论文检索

摘要暂缺

全条件分布近似正态时的联合后验大样本近似AI 解读

Modern Bayesian statistical methods, such as Gibbs and Metropolis–Hastings sampling, were developed to liberate statisticians from the necessity of making large-sample assumptions and to facilitate the numerical approximation of problems that had previously been analytically intractable. Counter to this trend, we develop a method for constructing asymptotic joint posterior approximations based on models with k blocks of parameters and where the corresponding properly…

高维协变量下的切片逆回归AI 解读

Sliced inverse regression is a promising method for the estimation of the central dimension-reduction subspace (CDR space) in semiparametric regression models. It is particularly useful in tackling cases with high-dimensional covariates. In this article we study the asymptotic behavior of the estimate of the CDR space with high-dimensional covariates, that is, when the dimension of the covariates goes to infinity as the sample size goes to infinity. Strong and weak…

非高斯贝叶斯地统计建模AI 解读

Sampling models for geostatistical data are usually based on Gaussian processes. However, real data often display non-Gaussian features, such as heavy tails. In this article we propose a more flexible class of sampling models. We start from the spatial linear model that has a spatial trend plus a stationary Gaussian error process. We extend the sampling model to non-Gaussianity by including a scale parameter at each location. We make sure that we obtain a valid stochastic…

通过交互粒子系统实现贝叶斯最优设计AI 解读

We propose a new stochastic algorithm for Bayesian-optimal design in nonlinear and high-dimensional contexts. Following Peter Müller, we solve an optimization problem by exploring the expected utility surface through Markov chain Monte Carlo simulations. The optimal design is the mode of this surface considered a probability distribution. Our algorithm relies on a “particle” method to efficiently explore high-dimensional multimodal surfaces, with simulated annealing to…

病例对照研究的贝叶斯样本量确定AI 解读

Case-control studies are among the most commonly used means of assessing association between exposure and outcome. Sample size determination and the optimal control-to-case ratio are vital to the design of such studies. In this article we investigate Bayesian sample size determination and the control-to-case ratio for case-control studies, when interval estimation is the goal of the eventual statistical analysis. In certain cases we are able to derive approximate closed-form…

混合治疗比较中的证据不一致性评估AI 解读

Randomized comparisons among several treatments give rise to an incomplete-blocks structure known as mixed treatment comparisons (MTCs). To analyze such data structures, it is crucial to assess whether the disparate evidence sources provide consistent information about the treatment contrasts. In this article we propose a general method for assessing evidence inconsistency in the framework of Bayesian hierarchical models. We begin with the distinction between basic…

单变量偏斜分布的构造性表示AI 解读

We introduce a general perspective on the introduction of skewness into symmetric distributions. Through inverse probability integral transformations we provide a constructive representation of skewed distributions, where the skewing mechanism and the original symmetric distributions are specified separately. We study the effects of the skewing mechanism on, e.g., modality, tail behavior and the amount of skewness generated. The representation is used to introduce novel…

归一化常数难以计算时的高效马尔可夫链蒙特卡洛方法AI 解读

Maximum likelihood parameter estimation and sampling from Bayesian posterior distributions are problematic when the probability density for the parameter of interest involves an intractable normalising constant which is also a function of that parameter. In this paper, an auxiliary variable method is presented which requires only that independent samples can be drawn from the unnormalised density at any particular parameter value. The proposal distribution is constructed so…

基于层级模型的贝叶斯配准及其蛋白质生物信息学应用AI 解读

An important problem in shape analysis is to match configurations of points in space after filtering out some geometrical transformation. In this paper we introduce hierarchical models for such tasks, in which the points in the configurations are either unlabelled or have at most a partial labelling constraining the matching, and in which some points may only appear in one of the configurations. We derive procedures for simultaneous inference about the matching and the…

离散观测扩散过程的精确且计算高效的似然估计（含讨论）AI 解读

Summary The objective of the paper is to present a novel methodology for likelihood-based inference for discretely observed diffusions. We propose Monte Carlo methods, which build on recent advances on the exact simulation of diffusions, for performing maximum likelihood and Bayesian estimation.

序贯蒙特卡洛采样器AI 解读

Summary We propose a methodology to sample sequentially from a sequence of probability distributions that are defined on a common space, each distribution being known up to a normalizing constant. These probability distributions are approximated by a cloud of weighted random samples which are propagated over time by using sequential Monte Carlo methods. This methodology allows us to derive simple algorithms to make parallel Markov chain Monte Carlo algorithms interact to…

针对高维备择假设的检验AI 解读

Summary As the dimensionality of the alternative hypothesis increases, the power of classical tests tends to diminish quite rapidly. This is especially true for high dimensional data in which there are more parameters than observations. We discuss a score test on a hyperparameter in an empirical Bayesian model as an alternative to classical tests. It gives a general test statistic which can be used to test a point null hypothesis against a high dimensional alternative, even…

贝叶斯样本量的闭式表达AI 解读

Sample size criteria are often expressed in terms of the concentration of the posterior density, as controlled by some sort of error bound. Since this is done pre-experimentally, one can regard the posterior density as a function of the data. Thus, when a sample size criterion is formalized in terms of a functional of the posterior, its value is a random variable. Generally, such functionals have means under the true distribution. We give asymptotic expressions for the…

We introduce a natural conjugate prior for the transition matrix of a reversible Markov chain. This allows estimation and testing. The prior arises from random walk with reinforcement in the same way the Dirichlet prior arises from Pólya’s urn. We give closed form normalizing constants, a simple method of simulation from the posterior and a characterization along the lines of W. E. Johnson’s characterization of the Dirichlet prior.

二元回归函数贝叶斯估计的一致性AI 解读

When do nonparametric Bayesian procedures “overfit”? To shed light on this question, we consider a binary regression problem in detail and establish frequentist consistency for a certain class of Bayes procedures based on hierarchical priors, called uniform mixture priors. These are defined as follows: let ν be any probability distribution on the nonnegative integers. To sample a function f from the prior πν, first sample m from ν and then sample f uniformly from the set of…

基于贝叶斯小波方法的函数型数据聚类AI 解读

Summary We propose a nonparametric Bayes wavelet model for clustering of functional data. The wavelet-based methodology is aimed at the resolution of generic global and local features during clustering and is suitable for clustering high dimensional data. Based on the Dirichlet process, the nonparametric Bayes model extends the scope of traditional Bayes wavelet methods to functional clustering and allows the elicitation of prior belief about the regularity of the functions…

基于小波的函数型混合模型AI 解读

Summary Increasingly, scientific studies yield functional data, in which the ideal units of observation are curves and the observed data consist of sets of curves that are sampled on a fine grid. We present new methodology that generalizes the linear mixed model to the functional mixed model framework, with model fitting done by using a Bayesian wavelet-based approach. This method is flexible, allowing functions of arbitrary form and the full range of fixed effects…

利用 S 路径估计单调风险率的贝叶斯方法AI 解读

A class of random hazard rates, which is defined as a mixture of an indicator kernel convolved with a completely random measure, is of interest. We provide an explicit characterization of the posterior distribution of this mixture hazard rate model via a finite mixture of S-paths. A closed and tractable Bayes estimator for the hazard rate is derived to be a finite sum over S-paths. The path characterization or the estimator is proved to be a Rao–Blackwellization of an…

贝叶斯预测中的收缩先验AI 解读

We investigate shrinkage priors for constructing Bayesian predictive distributions. It is shown that there exist shrinkage predictive distributions asymptotically dominating Bayesian predictive distributions based on the Jeffreys prior or other vague priors if the model manifold satisfies some differential geometric conditions. Kullback–Leibler divergence from the true distribution to a predictive distribution is adopted as a loss function. Conformal transformations of model…

高斯与非高斯噪声下贝叶斯小波收缩规则的频率学派最优性AI 解读

The present paper investigates theoretical performance of various Bayesian wavelet shrinkage rules in a nonparametric regression model with i.i.d. errors which are not necessarily normally distributed. The main purpose is comparison of various Bayesian models in terms of their frequentist asymptotic optimality in Sobolev and Besov spaces. We establish a relationship between hyperparameters, verify that the majority of Bayesian models studied so far achieve theoretical…

无限维贝叶斯统计中的模型误设AI 解读

We consider the asymptotic behavior of posterior distributions if the model is misspecified. Given a prior distribution and a random sample from a distribution P0, which may not be in the support of the prior, we show that the posterior concentrates its mass near the points in the support of the prior that minimize the Kullback–Leibler divergence with respect to P0. An entropy condition and a prior-mass condition determine the rate of convergence. The method is applied to…

货币政策变化如何影响银行贷款：奥地利银行数据分析AI 解读

Abstract Using a panel of Austrian bank data we show that the lending decisions of the smallest banks are more sensitive to interest rate changes, and that for all banks, sensitivity changes over time. We propose to estimate the groups of banks that display similar lending reactions by means of a group indicator which, after estimation, indicates each bank's classification. Additionally, we estimate a state indicator that indicates the periods during which the lending…

利用可逆跳跃算法输出高效估计贝叶斯因子AI 解读

We propose a class of estimators of the Bayes factor which is based on an extension of the bridge sampling identity of Meng & Wong (1996) and makes use of the output of the reversible jump algorithm of Green (1995). Within this class we give the optimal estimator and also a suboptimal one which may be simply computed on the basis of the acceptance probabilities used within the reversible jump algorithm for jumping between models. The proposed estimators are very easily…