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非独立同分布数据下弹着精度分位数的可行贝叶斯估计AI 解读

An important measure of accuracy for problems of directing projectiles at targets is the circular error probable (CEP), a bivariate version of a 50% quantile point. This article presents a Bayesian procedure for estimating CEP when the projectile impact measurements are not iid, which is the case of usual practical interest. Our interest in a Bayesian procedure is motivated by a desire to combine accuracy information from several different sources. Except for the simplest…

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…

似然比与条件似然比检验的贝叶斯及频率学派 Bartlett 修正AI 解读

SUMMARY This paper characterizes priors under which the Bayesian and frequentist Bartlett corrections for the likelihood ratio and the conditional likelihood ratio (CLR) statistics differ by o(1). It is seen that, except for sample points with negligible probability, the CLR statistic has a posterior distribution for which a posterior Bartlett correction exists. This observation leads to an alternative proof of the existence of a frequentist Bartlett correction for the CLR…

正态位置参数后验矩的精确与近似表达AI 解读

SUMMARY The forms of first and second posterior moments for a normal location parameter are identified for a rather general class of prior distributions. Exact and approximate illustrations are given where the prior distribution is double exponential or Student t respectively.

贝叶斯先验征询的诊断方法AI 解读

One elicitation diagnostic identifies a family of prior distributions that are so diffuse that they are practically equivalent to the "completely" diffuse prior. Another elicitation diagnostic identifies a family of prior distributions that concentrate enough mass in the neighborhood of zero that they are practically equivalent to the dogmatic prior that sets a parameter exactly equal to zero. If either question thus posed can be answered in the affirmative then there is no…

利用虚拟观测构造异常值模型的贝叶斯因子AI 解读

Suppose we think that most observations in a sample have been generated from a distribution with density f(x) but we fear that a few outliers from a distribution with density g(x) may have contaminated our sample. In many situations, we might assume that f(x) is a density depending on a parameter θ and that g(x) is of the same form as f but with parameter θ + δ or θδ. A number of Bayesian models for this problem when f is normal have been discussed by Freeman. He points out…

约束贝叶斯估计及其应用AI 解读

Bayesian techniques are widely used in these days for simultaneous estimation of several parameters in compound decision problems. Often, however, the main objective is to produce an ensemble of parameter estimates whose histogram is in some sense close to the histogram of population parameters. This is for example the situation in subgroup analysis, where the problem is not only to estimate the different components of a parameter vector, but also to identify the parameters…

用扩展卡尔曼滤波估计多变量动态广义线性模型的后验众数AI 解读

A family of multivariate dynamic generalized linear models is introduced as a general framework for the analysis of time series with observations from the exponential family. Besides common conditionally Gaussian models, this article deals with univariate models for counted and binary data and, as the most interesting multivariate case, models for nonstationary multicategorical time series. For univariate responses, a related yet different class of models has been introduced…

基于 DNA 指纹的法医推断AI 解读

The recent discovery of hypervariable regions of the human genome provides scientists with an important new tool for forensic inference. The DNA data obtained from these hypervariable regions have been dubbed DNA fingerprints. Despite the potential power of DNA fingerprints, their use has been fraught with controversy, deriving in part from a lack of statistical methods to summarize the information contained in a DNA fingerprint. This article provides such a method, useful…

预测工作记忆失误：主观贝叶斯模型选择方法AI 解读

We use Bayes factors to compare two alternative characterizations of human working memory load in their ability to predict errors in database query-writing tasks. The first measures working memory load by the number of different features each task contains, while the second attempts instead to measure the complexity of the task by giving more weight to features that require more mental time for their correct execution. We reanalyze data from a previously conducted experiment…

利用 Gibbs 采样分析参数约束与截断数据问题AI 解读

Constrained parameter problems arise in a wide variety of applications, including bioassay, actuarial graduation, ordinal categorical data, response surfaces, reliability development testing, and variance component models. Truncated data problems arise naturally in survival and failure time studies, ordinal data models, and categorical data studies aimed at uncovering underlying continuous distributions. In many applications both parameter constraints and data truncation are…

期望界限的计算AI 解读

One method for evaluating the sensitivity of a Bayesian analysis is to embed the prior into a class of priors. Then bounds on prior and posterior quantities of interest must be computed. This approach to inference, often called robust Bayesian inference, has received much attention lately. Implementing robust Bayesian methods entails difficult computations, especially if the parameter space is high dimensional. In this article we develop a Monte Carlo approach to computing…

基于DNA指纹的法医学推断AI 解读

The recent discovery of hypervariable regions of the human genome provides scientists with an important new tool for forensic inference. The DNA data obtained from these hypervariable regions have been dubbed DNA fingerprints. Despite the potential power of DNA fingerprints, their use has been fraught with controversy, deriving in part from a lack of statistical methods to summarize the information contained in a DNA fingerprint. This article provides such a method, useful…

贝叶斯分析中的适当似然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…

大量干扰参数下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…

参数非线性函数后验密度的拉普拉斯展开AI 解读

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…

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信息不对称下的汽车保险费率制定AI 解读

Abstract Automobile insurance is an example of a market where multi‐period contracts are observed. This form of contract can be justified by asymmetrical information between the insurer and the insured. Insurers use risk classification together with bonus‐malus systems. In this paper we show that the actual methodology for the integration of these two approaches can lead to inconsistencies. We develop a statistical model that adequately integrates risk classification and…

利用先验信息比较试验处理与对照的最优设计AI 解读

Bayes $A$-optimal designs for the one-way and the two-way elimination of heterogeneity models and optimal $\Gamma$-minimax designs for the one-way elimination of heterogeneity model for experiments to compare test treatments with a control are given. Properties such as robustness, of these designs are studied. Optimality results are derived in the exact theory setup.

有限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.

非贝叶斯分类规则的错误率与 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.

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.

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