论文检索

大型空间数据集似然估计中的协方差截尾AI 解读

Maximum likelihood is an attractive method of estimating covariance parameters in spatial models based on Gaussian processes. But calculating the likelihood can be computationally infeasible for large data sets, requiring O(n3) calculations for a data set with n observations. This article proposes the method of covariance tapering to approximate the likelihood in this setting. In this approach, covariance matrixes are “tapered,” or multiplied element wise by a sparse…

非参数问题中后验分布的一致性AI 解读

We give conditions that guarantee that the posterior probability of every Hellinger neighborhood of the true distribution tends to 1 almost surely. The conditions are (1) a requirement that the prior not put high mass near distributions with very rough densities and (2) a requirement that the prior put positive mass in Kullback-Leibler neighborhoods of the true distribution. The results are based on the idea of approximating the set of distributions with a finite-dimensional…

统计决策理论导论AI 解读

The Bayesian revolution in statistics -- where statistics is integrated with decision making in areas such as management, public policy, engineering, and clinical medicine -- is here to stay. Introduction to Statistical Decision Theory states the case and in a self-contained, comprehensive way shows how the approach is operational and relevant for real-world decision making under uncertainty. Starting with an extensive account of the foundations of decision theory, the…

偏序偏好的表示AI 解读

This essay considers decision-theoretic foundations for robust Bayesian statistics. We modify the approach of Ramsey, de Finetti, Savage and Anscombe and Aumann in giving axioms for a theory of robust preferences. We establish that preferences which satisfy axioms for robust preferences can be represented by a set of expected utilities. In the presence of two axioms relating to state-independent utility, robust preferences are represented by a set of probability/utility…

状态依赖效用AI 解读

Several axiom systems for preference among acts lead to a unique probability and a state-independent utility such that acts are ranked according to their expected utilities. These axioms have been used as a foundation for Bayesian decision theory and subjective probability calculus. In this article we note that the uniqueness of the probability is relative to the choice of what counts as a constant outcome. Although it is sometimes clear what should be considered constant,…

并行计算在统计推断中的应用AI 解读

Recent advances in parallel computation (e.g., Eddy and Schervish 1986; Gardner, Gerard, Mowers, Nemeth, and Schnabel 1986) have made it possible for a network of microcomputers to act together as a parallel processor using data-flow algorithms (see O'Leary and Stewart 1985). A data-flow algorithm is one in which the sequence of computations is not scheduled a priori, but rather is determined by the order in which computations are completed. Many statistical problems can be…

并行计算在统计推断中的应用AI 解读

Recent advances in parallel computation (e.g., Eddy and Schervish 1986; Gardner, Gerard, Mowers, Nemeth, and Schnabel 1986) have made it possible for a network of microcomputers to act together as a parallel processor using data-flow algorithms (see O'Leary and Stewart 1985). A data-flow algorithm is one in which the sequence of computations is not scheduled a priori, but rather is determined by the order in which computations are completed. Many statistical problems can be…

外部贝叶斯意见汇总算子的刻画AI 解读

When a panel of experts is asked to provide some advice in the form of a group probability distribution, the question arises as to whether they should synthesize their opinions before or after they learn the outcome of an experiment. If the group posterior distribution is the same whatever the order in which the pooling and the updating are done, the pooling mechanism is said to be externally Bayesian by Madansky (1964). In this paper, we characterize all externally Bayesian…

用于贝叶斯更新的专家判断建模AI 解读

This paper examines how a Bayesian decision maker would update his/her probability $p$ for the occurrence of an event $A$ in the light of a number of expert opinions expressed as probabilities $q_1, \cdots, q_n$ of $A$. It is seen, among other things, that the linear opinion pool, $\lambda_0p + \sum^n_{i = 1} \lambda_iq_i$, corresponds to an application of Bayes' Theorem when the decision maker has specified only the mean of the marginal distribution for $(q_1, \cdots, q_n)$…

面向使用者的统计推断AI 解读

A class of inferential procedures (called user-oriented procedures) related to the equal probability test of Arrow (1960) is introduced for use in many univariate problems. These procedures require that experimenters be able to interpret the parameters about which they wish to make inference. The class of procedures include confidence intervals associated with the equal probability test as well as an analogue to the P value. The confidence intervals are easier to interpret…

面向使用者的统计推断AI 解读

A class of inferential procedures (called user-oriented procedures) related to the equal probability test of Arrow (1960) is introduced for use in many univariate problems. These procedures require that experimenters be able to interpret the parameters about which they wish to make inference. The class of procedures include confidence intervals associated with the equal probability test as well as an analogue to the P value. The confidence intervals are easier to interpret…

判别分析中正确分类率的渐近展开AI 解读

When classifying an observation into one of $k$ multivariate normal distributions based on samples of correctly classified observations, two estimates of the probability of correct classification, called the apparent and plug-in correct classification rates, are considered. Asymptotic expansions are found for the means and variances of these estimates. It is shown that these expansions can be used to help reduce the bias of the estimates. In the course of finding the…

分类错误率均值与方差的渐近展开AI 解读

The problem of classifying an observation X into one of k multivariate normal distributions is considered. When samples are used to estimate the population parameters, the probabilities of correct classification, and the associated error rates, are random variables. Asymptotic expansions for the expected values and variances of these random variables, in terms of the inverses of the sample sizes, are found. Simulations have been performed to evaluate the expansions.

分类错误率均值与方差的渐近展开AI 解读

The problem of classifying an observation X into one of k multivariate normal distributions is considered. When samples are used to estimate the population parameters, the probabilities of correct classification, and the associated error rates, are random variables. Asymptotic expansions for the expected values and variances of these random variables, in terms of the inverses of the sample sizes, are found. Simulations have been performed to evaluate the expansions.