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错误发现率回归及初级视觉皮层神经同步检测应用AI 解读

Many approaches for multiple testing begin with the assumption that all tests in a given study should be combined into a global false-discovery-rate analysis. But this may be inappropriate for many of today's large-scale screening problems, where auxiliary information about each test is often available, and where a combined analysis can lead to poorly calibrated error rates within different subsets of the experiment. To address this issue, we introduce an approach called…

状态空间模型的近似方法AI 解读

State-space models provide an important body of techniques for analyzing time-series, but their use requires estimating unobserved states. The optimal estimate of the state is its conditional expectation given the observation histories, and computing this expectation is hard when there are nonlinearities. Existing filtering methods, including sequential Monte Carlo, tend to be either inaccurate or slow. In this paper, we study a nonlinear filter for nonlinear/non-Gaussian…

广义线性混合模型的参考贝叶斯方法AI 解读

Bayesian methods furnish an attractive approach to inference in generalized linear mixed models. In the absence of subjective prior information for the random-effect variance components, these analyses are typically conducted using either the standard invariant prior for normal responses or diffuse conjugate priors. Previous work has pointed out serious difficulties with both strategies, and we show here that as in normal mixed models, the standard invariant prior leads to…

方差分量模型的贝叶斯因子及其近似AI 解读

In this article we consider tests of variance components using Bayes factors. Such tests arise in many fields of application, including medicine, agriculture, and engineering. When using Bayes factors, the choice of prior distribution on the parameter of interest is of great importance; we propose a “unit-information” reference method for variance component models. The calculation of Bayes factors in this context is not straightforward; there are well-documented difficulties…

协方差矩阵的非共轭贝叶斯估计及其在层级模型中的应用AI 解读

The problem of estimating a covariance matrix in small samples has been considered by several authors following early work by Stein. This problem can be especially important in hierarchical models where the standard errors of fixed and random effects depend on estimation of the covariance matrix of the distribution of the random effects. We propose a set of hierarchical priors (HPs) for the covariance matrix that produce posterior shrinkage toward a specified structure—here…

渐近推断的几何基础AI 解读

Overview and Preliminaries. ONE-PARAMETER CURVED EXPONENTIAL FAMILIES. First-Order Asymptotics. Second-Order Asymptotics. MULTIPARAMETER CURVED EXPONENTIAL FAMILIES. Extensions of Results from the One-Parameter Case. Exponential Family Regression and Diagnostics. Curvature in Exponential Family Regression. DIFFERENTIAL-GEOMETRIC METHODS. Information-Metric Riemannian Geometry. Statistical Manifolds. Divergence Functions. Recent Developments. Appendices. References. Indexes.

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结合模拟与渐近近似计算贝叶斯因子AI 解读

The Bayes factor is a ratio of two posterior normalizing constants, which may be difficult to compute. We compare several methods of estimating Bayes factors when it is possible to simulate observations from the posterior distributions, via Markov chain Monte Carlo or other techniques. The methods that we study are all easily applied without consideration of special features of the problem, provided that each posterior distribution is well behaved in the sense of having a…

嵌套假设的参考贝叶斯检验及其与 Schwarz 准则的关系AI 解读

To compute a Bayes factor for testing H 0: ψ = ψ0 in the presence of a nuisance parameter β, priors under the null and alternative hypotheses must be chosen. As in Bayesian estimation, an important problem has been to define automatic, or “reference,” methods for determining priors based only on the structure of the model. In this article we apply the heuristic device of taking the amount of information in the prior on ψ equal to the amount of information in a single…

贝叶斯因子AI 解读

In a 1935 paper and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null is one-half. Although there has been much discussion of Bayesian hypothesis testing in the context of criticism of P-values, less attention has been given to the Bayes factor as a…

最大似然估计与后验分布非正态性的若干诊断AI 解读

Standard large-sample maximum likelihood and Bayesian inference, based on limiting multivariate normal distributions, may be dubious when applied with small or moderate sample sizes. We define and discuss several measures of nonnormality of MLE and posterior distributions that may be used as diagnostics and can indicate whether reparameterization will be effective in improving inferences. We begin by showing how the nonlinearity measures introduced by Beale and Bates and…

近似贝叶斯因子与正交参数：两个二项比例相等性检验AI 解读

SUMMARY We use asymptotic expansions to approximate Bayes factors, improving on a method used by Jeffreys. Suppose that the hypothesis H 0: ψ = ψ0 is to be tested against H A: ψ ≠ ψ0 in the presence of a nuisance parameter β, and initially priors π0(β) under H 0 and π(β, ψ) under H A are used. We consider the problem of assessing sensitivity of the Bayes factor to small changes in π0 and π. We show that for local alternatives (which, for moderate sample sizes, are consistent…

预测工作记忆失误：主观贝叶斯模型选择方法AI 解读

We use Bayes factors to compare two alternative characterizations of human working memory load in their ability to predict errors in database query-writing tasks. The first measures working memory load by the number of different features each task contains, while the second attempts instead to measure the complexity of the task by giving more weight to features that require more mental time for their correct execution. We reanalyze data from a previously conducted experiment…

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非正函数期望与方差的完全指数型拉普拉斯近似AI 解读

Tierney and Kadane (1986) presented a simple second-order approximation for posterior expectations of positive functions. They used Laplace's method for asymptotic evaluation of integrals, in which the integrand is written as f(θ)exp(-nh(θ)) and the function h is approximated by a quadratic. The form in which they applied Laplace's method, however, was fully exponential: The integrand was written instead as exp[− nh(θ) + log f(θ)]; this allowed first-order approximations to…

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非线性函数的边际密度近似AI 解读

This paper presents an asymptotic approximation for the marginal density of a nonlinear function g(θ) that is applicable when the joint density of θ is dominated by a single mode and the Jacobian of g is of full rank near that mode. The approximation is based on Laplace's method and its asymptotic properties are similar to those of the saddlepoint approximation. The approximation is applied to the computation of a marginal posterior density, a marginal sampling density and a…

典范参数化与零参数效应曲率AI 解读

SUMMARY An equation derived by Hougaard (1982) characterizes certain canonical parameterizations of curved exponential families. The geometrical interpretation of Hougaard's equation is presented and, with this background, the relationship of work on Gaussian non-linear regression, by Bates and Watts (1980) and others, to that on general asymptotic inference, by Efron (1975) and Amari (1982a, b), is discussed. Hougaard's δ-parameterization is that in which there is zero…