TY - BOOK ID - 16794293 TI - Discretization and MCMC convergence assessment PY - 1998 VL - 135 SN - 0387985913 1461217164 9780387985916 PB - New York (N.Y.) : Springer, DB - UniCat KW - Convergence KW - Markov processes KW - Monte Carlo method KW - Convergence. KW - Markov processes. KW - Monte Carlo method. KW - Discretization (Mathematics) KW - Engineering & Applied Sciences KW - Applied Mathematics KW - Applied mathematics. KW - Engineering mathematics. KW - Applications of Mathematics. KW - Engineering KW - Engineering analysis KW - Mathematical analysis KW - Mathematics KW - Mathematical models. KW - Analysis, Markov KW - Chains, Markov KW - Markoff processes KW - Markov analysis KW - Markov chains KW - Markov models KW - Models, Markov KW - Processes, Markov KW - Stochastic processes KW - Functions UR - https://www.unicat.be/uniCat?func=search&query=sysid:16794293 AB - The exponential increase in the use of MCMC methods and the corre­ sponding applications in domains of even higher complexity have caused a growing concern about the available convergence assessment methods and the realization that some of these methods were not reliable enough for all-purpose analyses. Some researchers have mainly focussed on the con­ vergence to stationarity and the estimation of rates of convergence, in rela­ tion with the eigenvalues of the transition kernel. This monograph adopts a different perspective by developing (supposedly) practical devices to assess the mixing behaviour of the chain under study and, more particularly, it proposes methods based on finite (state space) Markov chains which are obtained either through a discretization of the original Markov chain or through a duality principle relating a continuous state space Markov chain to another finite Markov chain, as in missing data or latent variable models. The motivation for the choice of finite state spaces is that, although the resulting control is cruder, in the sense that it can often monitor con­ vergence for the discretized version alone, it is also much stricter than alternative methods, since the tools available for finite Markov chains are universal and the resulting transition matrix can be estimated more accu­ rately. Moreover, while some setups impose a fixed finite state space, other allow for possible refinements in the discretization level and for consecutive improvements in the convergence monitoring. ER -