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多参数指数族中简单假设贝叶斯检验的渐近行为AI 解读

The asymptotic form of the Bayes acceptance region is derived for testing simple null-hypotheses in multiparameter exponential families. This result suggests a reasonable definition for tests which might be called "almost-Bayes". The rate at which the risk of the Bayes test converges to zero is obtained, showing the nature of its dependence on the prior distribution and providing a basis for comparison of almost-Bayes procedures. Concluding remarks contain a brief discussion…

有限可加先验、融贯性与扩展容许性AI 解读

A decision maker is seen to be coherent in the sense of de Finetti if, and only if, his probabilities are computed in accordance with some finitely additive prior. If a bounded loss function is specified, then a decision rule is extended admissible (i.e., not uniformly dominated) if and only if it is Bayes for some finitely additive prior. However, if an improper countably additive prior is used, then decisions need not cohere and decision rules need not be extended…

模型维度的估计AI 解读

The problem of selecting one of a number of models of different dimensions is treated by finding its Bayes solution, and evaluating the leading terms of its asymptotic expansion. These terms are a valid large-sample criterion beyond the Bayesian context, since they do not depend on the a priori distribution.

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生存时间数据的非参数贝叶斯分析AI 解读

Summary A Bayesian analysis of the semi-parametric regression and life model of Cox (1972) is given. The cumulative hazard function is modelled as a gamma process. Both estimation of the regression parameters and of the underlying survival distribution are considered. The results are compared to the results obtained by other approaches.

密度估计、随机过程与先验信息AI 解读

Summary A method is proposed for the non-parametric estimation of a probability density, based upon a finite number of observations and prior information about the smoothness of the density. A logistic density transform and a reproducing inner product from the first-order autoregressive stochastic process are employed to represent prior information that the derivative of the transform is unlikely to change radically within small intervals. The posterior estimate of the…

Dirichlet 先验下的秩次估计AI 解读

Suppose that a sample of size $n$ from a distribution function $F$ is obtained. However, only $r(< n)$ values from the sample are observed, say $X_1,\cdots, X_r$. Without loss of generality, we can consider $X_1,\cdots, X_r$ to be the first $r$ values in the (unordered) sample. The problem is to estimate the rank order $G$ of $X_1$ among $X_1,\cdots, X_n$. The situations of interest include $F$ nonrandom, either known or unknown, and $F$ random. The random case assumes that $F$…

因果效应的贝叶斯推断：随机化的作用AI 解读

Causal effects are comparisons among values that would have been observed under all possible assignments of treatments to experimental units. In an experiment, one assignment of treatments is chosen and only the values under that assignment can be observed. Bayesian inference for causal effects follows from finding the predictive distribution of the values under the other assignments of treatments. This perspective makes clear the role of mechanisms that sample experimental…

方程系统参数的贝叶斯估计：蒙特卡洛积分的应用AI 解读

textabstractMonte Carlo (MC) is used to draw parameter values from a distribution defined on the structural parameter space of an equation system. Making use of the prior density, the likelihood, and Bayes' Theorem it is possible to estimate posterior moments of both structural and reduced form parameters. The MC method allows a rather liberal choice of prior distributions. The number of elementary operations to be preformed need not be an explosive function of the number of…

关于似然、贝叶斯与对预设值倾向的一则评论AI 解读

As judged by large sample efficiency, one can make use of a preconceived value in a considerably less modest way than Bayes's theorem permits, provided one respects the likelihood function.

二维列联表的经验贝叶斯方法AI 解读

An empirical Bayes method for smoothing two-way tables is presented. It is based on the use of the log linear model and a normal prior distribution. Estimation of the variance component in the prior is discussed, and two approximations are considered, one which utilizes the EM algorithm.

贝叶斯推断的必要性与接近贝叶斯形式的度量构造AI 解读

Many mathematical proofs of the necessity of Bayesian inference show, in effect, that betting procedures which have positive expected return for every value of an unknown parameter can be constructed to win money from non-Bayesian bookmakers. The yield of such betting procedures is here used as the basis for measures of the nearness to Bayesian form of the odds quoted by non-Bayesian bookmakers. Using one of these measures it is shown that the usual confidence intervals for…

用于回归模型选择的后验概率AI 解读

SUMMARY A simple Bayesian formula for the posterior probability of one of several regression models is shown to be systematically misleading unless all models have the same number of para- meters. Even in this case the use of improper priors leads to arbitrary inferences, as it does more generally. An alternative weighting for choosing a model is suggested and the relation- ship between significance tests and data-dependent priors mentioned. An alternative to the analysis of…

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多项概率估计与预检验问题的贝叶斯方法AI 解读

New Bayesian estimates are proposed for multinomial probabilities, when the prior distribution is a mixture of Dirichlet distributions. They are based upon a distributional approximation for the χ2 statistic and may be contrasted with the frequentist approximations recommended by other authors. An alternative is also suggested to the χ2 goodness-of-fit test, when it is employed as a preliminary test of significance. The new procedure possesses remarkably different…

用于社会项目评估的贝叶斯数据分析系统AI 解读

The evaluation of social programs is typically hampered by serious methodological problems. Adopting the approach of Bayesian simultaneous estimation proposed by Lindley and Smith (1972) and operationally developed by Jackson, Novick, and Thayer (1971), Novick, Lewis, and Jackson (1973), and Lewis, Wang, and Novick (1975), we demonstrate how some of these problems can be avoided or solved. To accomplish this, we extend the operational method to marginal m-group mean analysis…

基于选择性报告数据的似然与贝叶斯推断AI 解读

If the reported data of an experiment have been subject to selection, then inference from such data should be modified accordingly. We investigate the modification required to the face-value likelihood. In particular, we derive conditions under which no modification is necessary and the data can be taken at face value.

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指数族分布贝叶斯估计量的收缩变换AI 解读

Sufficient conditions are provided to ensure that the Bayes estimator with squared error loss for the natural parameter of an exponential family distribution is a linear function of the sample value, given that various contractions of the Bayes estimator are also Bayes estimators, generalizing a result of Meeden (1976).

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贝叶斯生命表分析AI 解读

Summary The moments of the posterior p.d.f. of the probability of surviving to time t, P(t), are obtained, assuming a time-dependent Poisson process for failures and i.i.d. gamma prior densities for the hazard function. For improper densities the results reduce to the Kaplan–Meier estimate of p(t) and to the Cox result for the comparison of two survival curves, which, because of the use of improper priors, may be inadmissible with respect to mean square error loss. A way of…

选择包含最优总体的子集：贝叶斯方法AI 解读

The problem of selecting a subset of $k$ populations $\pi_1, \cdots, \pi_k,$ which contains the "best" population, is considered. The unknown values $\theta_1, \cdots, \theta_k$ are the characteristics associated with $\pi_1, \cdots, \pi_k$ and the unknown population associated with $\theta_{\lbrack k\rbrack} = \max_i\theta_i$ is called the "best." It is assumed that, given $\mathbf{\theta} = (\theta_1, \cdots, \theta_k)$ the $\operatorname{pdf}$ of the independent random…