Free energy surface reconstruction from umbrella samples using Gaussian process regression

We demonstrate how the Gaussian process regression approach can be used to efficiently reconstruct free energy surfaces from umbrella sampling simulations. By making a prior assumption of smoothness and taking account of the sampling noise in a consistent fashion, we achieve a significant improvement in accuracy over the state of the art in two or more dimensions or, equivalently, a significant cost reduction to obtain the free energy surface within a prescribed tolerance in both regimes of spatially sparse data and short sampling trajectories. Stemming from its Bayesian interpretation the method provides meaningful error bars without significant additional computation. A software implementation is made available on www.libatoms.org.

Free energy surface reconstruction from umbrella samples using Gaussian process regression II: Multiple collective variables

We demonstrate how a prior assumption of smoothness can be used to enhance the reconstruction of free energy profiles from multiple umbrella sampling simulations using the Bayesian Gaussian process regression approach. The method we derive allows the concurrent use of histograms and free energy gradients and can easily be extended to include further data. In Part I we review the necessary theory and test the method for one collective variable. We demonstrate improved performance with respect to the weighted histogram analysis method and obtain meaningful error bars without any significant additional computation. In Part II we consider the case of multiple collective variables and compare to a reconstruction using least squares fitting of radial basis functions. We find substantial improvements in the regimes of spatially sparse data or short sampling trajectories. A software implementation is made available on www.libatoms.org.

Communicating musical knowledge through gesture: Piano teachers’ gestural behaviours across different levels of student proficiency

Teachers’ communication of musical knowledge through physical gesture represents a valuable pedagogical field in need of investigation. This exploratory case study compares the gestural behaviour of three piano teachers while giving individual lessons to students who differed according to piano proficiency levels. The data was collected by video recordings of one-to-one piano lessons and gestures were categorized using two gesture classifications: the spontaneous co-verbal gesture classification (McNeill, 1992; 2005) and spontaneous co-musical gesture classification (Simones, Schroeder & Rodger, 2013). Poisson regression analysis and qualitative observation suggest a relationship between teachers’ didactic intentions and the types of gesture they produced while teaching, as shown by differences in gestural category frequency between teaching students of higher and lower levels of proficiency. Such reported agreement between teachers’ gestural approach in relation to student proficiency levels indicates a teachers’ gestural scaffolding approach whereby teachers adapted gestural communicative channels to suit students’ specific conceptual skill levels.

Approximation de la distribution a posteriori d'un modèle Gamma-Poisson hiérarchique à effets mixtes

La méthode que nous présentons pour modéliser des données dites de "comptage" ou données de Poisson est basée sur la procédure nommée Modélisation multi-niveau et interactive de la régression de Poisson (PRIMM) développée par Christiansen et Morris (1997). Dans la méthode PRIMM, la régression de Poisson ne comprend que des effets fixes tandis que notre modèle intègre en plus des effets aléatoires. De même que Christiansen et Morris (1997), le modèle étudié consiste à faire de l'inférence basée sur des approximations analytiques des distributions a posteriori des paramètres, évitant ainsi d'utiliser des méthodes computationnelles comme les méthodes de Monte Carlo par chaînes de Markov (MCMC). Les approximations sont basées sur la méthode de Laplace et la théorie asymptotique liée à l'approximation normale pour les lois a posteriori. L'estimation des paramètres de la régression de Poisson est faite par la maximisation de leur densité a posteriori via l'algorithme de Newton-Raphson. Cette étude détermine également les deux premiers moments a posteriori des paramètres de la loi de Poisson dont la distribution a posteriori de chacun d'eux est approximativement une loi gamma. Des applications sur deux exemples de données ont permis de vérifier que ce modèle peut être considéré dans une certaine mesure comme une généralisation de la méthode PRIMM. En effet, le modèle s'applique aussi bien aux données de Poisson non stratifiées qu'aux données stratifiées; et dans ce dernier cas, il comporte non seulement des effets fixes mais aussi des effets aléatoires liés aux strates. Enfin, le modèle est appliqué aux données relatives à plusieurs types d'effets indésirables observés chez les participants d'un essai clinique impliquant un vaccin quadrivalent contre la rougeole, les oreillons, la rub\'eole et la varicelle. La régression de Poisson comprend l'effet fixe correspondant à la variable traitement/contrôle, ainsi que des effets aléatoires liés aux systèmes biologiques du corps humain auxquels sont attribués les effets indésirables considérés.

Modélisation bayésienne des changements aux niches écologiques causés par le réchauffement climatique

Cette thèse présente des méthodes de traitement de données de comptage en particulier et des données discrètes en général. Il s'inscrit dans le cadre d'un projet stratégique du CRNSG, nommé CC-Bio, dont l'objectif est d'évaluer l'impact des changements climatiques sur la répartition des espèces animales et végétales. Après une brève introduction aux notions de biogéographie et aux modèles linéaires mixtes généralisés aux chapitres 1 et 2 respectivement, ma thèse s'articulera autour de trois idées majeures. Premièrement, nous introduisons au chapitre 3 une nouvelle forme de distribution dont les composantes ont pour distributions marginales des lois de Poisson ou des lois de Skellam. Cette nouvelle spécification permet d'incorporer de l'information pertinente sur la nature des corrélations entre toutes les composantes. De plus, nous présentons certaines propriétés de ladite distribution. Contrairement à la distribution multidimensionnelle de Poisson qu'elle généralise, celle-ci permet de traiter les variables avec des corrélations positives et/ou négatives. Une simulation permet d'illustrer les méthodes d'estimation dans le cas bidimensionnel. Les résultats obtenus par les méthodes bayésiennes par les chaînes de Markov par Monte Carlo (CMMC) indiquent un biais relatif assez faible de moins de 5% pour les coefficients de régression des moyennes contrairement à ceux du terme de covariance qui semblent un peu plus volatils. Deuxièmement, le chapitre 4 présente une extension de la régression multidimensionnelle de Poisson avec des effets aléatoires ayant une densité gamma. En effet, conscients du fait que les données d'abondance des espèces présentent une forte dispersion, ce qui rendrait fallacieux les estimateurs et écarts types obtenus, nous privilégions une approche basée sur l'intégration par Monte Carlo grâce à l'échantillonnage préférentiel. L'approche demeure la même qu'au chapitre précédent, c'est-à-dire que l'idée est de simuler des variables latentes indépendantes et de se retrouver dans le cadre d'un modèle linéaire mixte généralisé (GLMM) conventionnel avec des effets aléatoires de densité gamma. Même si l'hypothèse d'une connaissance a priori des paramètres de dispersion semble trop forte, une analyse de sensibilité basée sur la qualité de l'ajustement permet de démontrer la robustesse de notre méthode. Troisièmement, dans le dernier chapitre, nous nous intéressons à la définition et à la construction d'une mesure de concordance donc de corrélation pour les données augmentées en zéro par la modélisation de copules gaussiennes. Contrairement au tau de Kendall dont les valeurs se situent dans un intervalle dont les bornes varient selon la fréquence d'observations d'égalité entre les paires, cette mesure a pour avantage de prendre ses valeurs sur (-1;1). Initialement introduite pour modéliser les corrélations entre des variables continues, son extension au cas discret implique certaines restrictions. En effet, la nouvelle mesure pourrait être interprétée comme la corrélation entre les variables aléatoires continues dont la discrétisation constitue nos observations discrètes non négatives. Deux méthodes d'estimation des modèles augmentés en zéro seront présentées dans les contextes fréquentiste et bayésien basées respectivement sur le maximum de vraisemblance et l'intégration de Gauss-Hermite. Enfin, une étude de simulation permet de montrer la robustesse et les limites de notre approche.

Sparse kernel density estimator using orthogonal regression based on D-optimality experimental design

A novel sparse kernel density estimator is derived based on a regression approach, which selects a very small subset of significant kernels by means of the D-optimality experimental design criterion using an orthogonal forward selection procedure. The weights of the resulting sparse kernel model are calculated using the multiplicative nonnegative quadratic programming algorithm. The proposed method is computationally attractive, in comparison with many existing kernel density estimation algorithms. Our numerical results also show that the proposed method compares favourably with other existing methods, in terms of both test accuracy and model sparsity, for constructing kernel density estimates.

Kernel density construction using orthogonal forward regression

An automatic algorithm is derived for constructing kernel density estimates based on a regression approach that directly optimizes generalization capability. Computational efficiency of the density construction is ensured using an orthogonal forward regression, and the algorithm incrementally minimizes the leave-one-out test score. Local regularization is incorporated into the density construction process to further enforce sparsity. Examples are included to demonstrate the ability of the proposed algorithm to effectively construct a very sparse kernel density estimate with comparable accuracy to that of the full sample Parzen window density estimate.

Sparse kernel density construction using orthogonal forward regression with leave-one-out test score and local regularization

This paper presents an efficient construction algorithm for obtaining sparse kernel density estimates based on a regression approach that directly optimizes model generalization capability. Computational efficiency of the density construction is ensured using an orthogonal forward regression, and the algorithm incrementally minimizes the leave-one-out test score. A local regularization method is incorporated naturally into the density construction process to further enforce sparsity. An additional advantage of the proposed algorithm is that it is fully automatic and the user is not required to specify any criterion to terminate the density construction procedure. This is in contrast to an existing state-of-art kernel density estimation method using the support vector machine (SVM), where the user is required to specify some critical algorithm parameter. Several examples are included to demonstrate the ability of the proposed algorithm to effectively construct a very sparse kernel density estimate with comparable accuracy to that of the full sample optimized Parzen window density estimate. Our experimental results also demonstrate that the proposed algorithm compares favorably with the SVM method, in terms of both test accuracy and sparsity, for constructing kernel density estimates.

Regression based D-optimality experimental design for sparse kernel density estimation

This paper derives an efficient algorithm for constructing sparse kernel density (SKD) estimates. The algorithm first selects a very small subset of significant kernels using an orthogonal forward regression (OFR) procedure based on the D-optimality experimental design criterion. The weights of the resulting sparse kernel model are then calculated using a modified multiplicative nonnegative quadratic programming algorithm. Unlike most of the SKD estimators, the proposed D-optimality regression approach is an unsupervised construction algorithm and it does not require an empirical desired response for the kernel selection task. The strength of the D-optimality OFR is owing to the fact that the algorithm automatically selects a small subset of the most significant kernels related to the largest eigenvalues of the kernel design matrix, which counts for the most energy of the kernel training data, and this also guarantees the most accurate kernel weight estimate. The proposed method is also computationally attractive, in comparison with many existing SKD construction algorithms. Extensive numerical investigation demonstrates the ability of this regression-based approach to efficiently construct a very sparse kernel density estimate with excellent test accuracy, and our results show that the proposed method compares favourably with other existing sparse methods, in terms of test accuracy, model sparsity and complexity, for constructing kernel density estimates.

Parameter estimation of Poisson generalized linear mixed models based on three different statistical principles : a simulation study

Generalized linear mixed models are flexible tools for modeling non-normal data and are useful for accommodating overdispersion in Poisson regression models with random effects. Their main difficulty resides in the parameter estimation because there is no analytic solution for the maximization of the marginal likelihood. Many methods have been proposed for this purpose and many of them are implemented in software packages. The purpose of this study is to compare the performance of three different statistical principles - marginal likelihood, extended likelihood, Bayesian analysis-via simulation studies. Real data on contact wrestling are used for illustration.

Assessing global economic activity linkages: an empirical exercise based on global autoregressive regression

Economic performance increasingly relies on global economic environment due to the growing importance of trade and nancial links among countries. Literature on growth spillovers shows various gains obtained by this interaction. This work aims at analyzing the possible e ects of a potential economic growth downturn in China, Germany and United States on the growth of other economies. We use global autoregressive regression approach to assess interdependence among countries. Two types of phenomena are simulated. The rst one is a one time shock that hit these economies. Our simulations use a large shock of -2.5 standard deviations, a gure very similar to what we saw back in the 2008 crises. The second experiment simulate the e ect of a hypothetical downturn of the aforementioned economies. Our results suggest that the United States play the role of a global economy a ecting countries across the globe whereas Germany and China play a regional role.

An assessment of the economic impact of climate change on the health sector In Jamaica

Climate change is a naturally occurring phenomenon in which the earth‘s climate goes through cycles of warming and cooling; these changes usually take place incrementally over millennia. Over the past century, there has been an anomalous increase in global temperature, giving rise to accelerated climate change. It is widely accepted that greenhouse gas emissions from human activities such as industries have contributed significantly to the increase in global temperatures. The existence and survival of all living organisms is predicated on the ability of the environment in which they live not only to provide conditions for their basic needs but also conditions suitable for growth and reproduction. Unabated climate change threatens the existence of biophysical and ecological systems on a planetary scale. The present study aims to examine the economic impact of climate change on health in Jamaica over the period 2011-2050. To this end, three disease conditions with known climate sensitivity and importance to Jamaican public health were modelled. These were: dengue fever, leptospirosis and gastroenteritis in children under age 5. Historical prevalence data on these diseases were obtained from the Ministry of Health Jamaica, the Caribbean Epidemiology Centre, the Climate Studies Group Mona, University of the West Indies Mona campus, and the Meteorological Service of Jamaica. Data obtained spanned a twelve-year period of 1995-2007. Monthly data were obtained for dengue and gastroenteritis, while for leptospirosis, the annual number of cases for 1995-2005 was utilized. The two SRES emission scenarios chosen were A2 and B2 using the European Centre Hamburg Model (ECHAM) global climate model to predict climate variables for these scenarios. A business as usual (BAU) scenario was developed using historical disease data for the period 2000-2009 (dengue fever and gastroenteritis) and 1995-2005 (leptospirosis) as the reference decades for the respective diseases. The BAU scenario examined the occurrence of the diseases in the absence of climate change. It assumed that the disease trend would remain unchanged over the projected period and the number of cases of disease for each decade would be the same as the reference decade. The model used in the present study utilized predictive empirical statistical modelling to extrapolate the climate/disease relationship in time, to estimate the number of climate change-related cases under future climate change scenarios. The study used a Poisson regression model that considered seasonality and lag effects to determine the best-fit model in relation to the diseases under consideration. Zhang and others (2008), in their review of climate change and the transmission of vector-borne diseases, found that: ―Besides climatic variables, few of them have included other factors that can affect the transmission of vector-borne disease….‖ (Zhang 2008) Water, sanitation and health expenditure are key determinants of health. In the draft of the second communication to IPCC, Jamaica noted the vulnerability of public health to climate change, including sanitation and access to water (MSJ/UNDP, 2009). Sanitation, which in its broadest context includes the removal of waste (excreta, solid, or other hazardous waste), is a predictor of vector-borne diseases (e.g. dengue fever), diarrhoeal diseases (such as gastroenteritis) and zoonoses (such as leptospirosis). In conceptualizing the model, an attempt was made to include non-climate predictors of these climate-sensitive diseases. The importance of sanitation and water access to the control of dengue, gastroenteritis and leptospirosis were included in the Poisson regression model. The Poisson regression model obtained was then used to predict the number of disease cases into the future (2011-2050) for each emission scenario. After projecting the number of cases, the cost associated with each scenario was calculated using four cost components. 1. Treatment cost morbidity estimate. The treatment cost for the number of cases was calculated using reference values found in the literature for each condition. The figures were derived from studies of the cost of treatment and represent ambulatory and non-fatal hospitalized care for dengue fever and gastroenteritis. Due to the paucity of published literature on the health care cost associated with leptospirosis, only the cost of diagnosis and antibiotic therapy were included in the calculation. 2. Mortality estimates. Mortality estimates are recorded as case fatality rates. Where local data were available, these were utilized. Where these were unavailable, appropriate reference values from the literature were used. 3. Productivity loss. Productivity loss was calculated using a human capital approach, by multiplying the expected number of productive days lost by the caregiver and/or the infected person, by GDP per capita per day (US$ 14) at 2008 GDP using 2008 US$ exchange rates. 4. No-option cost. The no-option cost refers to adaptation strategies for the control of dengue fever which are ongoing and already a part of the core functions of the Vector Control Division of the Ministry of Health, Jamaica. An estimated US$ 2.1 million is utilized each year in conducting activities to prevent the post-hurricane spread of vector borne diseases and diarrhoea. The cost includes public education, fogging, laboratory support, larvicidal activities and surveillance. This no-option cost was converted to per capita estimates, using population estimates for Jamaica up to 2050 obtained from the Statistical Institute of Jamaica (STATIN, 2006) and the assumption of one expected major hurricane per decade. During the decade 2000-2009, Jamaica had an average inflation of 10.4% (CIA Fact book, last updated May 2011). This average decadal inflation rate was applied to the no-option cost, which was inflated by 10% for each successive decade to adjust for changes in inflation over time.

Avaliação e resolutividade do serviço odontológico no Sistema Único de Saúde

Pós-graduação em Odontologia Preventiva e Social - FOA

Childhood cancer and nuclear power plants in Switzerland: a census-based cohort study

Background Previous studies on childhood cancer and nuclear power plants (NPPs) produced conflicting results. We used a cohort approach to examine whether residence near NPPs was associated with leukaemia or any childhood cancer in Switzerland. Methods We computed person-years at risk for children aged 0–15 years born in Switzerland from 1985 to 2009, based on the Swiss censuses 1990 and 2000 and identified cancer cases from the Swiss Childhood Cancer Registry. We geo-coded place of residence at birth and calculated incidence rate ratios (IRRs) with 95% confidence intervals (CIs) comparing the risk of cancer in children born <5 km, 5–10 km and 10–15 km from the nearest NPP with children born >15 km away, using Poisson regression models. Results We included 2925 children diagnosed with cancer during 21 117 524 person-years of follow-up; 953 (32.6%) had leukaemia. Eight and 12 children diagnosed with leukaemia at ages 0–4 and 0–15 years, and 18 and 31 children diagnosed with any cancer were born <5 km from a NPP. Compared with children born >15 km away, the IRRs (95% CI) for leukaemia in 0–4 and 0–15 year olds were 1.20 (0.60–2.41) and 1.05 (0.60–1.86), respectively. For any cancer, corresponding IRRs were 0.97 (0.61–1.54) and 0.89 (0.63–1.27). There was no evidence of a dose–response relationship with distance (P > 0.30). Results were similar for residence at diagnosis and at birth, and when adjusted for potential confounders. Results from sensitivity analyses were consistent with main results. Conclusions This nationwide cohort study found little evidence of an association between residence near NPPs and the risk of leukaemia or any childhood cancer.

Modeling multilevel sleep transitional data via Poisson log-linear multilevel models

This paper proposes Poisson log-linear multilevel models to investigate population variability in sleep state transition rates. We specifically propose a Bayesian Poisson regression model that is more flexible, scalable to larger studies, and easily fit than other attempts in the literature. We further use hierarchical random effects to account for pairings of individuals and repeated measures within those individuals, as comparing diseased to non-diseased subjects while minimizing bias is of epidemiologic importance. We estimate essentially non-parametric piecewise constant hazards and smooth them, and allow for time varying covariates and segment of the night comparisons. The Bayesian Poisson regression is justified through a re-derivation of a classical algebraic likelihood equivalence of Poisson regression with a log(time) offset and survival regression assuming piecewise constant hazards. This relationship allows us to synthesize two methods currently used to analyze sleep transition phenomena: stratified multi-state proportional hazards models and log-linear models with GEE for transition counts. An example data set from the Sleep Heart Health Study is analyzed.