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Inference from Iterative Simulation Using Multiple Sequences
The Gibbs sampler, the algorithm of Metropolis and similar iterative simulation methods are potentially very helpful for summarizing multivariate distributions. Used naively, however, iterativeExpand
Bayesian Data Analysis
TLDR
Detailed notes on Bayesian Computation Basics of Markov Chain Simulation, Regression Models, and Asymptotic Theorems are provided. Expand
General methods for monitoring convergence of iterative simulations
We generalize the method proposed by Gelman and Rubin (1992a) for monitoring the convergence of iterative simulations by comparing between and within variances of multiple chains, in order to obtainExpand
Stan: A Probabilistic Programming Language
TLDR
Stan is a probabilistic programming language for specifying statistical models that provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the No-U-Turn sampler and an adaptive form of Hamiltonian Monte Carlo sampling. Expand
Data Analysis Using Regression and Multilevel/Hierarchical Models
Data Analysis Using Regression and Multilevel/Hierarchical Models is a comprehensive manual for the applied researcher who wants to perform data analysis using linear and nonlinear regression andExpand
Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper)
Various noninformative prior distributions have been suggested for scale parameters in hierarchical models. We construct a new folded-noncentral-t family of conditionally conjugate priors forExpand
Weak convergence and optimal scaling of random walk Metropolis algorithms
This paper considers the problem of scaling the proposal distribution of a multidimensional random walk Metropolis algorithm in order to maximize the efficiency of the algorithm. The main result is aExpand
The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo
TLDR
The No-U-Turn Sampler (NUTS), an extension to HMC that eliminates the need to set a number of steps L, and derives a method for adapting the step size parameter {\epsilon} on the fly based on primal-dual averaging. Expand
R2WinBUGS: A Package for Running WinBUGS from R
The R2WinBUGS package provides convenient functions to call WinBUGS from R. It automatically writes the data and scripts in a format readable by WinBUGS for processing in batch mode, which isExpand
POSTERIOR PREDICTIVE ASSESSMENT OF MODEL FITNESS VIA REALIZED DISCREPANCIES
This paper considers Bayesian counterparts of the classical tests for good- ness of fit and their use in judging the fit of a single Bayesian model to the observed data. We focus on posteriorExpand
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