## 2016 |

Koblents, Eugenia; Míguez, Joaquín; Rodríguez, Marco A; Schmidt, Alexandra M A Nonlinear Population Monte Carlo Scheme for the Bayesian Estimation of Parameters of α-stable Distributions Journal Article Computational Statistics &amp; Data Analysis, 95 , pp. 57–74, 2016, ISSN: 01679473. Abstract | Links | BibTeX | Tags: Animal movement, Bayesian inference, Importance sampling, L{é}vy process, α-stable distributions @article{Koblents2016, title = {A Nonlinear Population Monte Carlo Scheme for the Bayesian Estimation of Parameters of α-stable Distributions}, author = {Eugenia Koblents and Joaquín Míguez and Marco A Rodríguez and Alexandra M Schmidt}, url = {http://www.sciencedirect.com/science/article/pii/S0167947315002340}, doi = {10.1016/j.csda.2015.09.007}, issn = {01679473}, year = {2016}, date = {2016-03-01}, journal = {Computational Statistics &amp; Data Analysis}, volume = {95}, pages = {57--74}, abstract = {The class of $alpha$-stable distributions enjoys multiple practical applications in signal processing, finance, biology and other areas because it allows to describe interesting and complex data patterns, such as asymmetry or heavy tails, in contrast with the simpler and widely used Gaussian distribution. The density associated with a general $alpha$-stable distribution cannot be obtained in closed form, which hinders the process of estimating its parameters. A nonlinear population Monte Carlo (NPMC) scheme is applied in order to approximate the posterior probability distribution of the parameters of an $alpha$-stable random variable given a set of random realizations of the latter. The approximate posterior distribution is computed by way of an iterative algorithm and it consists of a collection of samples in the parameter space with associated nonlinearly-transformed importance weights. A numerical comparison of the main existing methods to estimate the $alpha$-stable parameters is provided, including the traditional frequentist techniques as well as a Markov chain Monte Carlo (MCMC) and a likelihood-free Bayesian approach. It is shown by means of computer simulations that the NPMC method outperforms the existing techniques in terms of parameter estimation error and failure rate for the whole range of values of $alpha$, including the smaller values for which most existing methods fail to work properly. Furthermore, it is shown that accurate parameter estimates can often be computed based on a low number of observations. Additionally, numerical results based on a set of real fish displacement data are provided.}, keywords = {Animal movement, Bayesian inference, Importance sampling, L{é}vy process, α-stable distributions}, pubstate = {published}, tppubtype = {article} } The class of $alpha$-stable distributions enjoys multiple practical applications in signal processing, finance, biology and other areas because it allows to describe interesting and complex data patterns, such as asymmetry or heavy tails, in contrast with the simpler and widely used Gaussian distribution. The density associated with a general $alpha$-stable distribution cannot be obtained in closed form, which hinders the process of estimating its parameters. A nonlinear population Monte Carlo (NPMC) scheme is applied in order to approximate the posterior probability distribution of the parameters of an $alpha$-stable random variable given a set of random realizations of the latter. The approximate posterior distribution is computed by way of an iterative algorithm and it consists of a collection of samples in the parameter space with associated nonlinearly-transformed importance weights. A numerical comparison of the main existing methods to estimate the $alpha$-stable parameters is provided, including the traditional frequentist techniques as well as a Markov chain Monte Carlo (MCMC) and a likelihood-free Bayesian approach. It is shown by means of computer simulations that the NPMC method outperforms the existing techniques in terms of parameter estimation error and failure rate for the whole range of values of $alpha$, including the smaller values for which most existing methods fail to work properly. Furthermore, it is shown that accurate parameter estimates can often be computed based on a low number of observations. Additionally, numerical results based on a set of real fish displacement data are provided. |

## 2015 |

Martino, Luca; Elvira, Victor; Luengo, David; Corander, Jukka An Adaptive Population Importance Sampler: Learning From Uncertainty Journal Article IEEE Transactions on Signal Processing, 63 (16), pp. 4422–4437, 2015, ISSN: 1053-587X. Abstract | Links | BibTeX | Tags: Adaptive importance sampling, adaptive multiple IS, adaptive population importance sampler, AMIS, APIS, Estimation, Importance sampling, IS estimators, iterative estimation, iterative methods, Journal, MC methods, Monte Carlo (MC) methods, Monte Carlo methods, population Monte Carlo, Proposals, Signal processing algorithms, simple temporal adaptation, Sociology, Standards, Wireless sensor network, Wireless Sensor Networks @article{Martino2015bbb, title = {An Adaptive Population Importance Sampler: Learning From Uncertainty}, author = {Luca Martino and Victor Elvira and David Luengo and Jukka Corander}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=7117437}, doi = {10.1109/TSP.2015.2440215}, issn = {1053-587X}, year = {2015}, date = {2015-08-01}, journal = {IEEE Transactions on Signal Processing}, volume = {63}, number = {16}, pages = {4422--4437}, publisher = {IEEE}, abstract = {Monte Carlo (MC) methods are well-known computational techniques, widely used in different fields such as signal processing, communications and machine learning. An important class of MC methods is composed of importance sampling (IS) and its adaptive extensions, such as population Monte Carlo (PMC) and adaptive multiple IS (AMIS). In this paper, we introduce a novel adaptive and iterated importance sampler using a population of proposal densities. The proposed algorithm, named adaptive population importance sampling (APIS), provides a global estimation of the variables of interest iteratively, making use of all the samples previously generated. APIS combines a sophisticated scheme to build the IS estimators (based on the deterministic mixture approach) with a simple temporal adaptation (based on epochs). In this way, APIS is able to keep all the advantages of both AMIS and PMC, while minimizing their drawbacks. Furthermore, APIS is easily parallelizable. The cloud of proposals is adapted in such a way that local features of the target density can be better taken into account compared to single global adaptation procedures. The result is a fast, simple, robust, and high-performance algorithm applicable to a wide range of problems. Numerical results show the advantages of the proposed sampling scheme in four synthetic examples and a localization problem in a wireless sensor network.}, keywords = {Adaptive importance sampling, adaptive multiple IS, adaptive population importance sampler, AMIS, APIS, Estimation, Importance sampling, IS estimators, iterative estimation, iterative methods, Journal, MC methods, Monte Carlo (MC) methods, Monte Carlo methods, population Monte Carlo, Proposals, Signal processing algorithms, simple temporal adaptation, Sociology, Standards, Wireless sensor network, Wireless Sensor Networks}, pubstate = {published}, tppubtype = {article} } Monte Carlo (MC) methods are well-known computational techniques, widely used in different fields such as signal processing, communications and machine learning. An important class of MC methods is composed of importance sampling (IS) and its adaptive extensions, such as population Monte Carlo (PMC) and adaptive multiple IS (AMIS). In this paper, we introduce a novel adaptive and iterated importance sampler using a population of proposal densities. The proposed algorithm, named adaptive population importance sampling (APIS), provides a global estimation of the variables of interest iteratively, making use of all the samples previously generated. APIS combines a sophisticated scheme to build the IS estimators (based on the deterministic mixture approach) with a simple temporal adaptation (based on epochs). In this way, APIS is able to keep all the advantages of both AMIS and PMC, while minimizing their drawbacks. Furthermore, APIS is easily parallelizable. The cloud of proposals is adapted in such a way that local features of the target density can be better taken into account compared to single global adaptation procedures. The result is a fast, simple, robust, and high-performance algorithm applicable to a wide range of problems. Numerical results show the advantages of the proposed sampling scheme in four synthetic examples and a localization problem in a wireless sensor network. |

Koblents, Eugenia; Miguez, Joaquin A Population Monte Carlo Scheme with Transformed Weights and Its Application to Stochastic Kinetic Models Journal Article Statistics and Computing, 25 (2), pp. 407–425, 2015, ISSN: 0960-3174. Abstract | Links | BibTeX | Tags: COMPREHENSION, degeneracy of importance weights, Importance sampling, Journal, population Monte Carlo, Stochastic kinetic models @article{Koblents2014b, title = {A Population Monte Carlo Scheme with Transformed Weights and Its Application to Stochastic Kinetic Models}, author = {Eugenia Koblents and Joaquin Miguez}, url = {http://link.springer.com/10.1007/s11222-013-9440-2 http://gts.tsc.uc3m.es/wp-content/uploads/2014/01/NPMC_A-population-Monte-Carlo-scheme-with-transformed_jma.pdf}, doi = {10.1007/s11222-013-9440-2}, issn = {0960-3174}, year = {2015}, date = {2015-03-01}, journal = {Statistics and Computing}, volume = {25}, number = {2}, pages = {407--425}, abstract = {This paper addresses the Monte Carlo approximation of posterior probability distributions. In particular, we consider the population Monte Carlo (PMC) technique, which is based on an iterative importance sampling (IS) approach. An important drawback of this methodology is the degeneracy of the importance weights (IWs) when the dimension of either the observations or the variables of interest is high. To alleviate this difficulty, we propose a new method that performs a nonlinear transformation of the IWs. This operation reduces the weight variation, hence it avoids degeneracy and increases the efficiency of the IS scheme, specially when drawing from proposal functions which are poorly adapted to the true posterior. For the sake of illustration, we have applied the proposed algorithm to the estimation of the parameters of a Gaussian mixture model. This is a simple problem that enables us to discuss the main features of the proposed technique. As a practical application, we have also considered the challenging problem of estimating the rate parameters of a stochastic kinetic model (SKM). SKMs are multivariate systems that model molecular interactions in biological and chemical problems. We introduce a particularization of the proposed algorithm to SKMs and present numerical results.}, keywords = {COMPREHENSION, degeneracy of importance weights, Importance sampling, Journal, population Monte Carlo, Stochastic kinetic models}, pubstate = {published}, tppubtype = {article} } This paper addresses the Monte Carlo approximation of posterior probability distributions. In particular, we consider the population Monte Carlo (PMC) technique, which is based on an iterative importance sampling (IS) approach. An important drawback of this methodology is the degeneracy of the importance weights (IWs) when the dimension of either the observations or the variables of interest is high. To alleviate this difficulty, we propose a new method that performs a nonlinear transformation of the IWs. This operation reduces the weight variation, hence it avoids degeneracy and increases the efficiency of the IS scheme, specially when drawing from proposal functions which are poorly adapted to the true posterior. For the sake of illustration, we have applied the proposed algorithm to the estimation of the parameters of a Gaussian mixture model. This is a simple problem that enables us to discuss the main features of the proposed technique. As a practical application, we have also considered the challenging problem of estimating the rate parameters of a stochastic kinetic model (SKM). SKMs are multivariate systems that model molecular interactions in biological and chemical problems. We introduce a particularization of the proposed algorithm to SKMs and present numerical results. |

## 2014 |

Koblents, Eugenia; Miguez, Joaquin A Population Monte Carlo Scheme with Transformed Weights and Its Application to Stochastic Kinetic Models Journal Article Statistics and Computing, ((to appear)), 2014, ISSN: 0960-3174. Abstract | Links | BibTeX | Tags: degeneracy of importance weights, Importance sampling, population Monte Carlo, Stochastic kinetic models @article{Koblents2014bb, title = {A Population Monte Carlo Scheme with Transformed Weights and Its Application to Stochastic Kinetic Models}, author = {Eugenia Koblents and Joaquin Miguez}, url = {http://link.springer.com/10.1007/s11222-013-9440-2 http://gts.tsc.uc3m.es/wp-content/uploads/2014/01/NPMC_A-population-Monte-Carlo-scheme-with-transformed_jma.pdf}, issn = {0960-3174}, year = {2014}, date = {2014-01-01}, journal = {Statistics and Computing}, number = {(to appear)}, abstract = {This paper addresses the Monte Carlo approximation of posterior probability distributions. In particular, we consider the population Monte Carlo (PMC) technique, which is based on an iterative importance sampling (IS) approach. An important drawback of this methodology is the degeneracy of the importance weights (IWs) when the dimension of either the observations or the variables of interest is high. To alleviate this difficulty, we propose a new method that performs a nonlinear transformation of the IWs. This operation reduces the weight variation, hence it avoids degeneracy and increases the efficiency of the IS scheme, specially when drawing from proposal functions which are poorly adapted to the true posterior. For the sake of illustration, we have applied the proposed algorithm to the estimation of the parameters of a Gaussian mixture model. This is a simple problem that enables us to discuss the main features of the proposed technique. As a practical application, we have also considered the challenging problem of estimating the rate parameters of a stochastic kinetic model (SKM). SKMs are multivariate systems that model molecular interactions in biological and chemical problems. We introduce a particularization of the proposed algorithm to SKMs and present numerical results.}, keywords = {degeneracy of importance weights, Importance sampling, population Monte Carlo, Stochastic kinetic models}, pubstate = {published}, tppubtype = {article} } This paper addresses the Monte Carlo approximation of posterior probability distributions. In particular, we consider the population Monte Carlo (PMC) technique, which is based on an iterative importance sampling (IS) approach. An important drawback of this methodology is the degeneracy of the importance weights (IWs) when the dimension of either the observations or the variables of interest is high. To alleviate this difficulty, we propose a new method that performs a nonlinear transformation of the IWs. This operation reduces the weight variation, hence it avoids degeneracy and increases the efficiency of the IS scheme, specially when drawing from proposal functions which are poorly adapted to the true posterior. For the sake of illustration, we have applied the proposed algorithm to the estimation of the parameters of a Gaussian mixture model. This is a simple problem that enables us to discuss the main features of the proposed technique. As a practical application, we have also considered the challenging problem of estimating the rate parameters of a stochastic kinetic model (SKM). SKMs are multivariate systems that model molecular interactions in biological and chemical problems. We introduce a particularization of the proposed algorithm to SKMs and present numerical results. |

## 2013 |

Koblents, Eugenia; Miguez, Joaquin A Population Monte Carlo Scheme for Computational Inference in High Dimensional Spaces Inproceedings 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 6318–6322, IEEE, Vancouver, 2013, ISSN: 1520-6149. Abstract | Links | BibTeX | Tags: Approximation methods, computational inference, degeneracy of importance weights, high dimensional spaces, Importance sampling, importance weights, iterative importance sampling, iterative methods, mixture-PMC, mixture-PMC algorithm, Monte Carlo methods, MPMC, nonlinear transformations, population Monte Carlo, population Monte Carlo scheme, Probability density function, probability distributions, Proposals, Sociology, Standards @inproceedings{Koblents2013a, title = {A Population Monte Carlo Scheme for Computational Inference in High Dimensional Spaces}, author = {Eugenia Koblents and Joaquin Miguez}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6638881}, issn = {1520-6149}, year = {2013}, date = {2013-01-01}, booktitle = {2013 IEEE International Conference on Acoustics, Speech and Signal Processing}, pages = {6318--6322}, publisher = {IEEE}, address = {Vancouver}, abstract = {In this paper we address the Monte Carlo approximation of integrals with respect to probability distributions in high-dimensional spaces. In particular, we investigate the population Monte Carlo (PMC) scheme, which is based on an iterative importance sampling (IS) approach. Both IS and PMC suffer from the well known problem of degeneracy of the importance weights (IWs), which is closely related to the curse-of-dimensionality, and limits their applicability in large-scale practical problems. In this paper we investigate a novel PMC scheme that consists in performing nonlinear transformations of the IWs in order to smooth their variations and avoid degeneracy. We apply the modified IS scheme to the well-known mixture-PMC (MPMC) algorithm, which constructs the importance functions as mixtures of kernels. We present numerical results that show how the modified version of MPMC clearly outperforms the original scheme.}, keywords = {Approximation methods, computational inference, degeneracy of importance weights, high dimensional spaces, Importance sampling, importance weights, iterative importance sampling, iterative methods, mixture-PMC, mixture-PMC algorithm, Monte Carlo methods, MPMC, nonlinear transformations, population Monte Carlo, population Monte Carlo scheme, Probability density function, probability distributions, Proposals, Sociology, Standards}, pubstate = {published}, tppubtype = {inproceedings} } In this paper we address the Monte Carlo approximation of integrals with respect to probability distributions in high-dimensional spaces. In particular, we investigate the population Monte Carlo (PMC) scheme, which is based on an iterative importance sampling (IS) approach. Both IS and PMC suffer from the well known problem of degeneracy of the importance weights (IWs), which is closely related to the curse-of-dimensionality, and limits their applicability in large-scale practical problems. In this paper we investigate a novel PMC scheme that consists in performing nonlinear transformations of the IWs in order to smooth their variations and avoid degeneracy. We apply the modified IS scheme to the well-known mixture-PMC (MPMC) algorithm, which constructs the importance functions as mixtures of kernels. We present numerical results that show how the modified version of MPMC clearly outperforms the original scheme. |