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某些序贯估计量的渐近最优性AI 解读

We give a decision-theoretic justification of a heuristic principle suggested by Robbins. Suppose a sequence $X_1, X_2, \cdots$ of independent random variables can be observed; they are known to be identically distributed with unknown mean and variance $u, \sigma^2(u)$ respectively. We assume further that the common distribution is of exponential type, so that the sample mean $\bar{X}$ is a sufficient statistic. The problem is to estimate $u$ taking into account the cost of…

判断估计量可容许性的启发式方法及其应用AI 解读

Questions of admissibility of statistical estimators are reduced to considerations involving differential inequalities. The coefficients of these inequalities involve moments of the underlying distributions; and so are, in principle, not difficult to derive. The methods are "heuristic" because it is necessary to verify on an ad-hoc basis that error terms are small. Some conditions on the structure of the problem are given which we believe will guarantee that these error…

单变量分布的多参数贝叶斯分析AI 解读

Bayesian analysis using Monte Carlo integration is a powerful method for univariate inference. This approach makes possible multiparameter flexibility within families of univariate distributions. These distributions are defined in this article by increasing spline functions superimposed on probability paper coordinate systems. Smoothing is controlled by the prior distribution. The prior distribution also can express uncertainties about the form of the tails when…

有限总体物种数的后验矩与发现新物种的后验概率AI 解读

By using a model of Hill for sampling from a finite population, the posterior moments of the number of species in the population and the posterior probability of finding a new species are obtained. Results are based on a negative binomial prior distribution on the number of species in the population and are appropriate for sampling both with and without replacement.

计量经济模型的统计分析AI 解读

In this article, a summary of some research bearing on the statistical analysis of econometric models is reviewed. Many estimation, testing, and prediction techniques used in econometrics have just large-sample justifications. Selected Bayesian inference results relating to econometric models are reviewed. On the problem of constructing econometric models, an approach that is a blend of traditional econometric and modern time series analysis techniques is described. Many…

推断、方法与决策：走向贝叶斯科学哲学AI 解读

One: Informative Inference.- 1 / Information.- 1. Introduction.- 2. The Utility of Information.- 3. Disinterested Information.- 4. Noiseless Information.- 5. Fisher's Information.- 6. Conclusion.- 2 / The Paradoxes of Confirmation.- 1. General Laws.- 2. Resolution of the Paradoxes.- 3. Lawlikeness.- 4. Conclusion.- 3 / Inductivism and Probabilism.- 1. The Induction Rule.- 2. The Import of Data.- 3. Uniformity and Discovery.- 4. Conditionalization.- 5. The Maximum Entropy…

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贝叶斯稳态预测模型的推广AI 解读

Summary The Bayesian Steady Forecasting model is generalized to a very wide class of processes other than the normal by defining the time series on the decision space. Examples of such processes are presented including a Beta-Binomial process, a Poisson-Gamma process and a Student-t sample distribution steady model. Simple updating relations are given for most of the processes discussed.

贝叶斯推断中的离群值排斥现象AI 解读

Summary Inference is considered for a location parameter given a random sample. Outliers are not explicitly modelled, but rejection of extreme observations occurs naturally in any Bayesian analysis of data from distributions with suitably thick tails. For other distributions outlier rejection behaviour can never occur. These phenomena motivate new definitions of outlier-proneness and outlier-resistance. The definitions and methodology are Bayesian but the conclusions also…

Lebesgue 指数族中接近最优速率的经验贝叶斯估计AI 解读

Asymptotically optimal (a.o.) empirical Bayes (EB) estimators are proposed. Speeds and the best possible speed at which these estimators are a.o. are investigated. The underlying component problem is the squared error loss estimation of $\theta$ based on an observation $X$ whose conditional (on $\theta$) $\operatorname{pdf}$ is of the form $u(x)C(\theta)\exp(\theta x)$. The function $u$ could have infinitely many discontinuities; $\theta$ is distributed according to an…

逐步贝叶斯程序AI 解读

Ordinarily a Bayesian estimation procedure uses one prior distribution to obtain a unique estimation rule (its Bayes rule). From the decision theoretical point of view, this procedure can be regarded as a convenient way to obtain admissible decision rules. However, many intuitively appealing, admissible estimation rules cannot be obtained directly in this way. We propose a new mechanism, called the Stepwise Bayesian Procedure (SBP). When the parameter space contains only…

预测似然AI 解读

The likelihood function is the common basis of all parametric inference. However, with the exception of an ad hoc definition by Fisher, there has been no such unifying basis for prediction of future events, given past observations. This article proposes a definition of predictive likelihood which can help to remove some nonuniqueness problems in sampling-theory predictive inference, and which can produce a simple prediction analog of the Bayesian parametric result, posterior…

(NOTE: Each chapter concludes with Problems and Complements, Notes, and References.) 1. Statistical Models, Goals, and Performance Criteria. Data, Models, Parameters, and Statistics. Bayesian Models. The Decision Theoretic Framework. Prediction. Sufficiency. Exponential Families. 2. Methods of Estimation. Basic Heuristics of Estimation. Minimum Contrast Estimates and Estimating Equations. Maximum Likelihood in Multiparameter Exponential Families. Algorithmic Issues. 3.…

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非加性模型的贝叶斯分析AI 解读

A Bayesian analysis of a model for two-group experimentation is given. This model assumes that responses in one group are systematically related to responses in the other group through a general linear function using both multiplicative and additive parameters.

近似贝叶斯预测分布与模型选择AI 解读

An observation is assumed to arise from one of k models that may depend on parameters. A prior distribution is specified by assigning probabilities to each of the models and by assigning probability densities to the parameters of each model. If an approximate prior distribution is used, the predictive distribution of a future observation will be approximate. Bounds on the error in the predictive distribution are derived from bounds on the error in the prior distribution. A…

样本对后验分布影响的一则札记AI 解读

This article studies when and how the posterior distribution responds monotonically to changing sample evidence. The monotone likelihood ratio (MLR) property, which implies stochastic order, is suggested as a convenient ordering to express and demonstrate this monotonicity.

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复合假设贝叶斯序贯检验的近似AI 解读

This paper deals with approximations to Bayesian sequential tests of composite hypotheses. If the distributions of the data form an exponential or truncation family, then such tests may be described by a continuation region in the space of $n$, the sample size, and $M_n$, the sufficient statistics, which are of fixed dimension. In this case Schwarz has been able to describe the asymptotic shape of the continuation region as the sampling cost $c$ approaches zero. We have…

利用狄利克雷过程混合估计二项分布参数AI 解读

The theory of Dirichlet processes is applied to the empirical Bayes estimation problem in the binomial case. The approach is Bayesian rather than being empirical Bayesian. When the prior is a Dirichlet process the posterior is a mixture of Dirichlet processes. Explicit estimators are given for the case of 2 and 3 parameters and compared with other empirical Bayes estimators by way of examples. Since the number of calculations become enormous when the number of parameters…

稀少记录错误的抽样与估计AI 解读

For each individual in a finite population a recorded value is available. A small proportion of the values is in error, all the errors being of the same sign and the maximum fractional error being known. It is required to obtain an upper confidence limit for the total error in the population. Various solutions, including a Bayesian one, are discussed for sampling with probability proportional to the recorded values, and the appropriateness of this form of sampling is…

Shannon 多样性指数的贝叶斯估计AI 解读

This paper is concerned with methods of estimating Shannon's information measure, and with the sampling properties of those estimates. A Bayesian approach is used to suggest two possible classes of estimators, and their properties are compared with those of the usual Shannon measure of diversity. Particular attention is given to comparisons involving the MacArthur model of species abundances.