Inference from iterative simulation using multiple sequences.¶
Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical Science, 7(4), 457-472.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Bayesian Updating
- T2 — Sequential coherence vs computational tractability. The mathematical elegance of Bayesian updating — posteriors become priors for the next observation — is a theoretical ideal that in practice often requires approximate methods (MCMC, variational inference, sequential Monte Carlo
This sourceIntroduces the between/within-chain convergence diagnostic (R-hat) for MCMC, directly substantiating that posterior approximations' convergence is not always guaranteed. SUPPORTS marker 013 (note: prior reference title said 'multiple chains'; correct title is 'multiple sequences').
- T2 — Sequential coherence vs computational tractability. The mathematical elegance of Bayesian updating — posteriors become priors for the next observation — is a theoretical ideal that in practice often requires approximate methods (MCMC, variational inference, sequential Monte Carlo
- Monte Carlo Simulation
- T3 — Convergence diagnostics vs practical stopping criteria. For MCMC specifically, determining when the chain has converged to its stationary distribution — and has produced enough effectively independent samples — is a subtle problem with no universally reliable diagnostic
This sourceGelman-Rubin MCMC convergence diagnostic methods for Bayesian posterior computation.
- T3 — Convergence diagnostics vs practical stopping criteria. For MCMC specifically, determining when the chain has converged to its stationary distribution — and has produced enough effectively independent samples — is a subtle problem with no universally reliable diagnostic
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