2010
Martino, Luca; Miguez, Joaquin
Generalized Rejection Sampling Schemes and Applications in Signal Processing Artículo de revista
En: Signal Processing, vol. 90, no 11, pp. 2981–2995, 2010.
Resumen | Enlaces | BibTeX | Etiquetas: Adaptive rejection sampling, Gibbs sampling, Monte Carlo integration, Rejection sampling, sensor networks, Target localization
@article{Martino2010a,
title = {Generalized Rejection Sampling Schemes and Applications in Signal Processing},
author = {Luca Martino and Joaquin Miguez},
url = {http://www.sciencedirect.com/science/article/pii/S0165168410001866},
year = {2010},
date = {2010-01-01},
journal = {Signal Processing},
volume = {90},
number = {11},
pages = {2981--2995},
abstract = {Bayesian methods and their implementations by means of sophisticated Monte Carlo techniques, such as Markov chain Monte Carlo (MCMC) and particle filters, have become very popular in signal processing over the last years. However, in many problems of practical interest these techniques demand procedures for sampling from probability distributions with non-standard forms, hence we are often brought back to the consideration of fundamental simulation algorithms, such as rejection sampling (RS). Unfortunately, the use of RS techniques demands the calculation of tight upper bounds for the ratio of the target probability density function (pdf) over the proposal density from which candidate samples are drawn. Except for the class of log-concave target pdf's, for which an efficient algorithm exists, there are no general methods to analytically determine this bound, which has to be derived from scratch for each specific case. In this paper, we introduce new schemes for (a) obtaining upper bounds for likelihood functions and (b) adaptively computing proposal densities that approximate the target pdf closely. The former class of methods provides the tools to easily sample from a posteriori probability distributions (that appear very often in signal processing problems) by drawing candidates from the prior distribution. However, they are even more useful when they are exploited to derive the generalized adaptive RS (GARS) algorithm introduced in the second part of the paper. The proposed GARS method yields a sequence of proposal densities that converge towards the target pdf and enable a very efficient sampling of a broad class of probability distributions, possibly with multiple modes and non-standard forms. We provide some simple numerical examples to illustrate the use of the proposed techniques, including an example of target localization using range measurements, often encountered in sensor network applications.},
keywords = {Adaptive rejection sampling, Gibbs sampling, Monte Carlo integration, Rejection sampling, sensor networks, Target localization},
pubstate = {published},
tppubtype = {article}
}
Bayesian methods and their implementations by means of sophisticated Monte Carlo techniques, such as Markov chain Monte Carlo (MCMC) and particle filters, have become very popular in signal processing over the last years. However, in many problems of practical interest these techniques demand procedures for sampling from probability distributions with non-standard forms, hence we are often brought back to the consideration of fundamental simulation algorithms, such as rejection sampling (RS). Unfortunately, the use of RS techniques demands the calculation of tight upper bounds for the ratio of the target probability density function (pdf) over the proposal density from which candidate samples are drawn. Except for the class of log-concave target pdf's, for which an efficient algorithm exists, there are no general methods to analytically determine this bound, which has to be derived from scratch for each specific case. In this paper, we introduce new schemes for (a) obtaining upper bounds for likelihood functions and (b) adaptively computing proposal densities that approximate the target pdf closely. The former class of methods provides the tools to easily sample from a posteriori probability distributions (that appear very often in signal processing problems) by drawing candidates from the prior distribution. However, they are even more useful when they are exploited to derive the generalized adaptive RS (GARS) algorithm introduced in the second part of the paper. The proposed GARS method yields a sequence of proposal densities that converge towards the target pdf and enable a very efficient sampling of a broad class of probability distributions, possibly with multiple modes and non-standard forms. We provide some simple numerical examples to illustrate the use of the proposed techniques, including an example of target localization using range measurements, often encountered in sensor network applications.
2009
Martino, Luca; Miguez, Joaquin
An Adaptive Accept/Reject Sampling Algorithm for Posterior Probability Distributions Proceedings Article
En: 2009 IEEE/SP 15th Workshop on Statistical Signal Processing, pp. 45–48, IEEE, Cardiff, 2009, ISBN: 978-1-4244-2709-3.
Resumen | Enlaces | BibTeX | Etiquetas: adaptive accept/reject sampling, Adaptive rejection sampling, arbitrary target probability distributions, Computer Simulation, Filtering, Monte Carlo integration, Monte Carlo methods, posterior probability distributions, Probability, Probability density function, Probability distribution, Proposals, Rejection sampling, Sampling methods, sensor networks, Signal processing algorithms, signal sampling, Testing
@inproceedings{Martino2009b,
title = {An Adaptive Accept/Reject Sampling Algorithm for Posterior Probability Distributions},
author = {Luca Martino and Joaquin Miguez},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5278644},
isbn = {978-1-4244-2709-3},
year = {2009},
date = {2009-01-01},
booktitle = {2009 IEEE/SP 15th Workshop on Statistical Signal Processing},
pages = {45--48},
publisher = {IEEE},
address = {Cardiff},
abstract = {Accept/reject sampling is a well-known method to generate random samples from arbitrary target probability distributions. It demands the design of a suitable proposal probability density function (pdf) from which candidate samples can be drawn. These samples are either accepted or rejected depending on a test involving the ratio of the target and proposal densities. In this paper we introduce an adaptive method to build a sequence of proposal pdf's that approximate the target density and hence can ensure a high acceptance rate. In order to illustrate the application of the method we design an accept/reject particle filter and then assess its performance and sampling efficiency numerically, by means of computer simulations.},
keywords = {adaptive accept/reject sampling, Adaptive rejection sampling, arbitrary target probability distributions, Computer Simulation, Filtering, Monte Carlo integration, Monte Carlo methods, posterior probability distributions, Probability, Probability density function, Probability distribution, Proposals, Rejection sampling, Sampling methods, sensor networks, Signal processing algorithms, signal sampling, Testing},
pubstate = {published},
tppubtype = {inproceedings}
}
Accept/reject sampling is a well-known method to generate random samples from arbitrary target probability distributions. It demands the design of a suitable proposal probability density function (pdf) from which candidate samples can be drawn. These samples are either accepted or rejected depending on a test involving the ratio of the target and proposal densities. In this paper we introduce an adaptive method to build a sequence of proposal pdf's that approximate the target density and hence can ensure a high acceptance rate. In order to illustrate the application of the method we design an accept/reject particle filter and then assess its performance and sampling efficiency numerically, by means of computer simulations.