Simple Monte Carlo and the Metropolis algorithm
We study the integration of functions with respect to an unknown density. Information is available as oracle calls to the integrand and to the non-normalized density function. We are interested in analyzing the integration error of optimal algorithms (or the complexity of the problem) with emphasis...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Berlin
WIAS
2006
|
| Schriftenreihe: | Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik
1182 |
| Schlagworte: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Tag hinzufügen | Zusammenfassung: | We study the integration of functions with respect to an unknown density. Information is available as oracle calls to the integrand and to the non-normalized density function. We are interested in analyzing the integration error of optimal algorithms (or the complexity of the problem) with emphasis on the variability of the weight function. For a corresponding large class of problem instances we show that the complexity grows linearly in the variability, and the simple Monte Carlo method provides an almost optimal algorithm. Under additional geometric restrictions (mainly log-concavity) for the density functions, we establish that a suitable adaptive local Metropolis algorithm is almost optimal and outperforms any non-adaptive algorithm. |
|---|---|
| Beschreibung: | Unterschiede zwischen dem gedruckten Dokument und der elektronischen Ressource können nicht ausgeschlossen werden. - Auch als elektronische Ausg. vorhanden Auch als elektronisches Dokument vorh |
| Beschreibung: | 23 S. |