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利用贝叶斯模型选择识别微阵列中的差异表达基因AI 解读

DNA microarrays open up a broad new horizon for investigators interested in studying the genetic determinants of disease. The high throughput nature of these arrays, where differential expression for thousands of genes can be measured simultaneously, creates an enormous wealth of information, but also poses a challenge for data analysis because of the large multiple testing problem involved. The solution has generally been to focus on optimizing false-discovery rates while…

贝叶斯聚类与乘积分割模型AI 解读

Summary We present a decision theoretic formulation of product partition models (PPMs) that allows a formal treatment of different decision problems such as estimation or hypothesis testing and clustering methods simultaneously. A key observation in our construction is the fact that PPMs can be formulated in the context of model selection. The underlying partition structure in these models is closely related to that arising in connection with Dirichlet processes. This allows…

用不完美模型解释统计证据：稳健调整似然函数AI 解读

Summary The strength of statistical evidence is measured by the likelihood ratio. Two key performance properties of this measure are the probability of observing strong misleading evidence and the probability of observing weak evidence. For the likelihood function associated with a parametric statistical model, these probabilities have a simple large sample structure when the model is correct. Here we examine how that structure changes when the model fails. This leads to…

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无限维正态分布均值的自适应贝叶斯推断AI 解读

We consider the problem of estimating the mean of an infinite-break dimensional normal distribution from the Bayesian perspective. Under the assumption that the unknown true mean satisfies a "smoothness condition," we first derive the convergence rate of the posterior distribution for a prior that is the infinite product of certain normal distributions and compare with the minimax rate of convergence for point estimators. Although the posterior distribution can achieve the…

比例风险模型的贝叶斯分析AI 解读

This paper is concerned with Bayesian analysis of the proportional hazard model with left truncated and right censored data. We use a process neutral to the right as the prior of the baseline survival function and a finite-dimensional prior is placed on the regression coefficient. We then obtain the exact form of the joint posterior distribution of the regression coefficient and the baseline cumulative hazard function. As a by-product, we prove the propriety of the posterior…

复合决策理论与经验贝叶斯方法：特邀论文AI 解读

Introduction.Compound decision theory and empirical Bayes methodology, acclaimed as "two breakthroughs" by Neyman (1962), are the most important contributions of Herbert Robbins to statistics.The purpose of this paper is to provide a brief description of his work in these two intimately connected fields, its impact and a number of important related developments.Robbins introduced compound decision theory in 1950 at the Second Berkeley Symposium on Mathematical Statistics and…

Robbins、经验贝叶斯与微阵列AI 解读

Empirical Bayes was Herbert Robbins' most influential contribution to statistical theory. It is also an idea of great practical potential. That potential is realized in the analysis of microarrays, a new biogenetic technology for the simultaneous measurement of thousands of gene expression levels.

摘要暂缺

用于决策的回归建模与元分析AI 解读

Regression models are often used, explicitly or implicitly, for decision making. However, the choices made in setting up the models (e.g., inclusion of predictors based on statistical significance) do not map directly into decision procedures. Bayesian inference works more naturally with decision analysis but presents problems in practice when noninformative prior distributions are used with sparse data. We do not attempt to provide a general solution to this problem, but…

利用匹配先验实现频率学派推断AI 解读

Nuisance parameters do not pose any problems in Bayesian inference as marginalisation allows for study of the posterior distribution solely in terms of the parameter of interest. However, no general solution is available for removing nuisance parameters under the frequentist paradigm. In this paper, we merge the two approaches to construct a general procedure for frequentist elimination of nuisance parameters through the use of matching priors. In particular, we perform…

非线性混合效应模型中的非参数估计AI 解读

A nonparametric approach is developed herein to estimate parameters in nonlinear mixed effects models. Asymptotic properties of the nonparametric maximum likelihood estimators and associated computational algorithms are provided. Empirical Bayes estimators of functionals of the random effects are also developed. Applications to population pharmacokinetics are given.

狄利克雷过程混合模型的边际似然与贝叶斯因子AI 解读

We present a method for comparing semiparametric Bayesian models, constructed under the Dirichlet process mixture (DPM) framework, with alternative semiparameteric or parameteric Bayesian models. A distinctive feature of the method is that it can be applied to semiparametric models containing covariates and hierarchical prior structures, and is apparently the first method of its kind. Formally, the method is based on the marginal likelihood estimation approach of Chib (1995)…

通过交替子空间张成重采样加速马尔可夫链蒙特卡洛模拟AI 解读

This article provides a simple method to accelerate Markov chain Monte Carlo sampling algorithms, such as the data augmentation algorithm and the Gibbs sampler, via alternating subspace-spanning resampling (ASSR). The ASSR algorithm often shares the simplicity of its parent sampler but has dramatically improved efficiency. The methodology is illustrated with Bayesian estimation for analysis of censored data from fractionated experiments. The relationships between ASSR and…

部分观测多元数据的边缘检测、空间平滑与图像重建AI 解读

Situations with incomplete multivariate spatial data on a lattice are considered. The goal is to impute the missing data in the presence of edges or boundaries and recover the image. Two methods based on Bayesian hierarchical models that iterate between edge detection and spatial smoothing to impute the missing data within identified homogeneous regions are examined. Their performance is compared with another method that imputes the missing values using edge-preserving…

每日生育力标记的贝叶斯建模AI 解读

Cervical mucus hydration increases during the fertile interval before ovulation. Because sperm can only penetrate mucus having a high water content, cervical secretions provide a reliable marker of the fertile days of the menstrual cycle. This article develops a Bayesian approach for modeling of daily observations of cervical mucus and applies the approach to assess heterogeneity among women and cycles from a given woman with respect to the increase in mucus hydration during…

相关多变量均值的筛选AI 解读

Quantitative performance monitoring of health care providers has become an increasingly prominent activity in health care delivery. As a consequence, multidimensional “report cards” comparing the quality of services provided by diverse health care organizations have begun to appear. We present a case study examining the performance of 22 geographically defined health care systems, known as Veterans Integrated Service Networks; involving the treatment of more than 37,000…

关联私人价值下第一价格拍卖的非对称性AI 解读

Abstract Collusion and heterogeneity across firms may introduce asymmetry in bidding games. A major difficulty in asymmetric auctions is that the Bayesian Nash equilibrium strategies are solutions of an intractable system of differential equations. We propose a simple method for estimating asymmetric first‐price auctions with affiliated private values. Considering two types of bidders, we show that these differential equations can be rewritten using the observed bid…

对 Brooks、Giudici 与 Roberts 论文的讨论AI 解读

This paper aims to develop general strategies for improving jumps between models in reversible jump Markov chain Monte Carlo (MCMC) algorithms, which is quite an important and timely goal. Indeed, in practical implementations of the method, we usually find that the choice of proposals is paramount: in many cases, the ‘natural choice’ leads to a zero acceptance probability and the construction of well-tuned moves is often quite costly. Given that the reversible jump MCMC…

偏序集上的序贯分类AI 解读

Summary A general theorem on the asymptotically optimal sequential selection of experiments is presented and applied to a Bayesian classification problem when the parameter space is a finite partially ordered set. The main results include establishing conditions under which the posterior probability of the true state converges to 1 almost surely and determining optimal rates of convergence. Properties of a class of experiment selection rules are explored.

通过混合表示进行凸约束模型的非参数估计AI 解读

We present a general approach to estimating probability measures constrained to lie in a convex set. We represent constrained measures as mixtures of simple, known extreme measures, and so the problem of estimating a constrained measure becomes one of estimating an unconstrained mixing measure. Convex constraints arise in many modeling situations, such as estimation of the mean and estimation under stochastic ordering constraints. We describe mixture representation…

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内生延迟门限模型的贝叶斯分析AI 解读

autoregressive models: endogenous delay threshold. We apply our methods to the commonly used sunspot data set and find strong evidence in favor of the Endogenous Delay Threshold Autoregressive (EDTAR) model over linear and traditional threshold autoregressions.

最终报价仲裁中的贝叶斯建模与计算AI 解读

behavior in final-offer arbitration. Posterior calculations are obtained using a Markov chain algorithm. An example is considered using salary data from Major League Baseball.