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Understanding Linchpin Variables in Markov Chain Monte Carlo
Dootika Vats, Felipe Acosta, Mark L. Huber +1
An introduction to the use of linchpin variables in Markov chain Monte Carlo (MCMC) is provided. Before the widespread adoption of MCMC methods, conditional sampling using linchpin…
Analyzing MCMC Output
Dootika Vats, Nathan Robertson, James M Flegal +1
Markov chain Monte Carlo (MCMC) is a sampling-based method for estimating features of probability distributions. MCMC methods produce a serially correlated, yet representative, sam…
Assessing and Visualizing Simultaneous Simulation Error
Nathan Robertson, James M. Flegal, Dootika Vats +1
Monte Carlo experiments produce samples in order to estimate features of a given distribution. However, simultaneous estimation of means and quantiles has received little attention…
Directional Metropolis-Hastings
Abhirup Mallik, Galin L. Jones
We propose a new kernel for Metropolis Hastings called Directional Metropolis Hastings (DMH) with multivariate update where the proposal kernel has state dependent covariance matri…
MCMC using Hamiltonian dynamics
Radford M. Neal
Hamiltonian dynamics can be used to produce distant proposals for the Metropolis algorithm, thereby avoiding the slow exploration of the state space that results from the diffusive…
Component-Wise Markov Chain Monte Carlo: Uniform and Geometric Ergodicity under Mixing and Composition
Alicia A. Johnson, Galin L. Jones, Ronald C. Neath
It is common practice in Markov chain Monte Carlo to update the simulation one variable (or sub-block of variables) at a time, rather than conduct a single full-dimensional update.…
Gibbs Sampling for a Bayesian Hierarchical General Linear Model
Alicia A. Johnson, Galin L. Jones
We consider a Bayesian hierarchical version of the normal theory general linear model which is practically relevant in the sense that it is general enough to have many applications…