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用于子空间收缩的函数型 Horseshoe 先验AI 解读

We introduce a new shrinkage prior on function spaces, called the functional horseshoe prior (fHS), that encourages shrinkage towards parametric classes of functions. Unlike other shrinkage priors for parametric models, the fHS shrinkage acts on the shape of the function rather than inducing sparsity on model parameters. We study the efficacy of the proposed approach by showing an adaptive posterior concentration property on the function. We also demonstrate consistency of…

论心理科学的可重复性AI 解读

Investigators from a large consortium of scientists recently performed a multi-year study in which they replicated 100 psychology experiments. Although statistically significant results were reported in 97% of the original studies, statistical significance was achieved in only 36% of the replicated studies. This article presents a reanalysis of these data based on a formal statistical model that accounts for publication bias by treating outcomes from unpublished studies as…

用于灵长类认知研究的二项与秩数据联合贝叶斯建模AI 解读

In recent years, substantial effort has been devoted to methods for analyzing data containing mixed response types, but such techniques typically do not include rank data among the response types. Some unique challenges exist in analyzing rank data, particularly when ties are prevalent. We present techniques for jointly modeling binomial and rank data using Bayesian latent variable models. We apply these techniques to compare the cognitive abilities of nonhuman primates…

一致最强贝叶斯检验AI 解读

Uniformly most powerful tests are statistical hypothesis tests that provide the greatest power against a fixed null hypothesis among all tests of a given size. In this article, the notion of uniformly most powerful tests is extended to the Bayesian setting by defining uniformly most powerful Bayesian tests to be tests that maximize the probability that the Bayes factor, in favor of the alternative hypothesis, exceeds a specified threshold. Like their classical counterpart,…

高维环境下的贝叶斯模型选择AI 解读

Standard assumptions incorporated into Bayesian model selection procedures result in procedures that are not competitive with commonly used penalized likelihood methods. We propose modifications of these methods by imposing nonlocal prior densities on model parameters. We show that the resulting model selection procedures are consistent in linear model settings when the number of possible covariates p is bounded by the number of observations n, a property that has not been…

非局部先验密度在贝叶斯假设检验中的应用AI 解读

Summary We examine philosophical problems and sampling deficiencies that are associated with current Bayesian hypothesis testing methodology, paying particular attention to objective Bayes methodology. Because the prior densities that are used to define alternative hypotheses in many Bayesian tests assign non-negligible probability to regions of the parameter space that are consistent with null hypotheses, resulting tests provide exponential accumulation of evidence in…

用于基因关联分析的对数线性模型AI 解读

We describe a class of log-linear models for the detection of interactions in high-dimensional genomic data. This class of models leads to a Bayesian model selection algorithm that can be applied to data that have been reduced to contingency tables using ranks of observations within subjects, and discretization of these ranks within gene/network components. Many normalization issues associated with the analysis of genomic data are thereby avoided. A prior density based on…

利用检验统计量进行贝叶斯模型选择AI 解读

Summary Existing Bayesian model selection procedures require the specification of prior distributions on the parameters appearing in every model in the selection set. In practice, this requirement limits the application of Bayesian model selection methodology. To overcome this limitation, we propose a new approach towards Bayesian model selection that uses classical test statistics to compute Bayes factors between possible models. In several test cases, our approach produces…

基于检验统计量的贝叶斯因子AI 解读

Summary Traditionally, the use of Bayes factors has required the specification of proper prior distributions on model parameters that are implicit to both null and alternative hypotheses. I describe an approach to defining Bayes factors based on modelling test statistics. Because the distributions of test statistics do not depend on unknown model parameters, this approach eliminates much of the subjectivity that is normally associated with the definition of Bayes factors.…

用于拟合优度评估的贝叶斯卡方检验AI 解读

This article describes an extension of classical χ2 goodness-of-fit tests to Bayesian model assessment. The extension, which essentially involves evaluating Pearson’s goodness-of-fit statistic at a parameter value drawn from its posterior distribution, has the important property that it is asymptotically distributed as a χ2 random variable on K−1 degrees of freedom, independently of the dimension of the underlying parameter vector. By examining the posterior distribution of…

用于诊断马尔可夫链蒙特卡洛收敛的耦合再生方案AI 解读

Here I propose a convergence diagnostic for Markov chain Monte Carlo (MCMC) algorithms based on couplings of a Markov chain with an auxiliary chain that is periodically restarted from a fixed parameter value. The diagnostic provides a mechanism for estimating the specific constants governing the rate of convergence of geometrically and uniformly ergodic chains, and provides a lower bound on the effective sample size of a MCMC run. It also provides a simple procedure for…

利用耦合样本路径研究 MCMC 算法的收敛AI 解读

I describe a simple procedure for investigating the convergence properties of Markov chain Monte Carlo sampling schemes. The procedure uses coupled chains from the same sampler, obtained by using the same sequence of random deviates for each run. By examining the distribution of the iteration at which all sample paths couple, convergence properties for the system can be established. The procedure also provides a simple diagnostic for detecting modes in multimodal posteriors.…

多评分者有序数据的贝叶斯分析：自动作文评分应用AI 解读

A framework is proposed for the analysis of ordinal categorical data when ratings from several judges are available. I emphasize the tasks of estimating latent trait characteristics of individual items, regressing these latent traits on observed covariates, and comparing the performance of raters. The model is illustrated in the design and evaluation of an automated essay grader. This grader is based on a regression of variables, obtained from a grammar checker, on essay…

含噪图像的分割与分析模型AI 解读

This article proposes a statistical model for image generation that provides automatic segmentation of images into intensity-differentiated regions and facilitates the quantitative assessment of uncertainty associated with identified image features. The model is specified hierarchically within the Bayesian paradigm. At the lowest level in the hierarchy, a Gibbs distribution is used to specify a probability distribution on the space of all possible partitions of the…

利用条件密度混合估计层级模型边际后验密度AI 解读

A technique called quantile integration is proposed for the estimation of marginal posterior densities arising in Bayesian models having hierarchical representations. The method is based on approximating marginal densities as mixtures of conditional densities, where the conditioning variables are selected deterministically from the mixing distributions. The form of the approximation makes it easy to implement, and the resulting approximations are computationally efficient to…

利用条件密度混合估计层级模型边际后验密度的方法AI 解读

A technique called quantile integration is proposed for the estimation of marginal posterior densities arising in Bayesian models having hierarchical representations. The method is based on approximating marginal densities as mixtures of conditional densities, where the conditioning variables are selected deterministically from the mixing distributions. The form of the approximation makes it easy to implement, and the resulting approximations are computationally efficient to…