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3 claims from 1 paper

1. Mathematics › Markov Chains and Monte Carlo Methods

   Inference from Iterative Simulation Using Multiple Sequences

   Gelman and Rubin · Statistical Science · 1992

   Gelman and Rubin propose simple methods for judging output from iterative simulation such as the Gibbs sampler, using several sequences, and illustrate them on reaction-time data from normal and schizophrenic patients.

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   1. UncheckedThe authors recommend running several independent simulation sequences, each started from widely spread-out starting points, when using iterative simulation.“Our recommended strategy is to use several independent sequences, with starting points sampled from an overdispersed distribution.”
   2. Unchecked“At each step of the iterative simulation, we obtain, for each univariate estimand of interest, a distributional estimate and an estimate of how much sharper the distributional estimate might become if the simulations were continued indefinitely.”
   3. Unchecked“Because our focus is on applied inference for Bayesian posterior distributions in real problems, which often tend toward normality after transformations and marginalization, we derive our results as normal-theory approximations to exact Bayesian inference, c…