Model comparison of linear and nonlinear Bayesian structural equation models with dichotomous data

In this article, dichotomous variables are used to compare between linear and nonlinear Bayesian structural equation models. Gibbs sampling method is applied for estimation and model comparison. Statistical inferences that involve estimation of parameters and their standard deviations and residuals analysis for testing the selected model are discussed. Hidden continuous normal distribution (censored normal distribution) is used to solve the problem of dichotomous variables. The proposed procedure is illustrated by a simulation data obtained from R program. Analyses are done by using R2WinBUGS package in R-program.     

Bayesian density regression for discrete outcomes

We develop Bayesian models for density regression with emphasis on discrete outcomes. The problem of density regression is approached by considering methods for multivariate density estimation of mixed scale variables, and obtaining conditional densities from the multivariate ones. The approach to multivariate mixed scale outcome density estimation that we describe represents discrete variables, either responses or covariates, as discretised versions of continuous latent variables. We present and compare several models for obtaining these thresholds in the challenging context of count data analysis where the response may be over‐ and/or under‐dispersed in some of the regions of the covariate space. We utilise a nonparametric mixture of multivariate Gaussians to model the directly observed and the latent continuous variables. The paper presents a Markov chain Monte Carlo algorithm for posterior sampling, sufficient conditions for weak consistency, and illustrations on density, mean and quantile regression utilising simulated and real datasets.     

Bayesian analysis of two overdispersed poisson regression models

Shookri and Consul (1989) and Scollnik (1995) have previously considered the Bayesian analysis of an overdispersed generalized Poisson model. Scollnik (1995) also considered the Bayesian analysis of an ordinary Poisson and over-dispersed generalized Poisson mixture model. In this paper, we discuss the Bayesian analysis of these models when they are utilised in a regression context. Markov chain Monte Carlo methods are utilised, and an illustrative analysis is provided.     

A hybrid Markov chain for the Bayesian analysis of the multinomial probit model

Bayesian inference for the multinomial probit model, using the Gibbs sampler with data augmentation, has been recently considered by some authors. The present paper introduces a modification of the sampling technique, by defining a hybrid Markov chain in which, after each Gibbs sampling cycle, a Metropolis step is carried out along a direction of constant likelihood. Examples with simulated data sets motivate and illustrate the new technique. A proof of the ergodicity of the hybrid Markov chain is also given.     

基于贝叶斯方法的比例数据分位数推断及其应用

为了尝试使用贝叶斯方法研究比例数据的分位数回归统计推断问题,首先基于Tobit模型给出了分位数回归建模方法,然后通过选取合适的先验分布得到了贝叶斯层次模型,进而给出了各参数的后验分布并用于Gibbs抽样。数值模拟分析验证了所提出的贝叶斯推断方法对于比例数据分析的有效性。最后,将贝叶斯方法应用于美国加州海洛因吸毒数据,在不同的分位数水平下揭示了吸毒频率的影响因素。     

A full Bayesian analysis of circular data using the von Mises distribution

This paper presents a full Bayesian analysis of circular data, paying special attention to the von Mises distribution. We obtain samples from the posterior distribution using the Gibbs sampler which, after the introduction of strategic latent variables, has all full conditional distributions of known type.     

An iterative Monte Carlo method for nonconjugate Bayesian analysis

The Gibbs sampler has been proposed as a general method for Bayesian calculation in Gelfand and Smith (1990). However, the predominance of experience to date resides in applications assuming conjugacy where implementation is reasonably straightforward. This paper describes a tailored approximate rejection method approach for implementation of the Gibbs sampler when nonconjugate structure is present. Several challenging applications are presented for illustration.     

Pareto Regression: A Bayesian Analysis

Abstract

In this article, a new model is presented that is based on the Pareto distribution of the second kind, when the location parameter depends on covariates as well as unobserved heterogeneity. Bayesian analysis of the model can be performed using Markov Chain Monte Carlo techniques. The new procedures are illustrated in the context of artificial data as well as international output data.     

A Bayesian analysis of directional data using the projected normal distribution

This paper presents a Bayesian analysis of the projected normal distribution, which is a flexible and useful distribution for the analysis of directional data. We obtain samples from the posterior distribution using the Gibbs sampler after the introduction of suitably chosen latent variables. The procedure is illustrated using simulated data as well as a real data set previously analysed in the literature.     

Bayesian identifiability and misclassification in multinomial data

The authors consider the Bayesian analysis of multinomial data in the presence of misclassification. Misclassification of the multinomial cell entries leads to problems of identifiability which are categorized into two types. The first type, referred to as the permutation‐type nonidentifiabilities, may be handled with constraints that are suggested by the structure of the problem. Problems of identifiability of the second type are addressed with informative prior information via Dirichlet distributions. Computations are carried out using a Gibbs sampling algorithm.     

Bayesian analysis for mixtures of discrete distributions with a non-parametric component

Bayesian finite mixture modelling is a flexible parametric modelling approach for classification and density fitting. Many areas of application require distinguishing a signal from a noise component. In practice, it is often difficult to justify a specific distribution for the signal component; therefore, the signal distribution is usually further modelled via a mixture of distributions. However, modelling the signal as a mixture of distributions is computationally non-trivial due to the difficulties in justifying the exact number of components to be used and due to the label switching problem. This paper proposes the use of a non-parametric distribution to model the signal component. We consider the case of discrete data and show how this new methodology leads to more accurate parameter estimation and smaller false non-discovery rate. Moreover, it does not incur the label switching problem. We show an application of the method to data generated by ChIP-sequencing experiments.     

Bayesian Methods for Missing Covariates in Cure Rate Models

We propose methods for Bayesian inference for missing covariate data with a novel class of semi-parametric survival models with a cure fraction. We allow the missing covariates to be either categorical or continuous and specify a parametric distribution for the covariates that is written as a sequence of one dimensional conditional distributions. We assume that the missing covariates are missing at random (MAR) throughout. We propose an informative class of joint prior distributions for the regression coefficients and the parameters arising from the covariate distributions. The proposed class of priors are shown to be useful in recovering information on the missing covariates especially in situations where the missing data fraction is large. Properties of the proposed prior and resulting posterior distributions are examined. Also, model checking techniques are proposed for sensitivity analyses and for checking the goodness of fit of a particular model. Specifically, we extend the Conditional Predictive Ordinate (CPO) statistic to assess goodness of fit in the presence of missing covariate data. Computational techniques using the Gibbs sampler are implemented. A real data set involving a melanoma cancer clinical trial is examined to demonstrate the methodology.     

基于Gibbs抽样的贝叶斯超高频金融数据协整关系研究

针对传统协整检验不能适用于具有随机性特征的超高频金融数据的问题,构建贝叶斯超高频金融数据协整模型,结合参数的后验条件分布设计Gibbs抽样方案,提出基于超高频金融数据的贝叶斯协整检验方法,并利用中国股市超高频金融数据进行实证分析。研究结果表明：贝叶斯方法把参数看作随机变量的思想适合超高频数据随机性的特点,贝叶斯超高频数据协整方法能够不断更新参数信息,避免了OLS估计的有偏性问题,可以得到更符合实际的结论。     

混合贝塔分布随机波动模型及其贝叶斯分析

为了更准确地揭示金融资产收益率数据的真实数据生成过程,提出了基于混合贝塔分布的随机波动模型,讨论了混合贝塔分布随机波动模型的贝叶斯估计方法,并给出了一种Gibbs抽样算法。以上证A股综指简单收益率为例,分别建立了基于正态分布和混合贝塔分布的随机波动模型,研究表明,基于混合贝塔分布的随机波动模型更准确地描述了样本数据的真实数据生成过程,而正态分布的随机波动模型将高峰厚尾等现象归结为波动冲击,从而低估了收益率的平均波动水平,高估了波动的持续性和波动的冲击扰动。     

Posterior analysis,prediction and reliability in three-parameter weibull distributions

The paper develops Bayesian analysis in the context of samples from three-parameter Weibull distributions and shows how to tackle the problems of prediction and estimation of reliability curves. As Johnson, Kotz and Balakrishnan ( 1994 ) mentioned, the prediction problems for the three-parameter Weibull model seem to be unresolved and is certainly worth looking into (p.671). Posterior analysis organized around Gibbs sampling is shown to perform well. An application to stock returns is used to illustrate the potential of the approach.     

The Use of Working Variables in the Bayesian Modeling of Mean and Dispersion Parameters in Generalized Nonlinear Models with Random Effects

This article is aimed at reviewing a novel Bayesian approach to handle inference and estimation in the class of generalized nonlinear models. These models include some of the main techniques of statistical methodology, namely generalized linear models and parametric nonlinear regression. In addition, this proposal extends to methods for the systematic treatment of variation that is not explicitly predicted within the model, through the inclusion of random effects, and takes into account the modeling of dispersion parameters in the class of two-parameter exponential family. The methodology is based on the implementation of a two-stage algorithm that induces a hybrid approach based on numerical methods for approximating the likelihood to a normal density using a Taylor linearization around the values of current parameters in an MCMC routine.     

A Bayesian model for multinomial sampling with misclassified data

In this paper the issue of making inferences with misclassified data from a noisy multinomial process is addressed. A Bayesian model for making inferences about the proportions and the noise parameters is developed. The problem is reformulated in a more tractable form by introducing auxiliary or latent random vectors. This allows for an easy-to-implement Gibbs sampling-based algorithm to generate samples from the distributions of interest. An illustrative example related to elections is also presented.     

Bayesian analysis of joint mean and covariance models for longitudinal data

Efficient estimation of the regression coefficients in longitudinal data analysis requires a correct specification of the covariance structure. If misspecification occurs, it may lead to inefficient or biased estimators of parameters in the mean. One of the most commonly used methods for handling the covariance matrix is based on simultaneous modeling of the Cholesky decomposition. Therefore, in this paper, we reparameterize covariance structures in longitudinal data analysis through the modified Cholesky decomposition of itself. Based on this modified Cholesky decomposition, the within-subject covariance matrix is decomposed into a unit lower triangular matrix involving moving average coefficients and a diagonal matrix involving innovation variances, which are modeled as linear functions of covariates. Then, we propose a fully Bayesian inference for joint mean and covariance models based on this decomposition. A computational efficient Markov chain Monte Carlo method which combines the Gibbs sampler and Metropolis–Hastings algorithm is implemented to simultaneously obtain the Bayesian estimates of unknown parameters, as well as their standard deviation estimates. Finally, several simulation studies and a real example are presented to illustrate the proposed methodology.     

A Bayesian approach of joint models for clustered zero-inflated count data with skewness and measurement errors

Count data with excess zeros are widely encountered in the fields of biomedical, medical, public health and social survey, etc. Zero-inflated Poisson (ZIP) regression models with mixed effects are useful tools for analyzing such data, in which covariates are usually incorporated in the model to explain inter-subject variation and normal distribution is assumed for both random effects and random errors. However, in many practical applications, such assumptions may be violated as the data often exhibit skewness and some covariates may be measured with measurement errors. In this paper, we deal with these issues simultaneously by developing a Bayesian joint hierarchical modeling approach. Specifically, by treating intercepts and slopes in logistic and Poisson regression as random, a flexible two-level ZIP regression model is proposed, where a covariate process with measurement errors is established and a skew-t-distribution is considered for both random errors and random effects. Under the Bayesian framework, model selection is carried out using deviance information criterion (DIC) and a goodness-of-fit statistics is also developed for assessing the plausibility of the posited model. The main advantage of our method is that it allows for more robustness and correctness for investigating heterogeneity from different levels, while accommodating the skewness and measurement errors simultaneously. An application to Shanghai Youth Fitness Survey is used as an illustrate example. Through this real example, it is showed that our approach is of interest and usefulness for applications.