A Note on Particle Gibbs Method and its Extensions and Variants

A note on Bayesian logistic regression for spatial exponential family Gibbs point processes

Recently, a very attractive logistic regression inference method for exponential family Gibbs spatial point processes was introduced. We combined it with the technique of quadratic tangential variational approximation and derived a new Bayesian technique for analysing spatial point patterns. The technique is described in detail, and demonstrated on numerical examples.

Geometric ergodicity of Gibbs samplers for the Horseshoe and its regularized variants

The Horseshoe is a widely used and popular continuous shrinkage prior for high-dimensional Bayesian linear regression. Recently, regularized versions of the Horseshoe prior have also been introduced in the literature. Various Gibbs sampling Markov chains have been developed in the literature to generate approximate samples from the corresponding intractable posterior densities. Establishing geometric ergodicity of these Markov chains provides crucial technical justification for the accuracy of asymptotic standard errors for Markov chain based estimates of posterior quantities. In this paper, w…

A Note on the Posterior Inference for the Yule-Simon Distribution

The Yule--Simon distribution has been out of the radar of the Bayesian community, so far. In this note, we propose an explicit Gibbs sampling scheme when a Gamma prior is chosen for the shape parameter. The performance of the algorithm is illustrated with simulation studies, including count data regression, and a real data application to text analysis. We compare our proposal to the frequentist counterparts showing better performance of our algorithm when a small sample size is considered.

A Note on Bayesian Modeling Specification of Censored Data in JAGS

Just Another Gibbs Sampling (JAGS) is a convenient tool to draw posterior samples using Markov Chain Monte Carlo for Bayesian modeling. However, the built-in function dinterval() to model censored data misspecifies the computation of deviance function, which may limit its usage to perform likelihood based model comparison. To establish an automatic approach to specify the correct deviance function in JAGS, we propose a simple alternative modeling strategy to implement Bayesian model selection for analysis of censored outcomes. The proposed approach is applicable to a broad spectrum of data typ…

Gibbs采样器及其阻塞和坍塌变体的固有原则扩展

Extensions of the solidarity principle of the spectral gap for Gibbs samplers to their blocked and collapsed variants

本文扩展了完整Gibbs采样器的固有原则，证明了阻塞和坍塌变体继承谱间隙，并通过例子说明其不继承几何平稳性。

关于发现概率的贝叶斯非参数估计的注记

A note on a Bayesian nonparametric estimator of the discovery probability

Favaro、Lijoi和Pruenster（2012，Biometrics，68，1188- 1196）推导了一种新的贝叶斯非参数估计，该估计是在$(n+m+1)$次观察时检测到一个物种的概率，该物种已经在$n+m$大小的扩大样本中以任何给定频率观察到，条件是大小为$n$的基本样本。不幸的是，吉布斯先验下的一般结果（定理2），以及因此在$(α, θ)$泊松-狄利克雷先验下的显式结果（命题3），似乎是错误的。在这里，我们提供了两个结果的正确公式，通过Cerquetti（2013）设计的新技术获得。我们验证了我们的推导的正确性，明确的反证的两个参数Poisson-Dirichlet的情况。