Warianty tytułu
Abstrakty
We prove explicit, i.e. non-asymptotic, error bounds for Markov chain Monte Carlo methods. The problem is to compute the expectation of a function f with respect to a measure π. Different convergence properties of Markov chains imply different error bounds. For uniformly ergodic and reversible Markov chains we prove a lower and an upper error bound with respect to ||f||₂. If there exists an L₂-spectral gap, which is a weaker convergence property than uniform ergodicity, then we show an upper error bound with respect to $||f||_{p}$ for p > 2. Usually a burn-in period is an efficient way to tune the algorithm. We provide and justify a recipe how to choose the burn-in period. The error bounds are applied to the problem of integration with respect to a possibly unnormalized density. More precise, we consider integration with respect to log-concave densities and integration over convex bodies. By the use of the Metropolis algorithm based on a ball walk and the hit-and-run algorithm it is shown that both problems are polynomial tractable.
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
485
Liczba stron
93
Liczba rozdzia³ów
Opis fizyczny
Daty
wydano
2012
Twórcy
autor
- Institute of Mathematics, University of Jena, Ernst-Abbe-Platz 2, D-07743 Jena, Germany
Bibliografia
Języki publikacji
EN |
Uwagi
Identyfikator YADDA
bwmeta1.element.bwnjournal-rm-doi-10_4064-dm485-0-1
Identyfikatory
DOI
10.4064/dm485-0-1
Kolekcja
DML-PL
