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利用 Metropolis–Hastings 输出估计边际似然AI 解读

This article provides a framework for estimating the marginal likelihood for the purpose of Bayesian model comparisons. The approach extends and completes the method presented in Chib (1995) by overcoming the problems associated with the presence of intractable full conditional densities. The proposed method is developed in the context of MCMC chains produced by the Metropolis–Hastings algorithm, whose building blocks are used both for sampling and marginal likelihood…

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In this paper, Markov chain Monte Carlo sampling methods are exploited to provide a unified, practical likelihood-based framework for the analysis of stochastic volatility models. A highly effective method is developed that samples all the unobserved volatilities at once using an approximating offset mixture model, followed by an importance reweighting procedure. This approach is compared with several alternative methods using real data. The paper also develops…

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计量经济学中的马尔可夫链蒙特卡洛模拟方法AI 解读

We present several Markov chain Monte Carlo simulation methods that have been widely used in recent years in econometrics and statistics. Among these is the Gibbs sampler, which has been of particular interest to econometricians. Although the paper summarizes some of the relevant theoretical literature, its emphasis is on the presentation and explanation of applications to important models that are studied in econometrics. We include a discussion of some implementation…

利用 Gibbs 抽样输出计算边际似然AI 解读

In the context of Bayes estimation via Gibbs sampling, with or without data augmentation, a simple approach is developed for computing the marginal density of the sample data (marginal likelihood) given parameter draws from the posterior distribution. Consequently, Bayes factors for model comparisons can be routinely computed as a by-product of the simulation. Hitherto, this calculation has proved extremely challenging. Our approach exploits the fact that the marginal…

通过马尔可夫链蒙特卡洛方法进行贝叶斯模型选择AI 解读

SUMMARY Markov chain Monte Carlo (MCMC) integration methods enable the fitting of models of virtually unlimited complexity, and as such have revolutionized the practice of Bayesian data analysis. However, comparison across models may not proceed in a completely analogous fashion, owing to violations of the conditions sufficient to ensure convergence of the Markov chain. In this paper we present a framework for Bayesian model choice, along with an MCMC algorithm that does not…

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二元响应回归模型的贝叶斯残差分析AI 解读

In a binary response regression model, classical residuals are difficult to define and interpret due to the discrete nature of the response variable. In contrast, Bayesian residuals have continuous-valued posterior distributions which can be graphed to learn about outlying observations. Two definitions of Bayesian residuals are proposed for binary regression data. Plots of the posterior distributions of the basic ‘observed –fitted’ residuals can be helpful in outlier…

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二元与多类别响应数据的贝叶斯分析AI 解读

A vast literature in statistics, biometrics, and econometrics is concerned with the analysis of binary and polychotomous response data. The classical approach fits a categorical response regression model using maximum likelihood, and inferences about the model are based on the associated asymptotic theory. The accuracy of classical confidence statements is questionable for small sample sizes. In this article, exact Bayesian methods for modeling categorical response data are…

均值与方差发生马尔可夫状态切换的自回归时间序列：Gibbs 抽样贝叶斯推断AI 解读

The authors examine autoregressive time series models subject to regime switching. A Bayesian framework is develope d in which the unobserved.states, one for each time point, are treated as missing data and then analyzed using the Gibbs sampler. This approac h is straightforward because the conditional posterior distribution of the parameters given the states, and the conditional posterior distribution of the states given the parameters, are amenable to simulation. The…

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