Effective sample size
Topic of Markov chains, Gibbs sampling, and Metropolis–Hastings, part of Bayesian statistics
Effective sample size
| Type | Topic |
| Taught in | Markov chains, Gibbs sampling, and Metropolis–Hastings |
| Part | Bayesian statistics |
| Questions using it | 1 |
The number of independent draws that would give the same Monte Carlo precision as M correlated MCMC draws, roughly M/(1+2\sum_{k\ge1}\rho_k) for lag-k autocorrelations \rho_k. Strong autocorrelation makes it much smaller than M.
In Markov chains, Gibbs sampling, and Metropolis–Hastings
where B is the number of discarded iterations. Because the draws are dependent, L correlated draws contain less information than L independent draws. Autocorrelation, trace plots, multiple chains, and effective sample size are therefore part of a serious analysis.
Used in
- Taught in Markov chains, Gibbs sampling, and Metropolis–Hastings
- Questions that use it (1) — Q19 (answer)
- All 31 questions on Markov chains, Gibbs sampling, and Metropolis–Hastings
See also
Monte Carlo method · Precision · Markov chain · Autocorrelation function · Warm-up is not a convergence proof · Stationarity and detailed balance · Detailed balance implies stationarity · Systematic-scan Gibbs sampler