Circularly-Coupled Markov Chain Sampling

Understand

I show how to run an N-time-step Markov chain simulation in a circular fashion, so that the state at time 0 follows the state at time N-1 in the same way as states at times t follow those at times t-1 for 0<t<N.

• This wrap-around of the chain is achieved using a coupling procedure, and produces states that all have close to the equilibrium distribution of the Markov chain, under the assumption that coupled chains are likely to coalesce in less than N/2 iterations.
• This procedure therefore automatically eliminates the initial portion of the chain that would otherwise need to be discarded to get good estimates of equilibrium averages.
• The assumption of rapid coalescence can be tested using auxiliary chains started at times spaced between 0 and N.