Effective Sample Size for Importance Sampling based on discrepancy measures

The Effective Sample Size (ESS) is an important measure of efficiency of Monte Carlo methods such as Markov Chain Monte Carlo (MCMC) and Importance Sampling (IS) techniques. In the IS context, an approximation $\widehat{ESS}$ of the theoretical ESS definition is widely applied, involving the inverse of the sum of the squares of the normalized importance weights. This formula, $\widehat{ESS}$, has become an essential piece within Sequential Monte Carlo (SMC) methods, to assess the convenience of a resampling step. From another perspective, the expression $\widehat{ESS}$ is related to the Euclidean distance between the probability mass described by the normalized weights and the discrete uniform probability mass function (pmf). In this work, we derive other possible ESS functions based on different discrepancy measures between these two pmfs. Several examples are provided involving, for instance, the geometric mean of the weights, the discrete entropy (including theperplexity measure, already proposed in literature) and the Gini coefficient among others. We list five theoretical requirements which a generic ESS function should satisfy, allowing us to classify different ESS measures. We also compare the most promising ones by means of numerical simulations

Group Importance Sampling for Particle Filtering and MCMC

Bayesian methods and their implementations by means of sophisticated Monte Carlo techniques have become very popular in signal processing over the last years. Importance Sampling (IS) is a well-known Monte Carlo technique that approximates integrals involving a posterior distribution by means of weighted samples. In this work, we study the assignation of a single weighted sample which compresses the information contained in a population of weighted samples. Part of the theory that we present as Group Importance Sampling (GIS) has been employed implicitly in different works in the literature. The provided analysis yields several theoretical and practical consequences. For instance, we discuss the application of GIS into the Sequential Importance Resampling framework and show that Independent Multiple Try Metropolis schemes can be interpreted as a standard Metropolis-Hastings algorithm, following the GIS approach. We also introduce two novel Markov Chain Monte Carlo (MCMC) techniques based on GIS. The first one, named Group Metropolis Sampling method, produces a Markov chain of sets of weighted samples. All these sets are then employed for obtaining a unique global estimator. The second one is the Distributed Particle Metropolis-Hastings technique, where different parallel particle filters are jointly used to drive an MCMC algorithm. Different resampled trajectories are compared and then tested with a proper acceptance probability. The novel schemes are tested in different numerical experiments such as learning the hyperparameters of Gaussian Processes, two localization problems in a wireless sensor network (with synthetic and real data) and the tracking of vegetation parameters given satellite observations, where they are compared with several benchmark Monte Carlo techniques. Three illustrative Matlab demos are also provided.Comment: To appear in Digital Signal Processing. Related Matlab demos are provided at https://github.com/lukafree/GIS.gi

Parallel Metropolis chains with cooperative adaptation

Monte Carlo methods, such as Markov chain Monte Carlo (MCMC) algorithms, have become very popular in signal processing over the last years. In this work, we introduce a novel MCMC scheme where parallel MCMC chains interact, adapting cooperatively the parameters of their proposal functions. Furthermore, the novel algorithm distributes the computational effort adaptively, rewarding the chains which are providing better performance and, possibly even stopping other ones. These extinct chains can be reactivated if the algorithm considers necessary. Numerical simulations shows the benefits of the novel scheme

ESR theory for interacting 1D quantum wires

We compute the electron spin resonance (ESR) intensity for one-dimensional quantum wires in semiconductor heterostructures, taking into account electron-electron interactions and spin-orbit coupling. The ESR spectrum is shown to be very sensitive to interactions. While in the absence of interactions, the spectrum is a flat band, characteristic threshold singularities appear in the interacting limit. This suggests the practical use of ESR to reveal spin dynamics in a Luttinger liquid.Comment: 7 pages, 2 figures. To be published in Europhys. Let

Thermodynamics of rotating self-gravitating systems

We investigate the statistical equilibrium properties of a system of classical particles interacting via Newtonian gravity, enclosed in a three-dimensional spherical volume. Within a mean-field approximation, we derive an equation for the density profiles maximizing the microcanonical entropy and solve it numerically. At low angular momenta, i.e. for a slowly rotating system, the well-known gravitational collapse ``transition'' is recovered. At higher angular momenta, instead, rotational symmetry can spontaneously break down giving rise to more complex equilibrium configurations, such as double-clusters (``double stars''). We analyze the thermodynamics of the system and the stability of the different equilibrium configurations against rotational symmetry breaking, and provide the global phase diagram.Comment: 12 pages, 9 figure

Orthogonal parallel MCMC methods for sampling and optimization

Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In order to foster better exploration of the state space, specially in high-dimensional applications, several schemes employing multiple parallel MCMC chains have been recently introduced. In this work, we describe a novel parallel interacting MCMC scheme, called {\it orthogonal MCMC} (O-MCMC), where a set of "vertical" parallel MCMC chains share information using some "horizontal" MCMC techniques working on the entire population of current states. More specifically, the vertical chains are led by random-walk proposals, whereas the horizontal MCMC techniques employ independent proposals, thus allowing an efficient combination of global exploration and local approximation. The interaction is contained in these horizontal iterations. Within the analysis of different implementations of O-MCMC, novel schemes in order to reduce the overall computational cost of parallel multiple try Metropolis (MTM) chains are also presented. Furthermore, a modified version of O-MCMC for optimization is provided by considering parallel simulated annealing (SA) algorithms. Numerical results show the advantages of the proposed sampling scheme in terms of efficiency in the estimation, as well as robustness in terms of independence with respect to initial values and the choice of the parameters

Skeletal muscle remodeling in response to eccentric vs. concentric loading: morphological, molecular, and metabolic adaptations

Skeletal muscle contracts either by shortening or lengthening (concentrically or eccentrically, respectively); however, the two contractions substantially differ from one another in terms of mechanisms of force generation, maximum force production and energy cost. It is generally known that eccentric action s generate greater force than isometric and concentric contractions and at a lower metabolic cost. Hence, by virtue of the greater mechanical loading involved in active lengthening, eccentric resistance training (ECC RT) is assumed to produce greater hypertrophy than concentric resistance training (CON RT). Nonetheless, prevalence of either ECC RT or CON RT in inducing gains in muscle mass is still an open issue, with some studies reporting greater hypertrophy with eccentric, some with concentric and some with similar hypertrophy within both training modes. Recent observations suggest that such hypertrophic responses to lengthening vs. shortening contractions are achieved by different adaptations in muscle architecture. Whilst the changes in muscle protein synthesis in response to acute and chronic concentric and eccentric exercise bouts seem very similar, the molecular mechanisms regulating the myogenic adaptations to the two distinct loading stimuli are still incompletely understood. Thus, the present review aims to, (a) critically discuss the literature on the contribution of eccentric vs. concentric loading to muscular hypertrophy and structural remodeling, and, (b) clarify the molecular mechanisms that may regulate such adaptations. We conclude that, when matched for either maximum load or work, similar increase in muscle size is found between ECC and CON RT. However, such hypertrophic changes appear to be achieved through distinct structural adaptations, which may be regulated by different myogenic and molecular responses observed between lengthening and shortening contractions

Indigenous and introduced species of the Bemisia tabaci complex in sweet potato crops from Argentina

La batata (Ipomoea batatas (L.) Lam) es uno de los cultivos más importantes en el mundo. Recientemente se observó una severa sintomatología viral en cultivos de la región pampeana argentina, en la que están identificados begomovirus y crinivirus, ambos transmitidos exclusivamente por mosca blanca. El objetivo de este estudio fue identificar las especies de B. tabaci en cultivos de batata en Colonia Caroya, mediante el análisis de secuencias mitocondriales de la citocromo oxidasa subunidad I (mtCOI). Se identificaron dos haplotipos (especies crípticas) ya descriptos en el mundo: New World2 (especie nativa) y MEAM1 (especie introducida). Los resultados indican la presencia de ambas especies, las cuales son potenciales vectores de begomovirus y crinivirus en batata en Argentina.Sweet potato (Ipomoea batatas (L.) Lam) is one of the most important crops worldwide. Recently, the appearance of severe viral symptoms has been observed in sweet potato crops in the pampas region of Argentina and both begomovirus and crinivirus, exclusively transmitted by whiteflies, have been identified. The aim of this study was to identify B. tabaci species from sweet potato crops in Colonia Caroya by analysing mitochondrial cytochrome c oxidase subunit I (mtCOI) sequences. Two previously described haplotypes were identified: New World2 (indigenous species) and MEAM1 (introduced species). The results indicate the presence of both species, which are potential vectors of begomovirus and crinivirus in Argentina.Fil: Alemandri, V.. Instituto Nacional de Tecnología Agropecuaria. Centro de Investigaciones Agropecuarias. Instituto de Patología Vegetal; ArgentinaFil: Martino, Julia Andrea. Instituto Nacional de Tecnología Agropecuaria. Centro de Investigaciones Agropecuarias. Instituto de Patología Vegetal; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Di Feo, Liliana del Valle. Instituto Nacional de Tecnología Agropecuaria. Centro de Investigaciones Agropecuarias. Instituto de Patología Vegetal; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Truol, G.. Instituto Nacional de Tecnología Agropecuaria. Centro de Investigaciones Agropecuarias. Instituto de Patología Vegetal; Argentin