Markov chains of infinite order and asymptotic satisfaction of balance: application to the adaptive integration method.
Adaptive Monte Carlo methods can be viewed as implementations of Markov chains with infinite memory. We derive a general condition for the convergence of a Monte Carlo method whose history dependence is contained within the simulated density distribution. In convergent cases, our result implies that the balance condition need only be satisfied asymptotically. As an example, we show that the adaptive integration method converges.
Earl
David J
DJ
Departments of Bioengineering and Physics & Astronomy, Rice University, 6100 Main Street-MS 142, Houston, Texas 77005-1892, USA.
Deem
Michael W
MW
D000465:Algorithms; D002627:Chemistry, Physical / Q000379:methods*; D003198:Computer Simulation; D007700:Kinetics; D008390:Markov Chains; D015233:Models, Statistical; D008962:Models, Theoretical; D009010:Monte Carlo Method; D009068:Movement; D013997:Time Factors