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序贯插补与贝叶斯缺失数据问题AI 解读

For missing data problems, Tanner and Wong have described a data augmentation procedure that approximates the actual posterior distribution of the parameter vector by a mixture of complete data posteriors. Their method of constructing the complete data sets is closely related to the Gibbs sampler. Both required iterations, and, similar to the EM algorithm, convergence can be slow. We introduce in this article an alternative procedure that involves imputing the missing data…

Laplace 方法在有限混合分布中的应用AI 解读

An exact Bayesian analysis of finite mixture distributions is often computationally infeasible, because the number of terms in the posterior density grows exponentially with the sample size. A modification of the Laplace method is presented and applied to estimation of posterior functions in a Bayesian analysis of finite mixture distributions. The procedure, which involves computations similar to those required in maximum likelihood estimation, is shown to have high…

参数空间边界众数情形下后验期望的Laplace近似AI 解读

This article gives asymptotic expansions for posterior expectations when the mode is on the boundary of the parameter space. The idea, based on the divergence theorem, is to reduce the high-dimensional integrals over the parameters space to surface integrals over the boundary of the parameter space and then apply the usual interior-mode Laplace method to the latter integrals. It is shown that these approximations have second-order accuracy. The method is illustrated with…

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…

用于预测的神经网络模型AI 解读

In this article we introduce a neural net designed for nonlinear statistical prediction. The net is based on a stochastic model featuring a multilayer feedforward architecture with random connections between units and noisy response functions. A Bayesian inferential procedure for this model, based on the Kalman filter, is derived. The resulting learning algorithm generalizes the so-called onedimensional Newton method, an updating algorithm currently popular in the neural net…

存在不可忽略无回答的分类数据模型AI 解读

When categorical outcomes are subject to nonignorable nonresponse, log-linear models may be used to adjust for the nonresponse. The models are fitted to the data in an augmented frequency table in which one index corresponds to whether or not the subject is a respondent. The likelihood function is maximized over pseudo-observed cell frequencies with respect to this log-linear model using an EM algorithm. Each E step of the EM algorithm determines the pseudo-observed cell…

参数空间边界众数情形下后验期望的 Laplace 近似AI 解读

This article gives asymptotic expansions for posterior expectations when the mode is on the boundary of the parameter space. The idea, based on the divergence theorem, is to reduce the high-dimensional integrals over the parameters space to surface integrals over the boundary of the parameter space and then apply the usual interior-mode Laplace method to the latter integrals. It is shown that these approximations have second-order accuracy. The method is illustrated with…

用于预测的神经网络模型AI 解读

In this article we introduce a neural net designed for nonlinear statistical prediction. The net is based on a stochastic model featuring a multilayer feedforward architecture with random connections between units and noisy response functions. A Bayesian inferential procedure for this model, based on the Kalman filter, is derived. The resulting learning algorithm generalizes the so-called onedimensional Newton method, an updating algorithm currently popular in the neural net…

Consider statistical inference about a scalar parameter and suppose that information about that parameter is to be summarized by a system of interval estimates. It is well known that methods of interval estimation that do not correspond to Bayesian inference with respect to some prior distribution have some logical difficulties. This article proposes a measure of how close a system of interval estimates is to being of Bayesian form. Using this measure, several non-Bayesian…

Gibbs 抽样的协方差结构：估计量与数据增广方案的比较AI 解读

We study the covariance structure of a Markov chain generated by the Gibbs sampler, with emphasis on data augmentation. When applied to a Bayesian missing data problem, the Gibbs sampler produces two natural approximations for the posterior distribution of the parameter vector: the empirical distribution based on the sampled values of the parameter vector, and a mixture of complete data posteriors. We prove that Rao-Blackwellization causes a one-lag delay for the…

基于扩散过程离散观测的贝叶斯因子AI 解读

We present an approach to model selection for a time series of data on a fine time scale. The underlying process generating the data is modelled as a continuous time stochastic process. The underlying continuous processes are assumed to be diffusions with time varying drift and diffusion coefficient. Several approaches to modelling the diffusion coefficient are described. To perform model selection, we propose an approximation to the Bayes factor that uses only the discrete…

摘要暂缺

使用加权似然 Bootstrap 的近似贝叶斯推断AI 解读

SUMMARY We introduce the weighted likelihood bootstrap (WLB) as a way to simulate approximately from a posterior distribution. This method is often easy to implement, requiring only an algorithm for calculating the maximum likelihood estimator, such as iteratively reweighted least squares. In the generic weighting scheme, the WLB is first order correct under quite general conditions. Inaccuracies can be removed by using the WLB as a source of samples in the…

基于椭圆模型混合的单位根假说决策理论分析AI 解读

This paper develops a formal decision theoretic approach to testing for a unit root in economic time series. The approach is empirically implemented by specifying a loss function based on predictive variances; models are chosen so as to minimize expected loss. In addition, the paper broadens the class of likelihood functions traditionally considered in the Bayesian unit root literature. Empirical results indicate that, while the posterior probability of trend-stationarity is…

一般不完整数据模型中的可忽略性AI 解读

Rubin (1976) defined ignorability conditions for frequentist and Bayes/likelihood analyses of data subject to missing observations. More recently, Heitjan & Rubin (1991) and Heitjan (1993) generalised the Rubin model to encompass other forms of incompleteness, establishing ignorability conditions for Bayes/likelihood inferences only. This paper extends the Heitjan-Rubin model by explicitly defining the observed degree of coarseness as a data element. This permits the…

状态空间模型的吉布斯抽样AI 解读

We show how to use the Gibbs sampler to carry out Bayesian inference on a linear state space model with errors that are a mixture of normals and coefficients that can switch over time. Our approach simultaneously generates the whole of the state vector given the mixture and coefficient indicator variables and simultaneously generates all the indicator variables conditional on the state vectors. The states are generated efficiently using the Kalman filter. We illustrate our…

正态不完整数据的一类模式混合模型AI 解读

Likelihood-based methods are developed for analyzing a random sample on two continuous variables when values of one of the variables are missing. Normal maximum likelihood estimates when values are missing completely at random were derived by Anderson (1957). They are also maximum likelihood providing the missing-data mechanism is ignorable, in Rubin's (1976) sense that the mechanism depends only on observed data. A new class of pattern-mixture models (Little, 1993) is…

离散时间生存数据的动态建模与惩罚似然估计AI 解读

This paper describes a dynamic or state-space approach for analyzing discrete time or grouped survival data. Simultaneous estimation of baseline hazard functions and of time-varying covariate effects is based on maximization of posterior densities or, equivalently, a penalized likelihood, leading to Kalman-type smoothing algorithms. Data-driven choice of unknown smoothing parameters is possible via an EM-type procedure. The methods are illustrated by applications to real…

椭圆轮廓误差下的贝叶斯卡尔曼滤波AI 解读

SUMMARY The basic recursive equations of the Kalman filter, for independent normally distributed error sources in both the observation and the system equations, are shown to hold for a larger class of distributions. It is shown that, for error sources following jointly a general elliptical distribution, the conditional posterior distribution of the parameters and the one-step ahead predictive distribution at every stage t are also elliptical. This generalizes some recent…

加权抽样的贝叶斯方法AI 解读

Bayesian statistical inference for sampling from weighted distribution models is studied. Small-sample Bayesian bootstrap clone (BBC) approximations to the posterior distribution are discussed. A second-order property for the BBC in unweighted i.i.d. sampling is given. A consequence is that BBC approximations to a posterior distribution of the mean and to the sampling distribution of the sample average, can be made asymptotically accurate by a proper choice of the random…

非参数二元回归：贝叶斯方法AI 解读

The performance of Bayes estimates are studied, under an assumption of conditional exchangeability. More exactly, for each subject in a data set, let $\xi$ be a vector of binary covariates and let $\eta$ be a binary response variable, with $P\{\eta = 1\mid \xi\} = f(\xi)$. Here, $f$ is an unknown function to be estimated from the data; the subjects are independent, and satisfy a natural "balance" condition. Define a prior distribution on $f$ as $\sum_kw_k\pi_k/\sum_kw_k$,…

基于信息更丰富样本的单调经验贝叶斯估计AI 解读

An empirical Bayes estimator is constructed for the case of nonidentical components coming from an exponential family of distributions that is closed under convolution. Examples are the normal, Poisson, and binomial distributions. The construction is based on Robbins' approach to empirical Bayes estimation and generalizes results of O'Bryan and Stijnen and Van Houwelingen. The method is elaborated for the normal and Poisson case, and examples are given that show that this…

信息冲突下的后验何时渐近正态？AI 解读

When data conflicts with quantified prior beliefs, seemingly small changes in the functional form of the prior and/or likelihood can have a profound effect on posterior inferences. This article provides results on asymptotic forms of the posterior when two information sources conflict. In particular, let x be from the likelihood p 2(x − θ) with an unknown location parameter θ, with p 1(θ) the prior on θ. Sufficient conditions on p 1 and p 2 are provided to ensure that as x →…

涉及指数族的贝叶斯推断中后验累积量的关系AI 解读

For Bayesian inference in one-parameter contexts where either the likelihood or the prior has an exponential family form, relationships are derived for posterior moments and cumulants of (functions of) both the canonical and the expectation parameters. The identities exhibited generalize the simple relationships well known in the conjugate analysis case. Applications of these results are indicated in the areas of Bayesian robustness and approximation. In particular, results…