A considerable amount of effort has been recently invested in developing a comprehensive theory for adaptive MCMC. In comparison, there are fewer adaptive algorithms designed for practical situations. I will review some of the theoretical approaches used for proving convergence of non-Markovian adaptation schemes and will discuss scenarios for which the original adaptive Random-Walk Metropolis is unsuitable. Alternative adaptive schemes involving inter-chain and regional adaptation are discussed. Some of the proposed solutions involve theoretical questions that are still open.
Group for Research in Decision Analysis