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Galton–Watson过程的后验渐近正态性与估计量渐近正态性AI 解读

SUMMARY For a Galton-Watson process with offspring distribution pθ, where θ is an unknown parameter, asymptotic posterior normality is established for θ and for the mean of the offspring distribution. A form of asymptotic normality for the mean of the offspring distribution is also obtained, without restriction on whether the process is supercritical or not, provided that the total number of offspring increases to infinity. A non-Bayesian procedure is suggested for testing…

精度、复杂度与贝叶斯模型确定AI 解读

SUMMARY In this paper a new criterion for model determination is proposed. An explicit decision theoretic approach to model selection is employed to derive a Bayes decision rule. The operational characteristics of the criterion are discussed and consistency is shown.

两人决策问题中的后验可实施性AI 解读

When a decision rule is implemented using a Bayesian incentive compatible mechanism in which the messages are publically obser vable, the players' information is augmented by their observation of each others' strategies. In this paper the authors study the set of Bayesian implementable decision rules which have the further property that the information c onveyed in the process of thier implementation does not invalidate the optimality of the players' strategies. Such rules…

稳定季节模式下的贝叶斯预测AI 解读

A multiplicative seasonal forecasting model for cumulative events in which, conditional on end- of-season totals being given and seasonal shape being known, it is shown that events occurring within the season are multinomially distributed is presented. The model uses the information contained in the arrival of new events to obtain a posterior distribution for end-of-season totals. Bayesian forecasts are obtained recursively in two stages: first, by predicting the expected…

删失生存数据的近似贝叶斯分析AI 解读

The Bayesian analysis of data arising from a location-scale regression model, and which may include a number of right-censored observations, is considered. The posterior distributions of the suitably normalized precision parameter and regression coefficient vector are shown to be well approximated by X2 and multivariate t distributions respectively. The ideas are illustrated using some clinical survival data.

估计总体规模与词汇量的多项分布贝叶斯方法AI 解读

We approach estimation of the size of a population or a vocabulary through a Bayesian analysis of the multinomial distribution. We view the sample as being generated from such a distribution with an unknown number of cells and unknown cell probabilities, and develop a Bayesian procedure to estimate the number of cells and the coverage of the sample. The prior distribution of the number of cells is arbitrary. Given that number, the cell probabilities are assumed to follow a…

关于多元岭回归AI 解读

A multivariate linear regression model with q responses as a linear function of p independent variables is considered with a p × q parameter matrix B. The least-squares or normal-theory maximum likelihood estimate of B is deficient in that it takes no account of the ‘across regression’ correlations, and ignores the Stein effect. A remedy was offered by Brown & Zidek (1980) in the form of a multivariate ridge estimator. A richer class of estimators is obtained here by casting…

三维列联表的贝叶斯对数线性估计AI 解读

This paper presents a Bayesian method to estimate the expected proportions in a three-way contingency table appropriate when prior knowledge about the main, first and second-order interaction effects can be described by a particular kind of exchange ability assumption. The proposed Bayes estimates are calculated by finding those values of the effects which maximize the resulting posterior distribution and can be used to explore the possibility that a nonsaturated submodel,…

优势比贝叶斯推断的最优样本分配AI 解读

The choice of ratio of sample sizes of two groups of binary observations for comparing two proportions is studied using a Bayesian approach. Prior uncertainty about the unknown proportions thus enters the design calculations.

确定线性时间序列模型的候选集合AI 解读

The paper applies selection criteria to order determination in linear time series models in a less mechanical fashion than is often found. This is achieved via posterior odds ratios and by applying concepts of grades of evidence advanced by Jeffreys (1961). It is shown how alternative specifications may be compared and this leads to the development of a practical method for determining a portfolio of different models, each of which may be regarded as reasonable for the data…

摘要暂缺

抽样未来：单变量时间序列模型预测的贝叶斯方法AI 解读

The Box–Jenkins methodology for modeling and forecasting from univariate time series models has long been considered a standard to which other forecasting techniques have been compared. To a Bayesian statistician, however, the method lacks an important facet—a provision for modeling uncertainty about parameter estimates. We present a technique called sampling the future for including this feature in both the estimation and forecasting stages. Although it is relatively easy…

贝叶斯模型监测AI 解读

SUMMARY A simple method of monitoring the predictive performance of a class of Bayesian models is introduced. The models involve sequential analyses of sequences of observations and are appropriate for a variety of monitoring and forecasting applications. For any given model, the monitoring technique is based on a comparison of the predictive ability of the model, measured by the observed values of predictive densities, with that of a single alternative. The alternative is…

区分时间序列中的异常值类型AI 解读

SUMMARY Distinguishing an outlier in a time series arising through measurement error from one arising through a perturbation of the underlying system can be of use in data validation. In this paper a method of testing for the presence of an outlier of unknown type is proposed. Then the properties of a rule based on the likelihood ratio which attempts to distinguish the two types of outlier are examined and compared with those of the corresponding Bayes rules. An example…

有限总体抽样的贝叶斯统计推断AI 解读

Bayesian statistical inference for sampling a finite population is studied by using the Dirichlet-multinomial process as prior. It is shown that if the finite population variables have a Dirichlet-multinomial prior, then the posterior distribution of the inobserved variables given a sample is also Dirichlet-multinomial. If the population size tends to infinity (the sample size is fixed), sampling without replacement from a Dirichlet multinomial process is equivalent to the…

二元响应临床试验模型的贝叶斯决策规则AI 解读

The risk in a trial to compare two medical treatments is borne by the patients who receive the inferior treatment during the experimental phase and by those remaining after the experiment who will all receive the inferior treatment if the results are misleading. The Bayes rule indicates, for the observed progression of successes and failures, when it is optimal to stop this experimental phase. This stopping rule can be described exactly, or nearly so, for symmetric two-point…

非参数贝叶斯回归AI 解读

It is desired to estimate a real valued function F on the unit square having observed F with error at N points in the square. F is assumed to be drawn from a particular Gaussian process and measured with independent Gaussian errors. The proposed estimate is the Bayes estimate of F given the data. The roughness penalty corresponding to the prior is derived and it is shown how the Bayesian technique can be regarded as a generalisation of variance components analysis. The…

贝叶斯预测模型的监控与适应AI 解读

Practical aspects of a new technique for monitoring and controlling the predictive performance of Bayesian forecasting models are discussed. The basic features of the approach to model monitoring introduced in a general setting in West (1986) are described and extended to a wide class of dynamic, nonnormal, and nonlinear Bayesian forecasting models. An associated method of automatically detecting and rejecting outliers and adapting models to abrupt structural changes in the…

抽样调查缺失值插补的贝叶斯程序AI 解读

A new method is proposed for imputation of missing values in sample survey data. The procedure uses standard statistical methodology, permits a general specification of the nonresponse process, and does not impose specific model assumptions. Prior information from past similar surveys or from other sources may be incorporated in a routine manner.

方差分量比的改进估计量AI 解读

The problem of estimating a ratio of variance components in the balanced one-way random effects model is considered. It is shown that in terms of mean squared error, the ML, REML (or truncated ANOVA), and Bayes modal estimators (using the noninformative prior) are inadmissible. An estimator that dominates all three is derived. Two other estimators that are adaptive in nature are also introduced. The new estimators are shown to possess much-improved mean squared error…

离散判别分析中核密度估计的另一种平滑选择AI 解读

The kernel method of estimating the cell probabilities of a multivariate categorical distribution, due to Aitchison & Aitken (1976), depends crucially on an unknown smoothing parameter λ. A method of estimating A is introduced which is explicitly connected to multivariate discrimination. The method, based on maximization of the leaving-one-out estimator of the nonerror rate, is shown to be Bayes risk strongly consistent. An example is given to illustrate the application.

近似预测似然AI 解读

A predictive likelihood is given which approximates both Bayes and maximum likelihood predictive inference by expansion of a posterior likelihood. This synthesizes and extends previous results and is widely applicable. The approximation usually differs from exact Bayes posterior predictive density by Op(n–2), and from exact predictive likelihood by Op(n–2) but does not depend on the availability of prior information and is applicable when exact predictive likelihood cannot…

摘要暂缺

回归中观测影响的决策理论度量AI 解读

SUMMARY A Bayesian decision-theoretic framework is used to define the influence of observations when fitting a regression model to data. Measures assessing an observation's influence on the posterior risk depend on the specification of the underlying loss function and prior assumptions. Illustrations are given for normal linear regression models.