Two Practical Uses of Coupling: Circular Coupling and Coupling to an
   Approximating Chain

   Radford M. Neal, University of Toronto

   I describe two ways of exploiting coupling to improve MCMC for many
   practical problems.  Circular coupling can discard burn-in iterations
   and diagnose convergence.  In this endeavour, it falls short of the 
   absolute guarantees obtained using coupling from the past, but is 
   likely to be much more widely applicable.  Coupling to an approximating 
   chain can greatly improve efficiency of estimation for distributions 
   for which a tractable approximation is available.  I describe coupling
   schemes that can support both these methods.  The modest overhead of 
   these coupling schemes is often more than paid back, especially when
   both methods are used.