter exponential family of probability distributions on $\mathscr{R} = (-\infty, \infty),$ each of which has a finite mean $\theta,$ depending on some unknown parameter $\omega \in \Omega.$ The main results of this paper determine an asymptotic lower bound for the local minimax regret, under a general smooth loss function and for a general class of estimators of $\theta.$ This bound is…

非正函数期望与方差的完全指数型拉普拉斯近似AI 解读

Tierney and Kadane (1986) presented a simple second-order approximation for posterior expectations of positive functions. They used Laplace's method for asymptotic evaluation of integrals, in which the integrand is written as f(θ)exp(-nh(θ)) and the function h is approximated by a quadratic. The form in which they applied Laplace's method, however, was fully exponential: The integrand was written instead as exp[− nh(θ) + log f(θ)]; this allowed first-order approximations to…

稳定美国癌症死亡率地图的经验贝叶斯方法AI 解读

"The geographic mapping of age-standardized, cause-specific death rates is a powerful tool for identifying possible etiologic factors, because the spatial distribution of mortality risks can be examined for correlations with the spatial distribution of disease-specific risk factors. This article presents a two-stage empirical Bayes procedure for calculating age-standardized cancer death rates, for use in mapping, which are adjusted for the stochasticity of rates in small…

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贝叶斯决策程序在遗传连锁推断中的应用AI 解读

The purpose of this article is to introduce the concept of O-Ki loss to the inference of genetic linkage. The prior information proposed by Elston and Lange (1975) was used. To help geneticists to understand the implications of the loss function and the Bayes decision rule, the Bayes decision procedure proposed in this article was suggested to be treated as a conventional test statistic. Then it seems almost natural to compare the performance of power of the statistic…

贝叶斯决策程序在遗传连锁推断中的应用AI 解读

The purpose of this article is to introduce the concept of O-Ki loss to the inference of genetic linkage. The prior information proposed by Elston and Lange (1975) was used. To help geneticists to understand the implications of the loss function and the Bayes decision rule, the Bayes decision procedure proposed in this article was suggested to be treated as a conventional test statistic. Then it seems almost natural to compare the performance of power of the statistic…

统计信息与似然：批判性论文集AI 解读

I Information and Likelihood.- I Recovery of Ancillary Information.- 0. Notes.- 1. Introduction.- 2. The Sample Size Analogy.- 3. A Logical Difficulty.- 4. Conceptual Statistical Experiments.- II Statistical Information and Likelihood Part I: Principles.- 0. Notes.- 1. Statistical Information.- 2. Basic Definitions and Relations.- 3. Some Principles of Inference.- 4. Information as a Function.- 5. Fisher Information.- 6. The Likelihood Principle.- III Statistical Information…

二元二项分布的贝叶斯推断AI 解读

A bivariate distribution is investigated in connection with an application in microbiology. It has binomial marginal and conditional distributions. The parameter structure is examined, and it is shown that a conjugate Bayesian prior distribution arises from prior independence specifications. Under these specifications the usual limiting conjugate prior can be obtained via invariance considerations.

二维列联表潜类别分析的贝叶斯方法AI 解读

Latent class analysis in two-way contingency tables usually suffers from unidentifiability problems. These an be overcome by using Bayesian techniques in which prior distributions are assumed on the latent parameters. Application of these techniques, however, involves some unusual computational difficulties. Bayesian techniques suitable for latent class analyses together with a remedy to the computational difficulties are discussed in this paper.

非正常先验与有限可加先验下的相容推断AI 解读

Conditions are given for the formal posterior of an improper prior to be coherent and applied to translation models. An example is given of a proper countably additive statistical model and a finitely additive prior for which there is no posterior.

正态均值估计：损失的频率学派估计AI 解读

In estimation of a $p$-variate normal mean with identity covariance matrix, Stein-type estimators can offer significant gains over the $\operatorname{mle}$ in terms of risk with respect to sum of squares error loss. Their maximum risk is still equal to $p$, however, which will typically be their "reported loss." In this paper we consider use of data-dependent "loss estimators." Two conditions that are attractive for such a loss estimator are that it be an improved loss…

单峰污染先验下后验量的取值范围AI 解读

We consider the problem of robustness or sensitivity of given Bayesian posterior criteria to specification of the prior distribution. Criteria considered include the posterior mean, variance and probability of a set (for credible regions and hypothesis testing). Uncertainty in an elicited prior, $\pi_0$, is modelled by an $\varepsilon$-contamination class $\Gamma = \{\pi = (1 - \varepsilon)\pi_0 + \varepsilon q, q \in Q\}$, where $\varepsilon$ reflects the amount of…

We consider dynamic procedures for sampling from a process (a Brownian motion) and stopping it after a change is detected. The basic idea is to conduct a sequence of similar SPRT's, each one of them done in negligible time, while not sampling at all between them. The procedures detect the change point much faster than the standard procedures with the same sampling rate and time to false alarm, but hold the sampling rate constant.

贝叶斯自助法均值的二阶渐近性质AI 解读

It is shown that the Bayesian bootstrap approximation to the posterior distribution of the unknown mean (with respect to a Dirichlet process prior) is more accurate than both the standard normal approximation and the bootstrap approximation. It is also shown that the Bayesian bootstrap approximation to the sampling distribution of the sample average is not as accurate as the bootstrap approximation.

存在干扰参数时假设显著性检验的广义 p 值AI 解读

This article examines some problems of significance testing for one-sided hypotheses of the form H 0 : θ ≤ θ 0 versus H 1 : θ > θ 0, where θ is the parameter of interest. In the usual setting, let x be the observed data and let T(X) be a test statistic such that the family of distributions of T(X) is stochastically increasing in θ. Define Cx as {X : T(X) — T(x) ≥ 0}. The p value is p(x) = sup θ≤θ0 Pr(X ∈ Cx | θ). In the presence of a nuisance parameter η, there may not exist…

卡尔曼滤波模型的稳健化AI 解读

Kalman filter models based on the assumption of multivariate Gaussian distributions are known to be nonrobust. This means that when a large discrepancy arises between the prior distribution and the observed data, the posterior distribution becomes an unrealistic compromise between the two. In this article we discuss a rationale for how to robustify the Kalman filter. Specifically, we develop a model wherein the posterior distribution will revert to the prior when extreme…

模型的局部影响AI 解读

This article develops a general method for assessing the influence of model assumptions in a Bayesian analysis. We assume that model choices are indexed by a hyperparameter with some given initial choice. We use the term “model” to encompass both the sampling model and the prior distribution. We wish to assess the effect of changing the hyperparameter away from the initial choice. We are performing a sensitivity analysis, with the hyperparameter defining our perturbations.…

含随机效应与 AR(1) 误差的纵向数据模型AI 解读

For longitudinal data on several individuals, linear models that contain both random effects across individuals and autocorrelation in the within-individual errors are studied. A score test for autocorrelation in the within-individual errors for the “conditional independence” random effects model is first developed. An explicit maximum likelihood estimation procedure using the scoring method for the model with random effects and (autoregressive) AR(1) errors is then derived.…

论参数密度估计AI 解读

The paper makes a critical assessment of Aitchison's criterion of density estimation. It seems not to satisfy certain intuitive requirements. A new criterion based on decisions theoretic considerations is introduced. It is shown through examples that the judgement about the choice of density estimates is seriously dependent on the criterion chosen. Some other density estimates are introduced which look similar to Bayesian predictive density estimates without using a prior…

预测分布的最优报告AI 解读

Consider a problem in which you and a group of other experts must report your individual predictive distributions for an observable random variable X to some decision maker. Suppose that the report of each expert is assigned a prior weight by the decision maker and that these weights are then updated based on the observed value of X. In this situation you will try to maximize your updated, or posterior, weight by appropriately choosing the distribution that you report,…

季节调整的敏感性分析：实证案例研究AI 解读

Three detailed case studies illustrating the seasonal analysis of economic time series are presented using component models for seasonal and nonseasonal behavior. Analyses are performed within a semi-Bayesian framework where inferences for target quantities of interest, such as seasonally adjusted values, are obtained as posterior distributions conditional on observed data and fitted parameter values. Such an approach is similar to previous model-based methods of seasonal…

均值乘积的估计：基于参考先验的贝叶斯分析AI 解读

Suppose that we observe X ∼ N(α, 1) and, independently, Y ∼ N(β, 1), and are concerned with inference (mainly estimation and confidence statements) about the product of means θ = αβ. This problem arises, most obviously, in situations of determining area based on measurements of length and width. It also arises in other practical contexts, however. For instance, in gypsy moth studies, the hatching rate of larvae per unit area can be estimated as the product of the mean of egg…