Wavelet Monte Carlo: a principle for sampling from complex distributions

We present Wavelet Monte Carlo (WMC), a new method for generating independent samples from complex target distributions. The methodology is based on wavelet decomposition of the difference between the target density and a user-specified initial density, and exploits both wavelet theory and survival...

Full description

Saved in:
Bibliographic Details
Published in:Statistics and computing 2023-10, Vol.33 (5), Article 92
Main Authors: Gilks, Walter R., Cironis, Lukas, Barber, Stuart
Format: Article
Language:English
Subjects:
Artificial Intelligence
Computational efficiency
Computer Science
Density
Methodology
Original Paper
Probability and Statistics in Computer Science
Statistical Theory and Methods
Statistics and Computing/Statistics Programs
Wavelet transforms
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We present Wavelet Monte Carlo (WMC), a new method for generating independent samples from complex target distributions. The methodology is based on wavelet decomposition of the difference between the target density and a user-specified initial density, and exploits both wavelet theory and survival analysis. In practice, WMC can process only a finite range of wavelet scales. We prove that the resulting L 1 approximation error converges to zero geometrically as the scale range tends to ( - ∞ , + ∞ ) . This provides a principled approach to trading off accuracy against computational efficiency. We offer practical suggestions for addressing some issues of implementation, but further development is needed for a computationally efficient methodology. We illustrate the methodology in one- and two-dimensional examples, and discuss challenges and opportunities for application in higher dimensions.
ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-023-10256-w