日期精度：到日 2009 篇 · 到月 2034 篇 · 到年 253 篇 · 未提供 1 篇
序贯估计程序可由固定样本实现的一类情形
Conditions are found under which the Bayes sequential estimate t of a parameter θ is obtained by working from a sample of fixed size. These conditions are outlined in the third paragraph of ξ1. The multi-parameter case is considered in ξ3.
统计推断的逻辑
Preface 1. Long run frequencies 2. The chance set-up 3. Support 4. The long run 5. The law of likelihood 6. Statistical tests 7. Theories of testing 8. Random sampling 9. The fiducial argument 10. Estimation 11. Point estimation 12. Bayes' theory 13. The subjective theory.
In this paper we consider the specification and estimation of the Cobb-Douglas production function model. After reviewing the "traditional " specifying assumptions for the model which are based on deterministic profit maximization, we develop a model in which profits are stochastic and in which maximization of the mathematical expectation of profits is posited. "Sampling theory " and Bayesian estimation techniques for this model are presented. 1.
若干经典假设的贝叶斯检验及其序贯临床试验应用
Consider someone who sets out to collect data sequentially in such a way as to disprove a hypothesis, H 0, about the value of θ, the mean of a normal distribution. Observation is continued as long as the posterior probability of H 0 exceeds α1 and stopped when it falls below it. It is shown that if a non-zero prior probability, p, is assigned to H 0(0≤α1 < p) and the remaining prior probability is spread over alternate values of θ that the probability that H 0 will…
有限总体抽样的新方法（二）：分布无关充分性
Summary The idea that in some situations the prior knowledge about the unknown parameters could be formulated as a class of prior distributions, which could be used, not necessarily through Bayes posterior probability, for subsequent inference, is already present in Godambe (1955). In the present paper, the concept of distribution-free linear sufficiency or in short linear sufficiency, originally due to Barnard (1963b) but redefined by the present author (Part I), is…
固定效应单因素方差分析中组间方差不等的贝叶斯视角
Abstract : The effect of inequality of variance on the standard F-tests for one-way and two-way analysis of variance classification has been examined previously. Certain results found by Box for the one-way classification are examined. A Bayesian analysis is shown to throw light on the consequences of Box's work in a given experimental situation.
两个随机变量的渐近序贯试验设计
Summary Given two independent random variables with densities f1 and f2, we test H1: f1 = f11, f2 = f12 versus H2: f1 = f21, f2 = f22, where the fij are known densities (i,j = 1,2). We study asymptotic Bayes sequential procedures as the cost of each observation approaches zero. An asymptotic expression for the Bayes risk is found, and necessary and sufficient conditions for a decision rule to be asymptotically Bayes are derived. We study a class of tests which we call tandem…
有限决策问题的序贯复合规则
Summary Asymptotically optimal rules are obtained for the sequential compound decision problem, where the component problem involves a finite parameter space and a finite action space. It is shown that under some regularity conditions the rule, which at each stage is a Bayes rule with respect to an estimate of the empirical distribution of the previous parameters, is asymptotically optimal. In the general situation, a randomized version of this rule is asymptotically…
关于 Welch–Peers 置信匹配先验的说明
Summary Welch and Peers have shown that it is possible to determine a prior distribution for a one-dimensional parameter by requiring that the associated one-sided Bayes intervals are asymptotically confidence intervals. It is shown in this note that their procedure does not apply if certain natural two-sided Bayes intervals are used.
方差分析中随机效应模型的贝叶斯分析
Bayesian methods are utilized to analyse a one-way random effect model yij = μ+ai+eij in which the errors eij are assumed to follow a first-order autoregressive series eij = ρei(j-1)+εij. For given value of ρ, the model can be reduced to that considered in our earlier paper (1965). It is shown that inferences about the variances σα2 = var(ai), and σ2 = var (εij) can be very sensitive to changes in the value of ρ assumed. In particular, in a set of data generated from a…
涉及两个随机变量的贝叶斯序贯设计
Sequential sampling is considered wherein, at each trial, the experimenter can choose to stop and take some action or else to perform one of two related experiments. An approximation to an asymptotically optimum decision rule is shown to be easily defined in practice and to be a Bayes rule in some cases. Average risks of this and other sequential design rules are compared.
单参数离散分布的平滑经验贝叶斯估计
A study is made of the simple empirical Bayes estimators proposed by Robbins (1956). These estimators are compared with ‘best’ conventional estimators in terms of their expected squared error ‘loss’. The object of the study is to determine the amount of prior data which would be needed for the empirical Bayes estimator to be preferred to the conventional estimator. It is concluded that the required number of previous observations is likely to be too large for the simple…
统计预测中的若干问题
SUMMARY A general framework is introduced for the study of inference and decision predictions about the outcome of a future experiment from the data of an independent informative experiment. This allows a simple classification of prediction problems, and shows the place of standard inference predictions within the framework. A Bayesian approach to decision prediction is then presented and techniques appropriate to a variety of realistic utility functions are developed.…
一种贝叶斯无差别先验构造程序
In a logical probability approach to inference, distributions on a parameter space are interpretable as representing states of knowledge, and any prevailing state of knowledge may be taken to have been arrived at from a previous state of ignorance (indifference) followed by an accumulation of prior data. In this paper an indifference procedure is introduced that requires postulating what size and what kind of samples will and will not (in a special sense) permit statistical…
概率论在刑事科学中的应用（二）
A general model for the evaluation of partial transfer evidence is developed in this article. This model is less restrictive than were the original models presented in an earlier paper, thus allowing it to be applied to a more general class of situations. A Bayesian approach to the problem of evidence evaluation is explored, and the probability of error calculated in the Bayesian model is shown to be a reasonable approximation to the probability of possible error calculated…