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复杂系统中的知识表示AI 解读

SUMMARY Modern sensor technologies, especially in biomedicine, produce increasingly detailed and informative image ensembles, many extremely complex. It will be argued that pattern theory can supply mathematical representations of subject-matter knowledge that can be used as a basis for algorithmic ‘understanding’ of such pictures. After a brief survey of the basic principles of pattern theory we shall illustrate them by an application to a concrete situation: high…

对《随机波动模型的贝叶斯分析》的评论AI 解读

This article contains comments on “Bayesian Analysis of Stochastic Volatility Models,” by Jacquier, Poison, and Rossi. The Markov-chain Monte Carlo (MCMC) method proposed is compared empirically with a simulated maximum likelihood (SML) method. The MCMC and SML estimators yield very similar results, both when applied to actual data and in a Monte Carlo experiment.

随机波动模型的贝叶斯分析AI 解读

New techniques for the analysis of stochastic volatility models in which the logarithm of conditional variance follows an autoregressive model are developed. A cyclic Metropolis algorithm is used to construct a Markov-chain simulation tool. Simulations from this Markov chain converge in distribution to draws from the posterior distribution enabling exact finite-sample inference. The exact solution to the filtering/smoothing problem of inferring about the unobserved variance…

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《随机波动模型的贝叶斯分析》评论AI 解读

This article contains comments on 'Bayesian Analysis of Stochastic Volatility Models,' by Jacquier, Polson, and Rossi. The Markov-chain Monte Carlo (MCMC) method proposed is compared empirically with a simulated maximum likelihood (SML) method. The MCMC and SML estimators yield very similar results, both when applied to actual data and in a Monte Carlo experiment.

排序 Logit 模型：安大略省选民偏好的实证分析AI 解读

Abstract This study provides a Bayesian investigation of rank‐ordered multinominal logit models employing conjugate priors for standard multinomial logit models as well as other priors. Also considered is a specification test of the independence of irrelevant alternatives assumption. The proposed techniques are demonstrated in an empirical investigation of Ontario voter preferences before the 1988 Canadian Federal Election.

贝叶斯模型选择：渐近分析与精确计算AI 解读

SUMMARY Model determination is a fundamental data analytic task. Here we consider the problem of choosing among a finite (without loss of generality we assume two) set of models. After briefly reviewing classical and Bayesian model choice strategies we present a general predictive density which includes all proposed Bayesian approaches that we are aware of. Using Laplace approximations we can conveniently assess and compare the asymptotic behaviour of these approaches.…

以给定一般指数族为共轭先验族的抽样模型AI 解读

Let $\mathscr{K} = \{K_\lambda: \lambda \in \Lambda\}$ be a family of sampling distributions for the data $x$ on a sample space $\mathscr{X}$ which is indexed by a parameter $\lambda \in \Lambda,$ and let $\mathscr{F}$ be a family of priors on $\Lambda$. Then $\mathscr{F}$ is said to be conjugate for $\mathscr{K}$ if it is closed under sampling, that is, if the posterior distributions of $\lambda$ given the data $x$ belong to $\mathscr{F}$ for almost all $x$. In this paper,…

相容推断与非正常先验AI 解读

Formal posteriors for improper priors are investigated in connection with coherence, both in the sense of Regazzini and of Heath and Sudderth. Those priors $\pi$ which are linked with the improper prior $\gamma$ by the relation $\pi(B) = 0$ whenever $\gamma(B) < +\infty$ are studied in particular. Moreover, a characterization of the inferences which are coherent according to Heath and Sudderth is found, and several examples, exhibiting several phenomena, are given.

后验预测 p 值AI 解读

Extending work of Rubin, this paper explores a Bayesian counterpart of the classical $p$-value, namely, a tail-area probability of a "test statistic" under a null hypothesis. The Bayesian formulation, using posterior predictive replications of the data, allows a "test statistic" to depend on both data and unknown (nuisance) parameters and thus permits a direct measure of the discrepancy between sample and population quantities. The tail-area probability for a "test…

使用参考先验估计协方差矩阵AI 解读

Estimation of a covariance matrix $\sum$ is a notoriously difficult problem; the standard unbiased estimator can be substantially suboptimal. We approach the problem from a noninformative prior Bayesian perspective, developing the reference noninformative prior for a covariance matrix and obtaining expressions for the resulting Bayes estimators. These expressions involve the computation of high-dimensional posterior expectations, which is done using a recent Markov chain…

基于选择性二项信息的估计：如何解读被挑选的击球率AI 解读

Often sports announcers, particularly in baseball, provide the listener with exaggerated information concerning a player's performance. For example, we may be told that Dave Winfield, a popular baseball player, has hit safely in 8 of his last 17 chances (a batting average of .471). This is biased, or selected information, as the “17” was chosen to maximize the reported percentage. We model this as observing a maximum success rate of a Bernoulli process and show how to…

贝叶斯计算中的折叠 Gibbs 抽样及基因调控应用AI 解读

This article describes a method of “grouping” and “collapsing” in using the Gibbs sampler and proves from an operator theory viewpoint that the method is in general beneficial. The norms of the forward operators associated with the corresponding nonreversible Markov chains are used to discriminate among different simulation schemes. When applied to Bayesian missing data problems, the idea of collapsing suggests skipping the steps of sampling parameter(s) values in standard…

用二元数据测量潜在子群变化：无条件、条件与半参数极大似然估计AI 解读

Changes in dichotomous data caused by treatments can be analyzed by means of the so-called linear logistic model with relaxed assumptions (LLRA). In contrast to models of the Rasch type, the LLRA allows incidental multidimensional parameters describing the response behavior of the subjects so that each observable criterion used for assessing the changes is governed by its own subject parameter. Because generalizability of the treatment effects over subjects and criteria is…

走向贝叶斯与频率学派点估计的协调AI 解读

The Bayesian and frequentist approaches to point estimation are reviewed. The status of the debate regarding the use of one approach over the other is discussed, and its inconclusive character is noted. A criterion for comparing Bayesian and frequentist estimators within a given experimental framework is proposed. The competition between a Bayesian and a frequentist is viewed as a contest with the following components: a random observable, a true prior distribution unknown…

利用平方累积和回顾检测方差变化AI 解读

This article studies the problem of multiple change points in the variance of a sequence of independent observations. We propose a procedure to detect variance changes based on an iterated cumulative sums of squares (ICSS) algorithm. We study the properties of the centered cumulative sum of squares function and give an intuitive basis for the ICSS algorithm. For series of moderate size (i.e., 200 observations and beyond), the ICSS algorithm offers results comparable to those…