Parallel Tempering with Equi-Energy Moves

The Equi-Energy Sampler (EES) introduced by Kou et al [2006] is based on a population of chains which are updated by local moves and global moves, also called equi-energy jumps. The state space is partitioned into energy rings, and the current state of a chain can jump to a past state of an adjacent chain that has energy level close to its level. This algorithm has been developed to facilitate global moves between different chains, resulting in a good exploration of the state space by the target chain. This method seems to be more efficient than the classical Parallel Tempering (PT) algorithm. However it is difficult to use in combination with a Gibbs sampler and it necessitates increased storage. In this paper we propose an adaptation of this EES that combines PT with the principle of swapping between chains with same levels of energy. This adaptation, that we shall call Parallel Tempering with Equi-Energy Moves (PTEEM), keeps the original idea of the EES method while ensuring good theoretical properties, and practical implementation even if combined with a Gibbs sampler. Performances of the PTEEM algorithm are compared with those of the EES and of the standard PT algorithms in the context of mixture models, and in a problem of identification of gene regulatory binding motifs

Likelihood-Free Parallel Tempering

Approximate Bayesian Computational (ABC) methods (or likelihood-free methods) have appeared in the past fifteen years as useful methods to perform Bayesian analyses when the likelihood is analytically or computationally intractable. Several ABC methods have been proposed: Monte Carlo Markov Chains (MCMC) methods have been developped by Marjoramet al. (2003) and by Bortotet al. (2007) for instance, and sequential methods have been proposed among others by Sissonet al. (2007), Beaumont et al. (2009) and Del Moral et al. (2009). Until now, while ABC-MCMC methods remain the reference, sequential ABC methods have appeared to outperforms them (see for example McKinley et al. (2009) or Sisson et al. (2007)). In this paper a new algorithm combining population-based MCMC methods with ABC requirements is proposed, using an analogy with the Parallel Tempering algorithm (Geyer, 1991). Performances are compared with existing ABC algorithms on simulations and on a real example

Bayesian Variable Selection for Probit Mixed Models Applied to Gene Selection

In computational biology, gene expression datasets are characterized by very few individual samples compared to a large number of measurements per sample. Thus, it is appealing to merge these datasets in order to increase the number of observations and diversify the data, allowing a more reliable selection of genes relevant to the biological problem. Besides, the increased size of a merged dataset facilitates its re-splitting into training and validation sets. This necessitates the introduction of the dataset as a random effect. In this context, extending a work of Lee et al. (2003), a method is proposed to select relevant variables among tens of thousands in a probit mixed regression model, considered as part of a larger hierarchical Bayesian model. Latent variables are used to identify subsets of selected variables and the grouping (or blocking) technique of Liu (1994) is combined with a Metropolis-within-Gibbs algorithm (Robert and Casella 2004). The method is applied to a merged dataset made of three individual gene expression datasets, in which tens of thousands of measurements are available for each of several hundred human breast cancer samples. Even for this large dataset comprised of around 20000 predictors, the method is shown to be efficient and feasible. As an illustration, it is used to select the most important genes that characterize the estrogen receptor status of patients with breast cancer

Bayesian functional linear regression with sparse step functions

The functional linear regression model is a common tool to determine the relationship between a scalar outcome and a functional predictor seen as a function of time. This paper focuses on the Bayesian estimation of the support of the coefficient function. To this aim we propose a parsimonious and adaptive decomposition of the coefficient function as a step function, and a model including a prior distribution that we name Bayesian functional Linear regression with Sparse Step functions (Bliss). The aim of the method is to recover areas of time which influences the most the outcome. A Bayes estimator of the support is built with a specific loss function, as well as two Bayes estimators of the coefficient function, a first one which is smooth and a second one which is a step function. The performance of the proposed methodology is analysed on various synthetic datasets and is illustrated on a black P\'erigord truffle dataset to study the influence of rainfall on the production

Experimental damage evaluation of open and fatigue cracks of multi-cracked beams by using wavelet transform of static response via image analysis

In this study, a method for crack detection and quantification in beams based on wavelet analysis is presented. The static deflection is measured at particular points along the length of (i) real damaged structures, using few displacement transducers and a laser sensor, and (ii) simulated structures, using closed-form analysis, for a given location of a concentrated load along the beam. Furthermore, the measurement of the beam displacements in a large number of spatially distributed points is made by processing digital photographs of the beam. The smoothed deflection responses of the cracked beams are then analyzed using the wavelet transform. For this purpose, a Gaus2 wavelet with two vanishing moments is utilized. The wavelet transform spikes are used as indicators to locate and quantify the damage; furthermore, the multi-scale theory of wavelet is employed, in order to eliminate or at least reduce the spurious peaks and enhance the true ones. Simply supported beams with single and double cracks are used to demonstrate the devised methodology. Open and fatigue cracks of different sizes and locations have been used in the examples. In a closed-form analysis, the damage is modeled as a bilinear rotational spring with reduced stiffness in the neighborhood of the crack location. Damage calibration of simply supported steel beams with open and fatigue cracks has been carried out experimentally using this technique. A generalized curve has been proposed to quantify the damage in a simply supported beam. Based on the experimental study, the spatial wavelet transform is proven to be effective to identify the damage zone even when the crack depth is around 3% of the height of the beam

Desarrollo de una implementación óptima de un algoritmo acelerado de proyección de bloques

El advenimiento de la computación paralela junto con las innovaciones tecnológicas producidas en este campo, han beneficiado la manera de atacar este tipo de problemas. Así, tenemos métodos de optimización paralelos, que introducen ideas y técnicas de la computación paralela en la teoría y en los algoritmos numéricos de optimización. A menudo la implementación de un algoritmo cambia la perspectiva que uno tiene del mismo. Es con los experimentos computacionales de testeo cuando uno puede tener realmente confianza en la eficiencia y robustez de un algoritmo de optimización matemático de gran envergadura. Una de las cosas que más nos motivó a emprender el desafío de este Trabajo de Grado es la posibilidad de que el mismo realice un aporte para poder resolver en forma más eficiente cada uno de los importantes problemas que se encuentran subyacentes en el modelo matemático a optimizar: reconstrucción de imágenes por proyecciones, aplicaciones médicas como el planeamiento de la terapia de radiación, programación no lineal para el planeamiento bajo incertidumbre, balanceo de matrices, optimización de redes, planeamiento financiero, etc.Tesis digitalizada en SEDICI gracias a la colaboración de la Biblioteca de la Facultad de Informática.Facultad de Informátic

Desarrollo de una implementación óptima de un algoritmo acelerado de proyección de bloques

El advenimiento de la computación paralela junto con las innovaciones tecnológicas producidas en este campo, han beneficiado la manera de atacar este tipo de problemas. Así, tenemos métodos de optimización paralelos, que introducen ideas y técnicas de la computación paralela en la teoría y en los algoritmos numéricos de optimización. A menudo la implementación de un algoritmo cambia la perspectiva que uno tiene del mismo. Es con los experimentos computacionales de testeo cuando uno puede tener realmente confianza en la eficiencia y robustez de un algoritmo de optimización matemático de gran envergadura. Una de las cosas que más nos motivó a emprender el desafío de este Trabajo de Grado es la posibilidad de que el mismo realice un aporte para poder resolver en forma más eficiente cada uno de los importantes problemas que se encuentran subyacentes en el modelo matemático a optimizar: reconstrucción de imágenes por proyecciones, aplicaciones médicas como el planeamiento de la terapia de radiación, programación no lineal para el planeamiento bajo incertidumbre, balanceo de matrices, optimización de redes, planeamiento financiero, etc.Tesis digitalizada en SEDICI gracias a la colaboración de la Biblioteca de la Facultad de Informática.Facultad de Informátic