For how many iterations should we run Markov chain Monte Carlo?

Understand

Standard Markov chain Monte Carlo (MCMC) admits three fundamental control parameters: the number of chains, the length of the warmup phase, and the length of the sampling phase.

• These control parameters play a large role in determining the amount of computation we deploy.
• In practice, we need to walk a line between achieving sufficient precision and not wasting precious computational resources and time.
• We review general strategies to check the length of the warmup and sampling phases, and examine the three control parameters of MCMC in the contexts of CPU- and GPU-based hardware.