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使用狄利克雷过程先验的贝叶斯多重比较AI 解读

We consider the problem of multiple comparisons from a Bayesian viewpoint. The family of Dirichlet process priors is applied in the form of baseline prior/likelihood combinations to obtain posterior probabilities for various hypotheses of equality among population means. The baseline prior/likelihood combinations considered here are beta/binomial and normal/inverted gamma with equal variances on treatment means. The prior probabilities of the hypotheses depend directly on…

组序贯临床试验：贝叶斯决策论设计的经典统计评价AI 解读

Bayesian decision-theoretic designs for a clinical trial comparing two treatments for a disease with binary outcomes are developed and evaluated. The probability of successful outcome with treatment i is denoted by pi , i = 1, 2, and prior knowledge regarding each pi is assumed to follow a beta distribution. The pi are assumed to be independent. To facilitate comparison with frequentist clinical trial designs, we take a hypothesis-testing approach. The null hypothesis is δ <…

贝叶斯非参数双臂老虎机AI 解读

Sequential selections are to be made from two stochastic processes, or "arms." At each stage the arm selected for observation depends on past observations. The objective is to maximize the expected sum of the first $n$ observations. For arm 1 the observations are identically distributed with probability measure $P$, and for arm 2 the observations have probability measure $Q; P$ is a Dirichlet process and $Q$ is known. An equivalent problem is deciding sequentially when to…

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…

不放回抽样的一类最优停止问题AI 解读

It is required to estimate exactly the number r of red balls in a population of n balls. The initial distribution of r is uniform on 0, …,n and further information can be obtained by sampling the balls sequentially without replacement at a cost of (i) 1, (ii) k, (iii) k2 for the kth ball. The problem is normalized by setting the optimal expected payoff for estimating prior to sampling and for estimating after sampling all n balls both equal to zero. Asymptotically as n ↑ ∞…

通过部件测试估计系统可靠性的最优抽样方案（一）：固定样本量AI 解读

A Bayesian decision theoretic approach is employed to compare sampling schemes designed to estimate the reliability of series and parallel systems by testing individual components. Quadratic loss is assumed and schemes are found which minimize Bayes risk plus sampling cost. Several kinds of initial information concerning the reliability of the individual components, all of which assume the components function independently, are considered. The case for which the initial…

不放回抽样中的一类最优停止问题AI 解读

It is required to estimate exactly the number r of red balls in a population of n balls. The initial distribution of r is uniform on 0, ..., n and further information can be obtained by sampling the balls sequentially without replacement at a cost of (i) 1, (ii) k, (iii) k2 for the kth ball. The problem is normalized by setting the optimal expected payoff for estimating prior to sampling and for estimating after sampling all n balls both equal to zero. Asymptotically as n -?…