Bayesian Estimation and Model Choice in Item Response Models

Item response models are essential tools for analyzing results from many educational and psychological tests. Such models are used to quantify the probability of correct response as a function of unobserved examinee ability and other parameters explaining the difficulty and the discriminatory power of the questions in the test. Some of these models also incorporate a threshold parameter for the probability of the correct response to account for the effect of guessing the correct answer in multiple choice type tests. In this article we consider fitting of such models using the Gibbs sampler. A data augmentation method to analyze a normal-ogive model incorporating a threshold guessing parameter is introduced and compared with a Metropolis-Hastings sampling method. The proposed method is an order of magnitude more efficient than the existing method. Another objective of this paper is to develop Bayesian model choice techniques for model discrimination. A predictive approach based on a variant of the Bayes factor is used and compared with another decision theoretic method which minimizes an expected loss function on the predictive space. A classical model choice technique based on a modified likelihood ratio test statistic is shown as one component of the second criterion. As a consequence the Bayesian methods proposed in this paper are contrasted with the classical approach based on the likelihood ratio test. Several examples are given to illustrate the methods.     

短篇小说 The Sampler 与《孔乙己》对照赏析

本文通过对照以赏析短篇小说The sample和《孔乙己》的相同和相异之处,从时代和社会背景来分析两位主人公的遭遇和命运的根源。通过解读两文的叙事方法以再现其艺术感染力,从而达到对比和鉴赏中西文学作品的目的。     

The Estimation of Dynamic Bivariate Mixture Models

Watanabe estimated the dynamic bivariate mixture models introduced by Tauchen and Pitts and modified by Andersen using a Bayesian method via Markov chain Monte Carlo techniques. Based on a maximum likelihood method via efficient importance sampling, Liesenfeld and Richard obtained estimates that are significantly different from those of Watanabe. This note corrects the error in the multimove sampler used by Watanabe and reproduces all analyses in the work of Watanabe using a corrected multimove sampler. The estimates using the correct multimove sampler are found to be close to those obtained by Liesenfeld and Richard.     

基于Gibbs抽样算法的面板数据分位回归方法

 文章讨论了含有随机效应的面板数据模型,利用非对称Laplace分布与分位回归之间的关系,文章建立了一种贝叶斯分层分位回归模型。通过对非对称Laplace分布的分解,文章给出了Gibbs抽样算法下模型参数的点估计及区间估计,模拟结果显示,在处理含随机效应的面板数据模型中,特别是在误差非正态的情况下,本文的方法优于传统的均值模型方法。文章最后利用新方法对我国各地区经济与就业面板数据进行了实证研究,得到了有利于宏观调控的有用信息。     

基于Bayesian Gibbs Sampler的状态空间模型估计方法研究及其在中国潜在产出估计上的应用

 本文将贝叶斯吉伯斯样本生成（Bayesian Gibbs Sampling,BGS）方法应用到状态空间模型的估计。首先介绍了BGS方法的基本内容和计算步骤,然后给定参数生成满足状态空间模型的模拟数据,并对模拟数据应用BGS方法估计。结果表明参数与状态向量的估计值与参数值与状态向量的真实值相当接近,明显优于基于Kalman滤波的最大似然估计结果。最后,本文将BGS算法应用于中国1980年至2008年的潜在增长率与增长率缺口的估计。     

Updating Schemes, Correlation Structure, Blocking and Parameterization for the Gibbs Sampler

In this paper many convergence issues concerning the implementation of the Gibbs sampler are investigated. Exact computable rates of convergence for Gaussian target distributions are obtained. Different random and non-random updating strategies and blocking combinations are compared using the rates. The effect of dimensionality and correlation structure on the convergence rates are studied. Some examples are considered to demonstrate the results. For a Gaussian image analysis problem several updating strategies are described and compared. For problems in Bayesian linear models several possible parameterizations are analysed in terms of their convergence rates characterizing the optimal choice.     

Comparisons of Three Approaches for Discrete Conditional Models

This article describes three methods for computing a discrete joint density from full conditional densities. They are the Gibbs sampler, a hybrid method, and an interaction-based method. The hybrid method uses the iterative proportional fitting algorithm, and it is derived from the mixed parameterization of a contingency table. The interaction-based approach is derived from the canonical parameters, while the Gibbs sampler can be regarded as based on the mean parameters. In short, different approaches are motivated by different parameterizations. The setting of a bivariate conditionally specified distribution is used as the premise for comparing the numerical accuracy of the three methods. Detailed comparisons of marginal distributions, odds ratios and expected values are reported. We give theoretical justifications as to why the hybrid method produces better approximation than the Gibbs sampler. Generalizations to more than two variables are discussed. In practice, Gibbs sampler has certain advantages: it is conceptually easy to understand and there are many software tools available. Nevertheless, the hybrid method and the interaction-based method are accurate and simple alternatives when the Gibbs sampler results in a slowly mixing chain and requires substantial simulation efforts.     

Bayesian analysis of bilinear time series models : a gibbs sampling approach

Nonlinear time series analysis plays an important role in recent econometric literature, especially the bilinear model. In this paper, we cast the bilinear time series model in a Bayesian framework and make inference by using the Gibbs sampler, a Monte Carlo method. The methodology proposed is illustrated by using generated examples, two real data sets, as well as a simulation study. The results show that the Gibbs sampler provides a very encouraging option in analyzing bilinear time series.     

On the application of improved symplectic integrators in Hamiltonian Monte Carlo

We explore the construction of new symplectic numerical integration schemes to be used in Hamiltonian Monte Carlo and study their efficiency. Integration schemes from Blanes et al., and a new scheme are considered as candidates to the commonly used leapfrog method. All integration schemes are tested within the framework of the No-U-Turn sampler (NUTS), both for a logistic regression model and a student t-model. The results show that the leapfrog method is inferior to all the new methods both in terms of asymptotic expected acceptance probability for a model problem and the efficient sample size per computing time for the realistic models.     

Convergence assessment techniques for Markov chain Monte Carlo

MCMC methods have effectively revolutionised the field of Bayesian statistics over the past few years. Such methods provide invaluable tools to overcome problems with analytic intractability inherent in adopting the Bayesian approach to statistical modelling.However, any inference based upon MCMC output relies critically upon the assumption that the Markov chain being simulated has achieved a steady state or converged. Many techniques have been developed for trying to determine whether or not a particular Markov chain has converged, and this paper aims to review these methods with an emphasis on the mathematics underpinning these techniques, in an attempt to summarise the current state-of-play for convergence assessment techniques and to motivate directions for future research in this area.