Random lattice models

This thesis deals with three different physical models, where each model involves a random component which is linked to a cubic lattice. First, a model is studied, which is used in numerical calculations of Quantum Chromodynamics.In these calculations random gauge-fields are distributed on the bonds of the lattice. The formulation of the model is fitted into the mathematical framework of ergodic operator families. We prove, that for small coupling constants, the ergodicity of the underlying probability measure is indeed ensured and that the integrated density of states of the Wilson-Dirac operator exists. The physical situations treated in the next two chapters are more similar to one another. In both cases the principle idea is to study a fermion system in a cubic crystal with impurities, that are modeled by a random potential located at the lattice sites. In the second model we apply the Hartree-Fock approximation to such a system. For the case of reduced Hartree-Fock theory at positive temperatures and a fixed chemical potential we consider the limit of an infinite system. In that case we show the existence and uniqueness of minimizers of the Hartree-Fock functional. In the third model we formulate the fermion system algebraically via C*-algebras. The question imposed here is to calculate the heat production of the system under the influence of an outer electromagnetic field. We show that the heat production corresponds exactly to what is empirically predicted by Joule's law in the regime of linear response.

RANDOM EFFECTS MODELS IN A META-ANALYSIS OF THE ACCURACY OF DIAGNOSTIC TESTS WITHIN A GOLD STANDARD IN THE PRESENCE OF MISSING DATA

In evaluating the accuracy of diagnosis tests, it is common to apply two imperfect tests jointly or sequentially to a study population. In a recent meta-analysis of the accuracy of microsatellite instability testing (MSI) and traditional mutation analysis (MUT) in predicting germline mutations of the mismatch repair (MMR) genes, a Bayesian approach (Chen, Watson, and Parmigiani 2005) was proposed to handle missing data resulting from partial testing and the lack of a gold standard. In this paper, we demonstrate an improved estimation of the sensitivities and specificities of MSI and MUT by using a nonlinear mixed model and a Bayesian hierarchical model, both of which account for the heterogeneity across studies through study-specific random effects. The methods can be used to estimate the accuracy of two imperfect diagnostic tests in other meta-analyses when the prevalence of disease, the sensitivities and/or the specificities of diagnostic tests are heterogeneous among studies. Furthermore, simulation studies have demonstrated the importance of carefully selecting appropriate random effects on the estimation of diagnostic accuracy measurements in this scenario.

Analysis of Melanoma Onset: Assessing Familial Aggregation by Using Estimating Equations and Fitting Variance Components via Bayesian Random Effects Models

We investigate whether relative contributions of genetic and shared environmental factors are associated with an increased risk in melanoma. Data from the Queensland Familial Melanoma Project comprising 15,907 subjects arising from 1912 families were analyzed to estimate the additive genetic, common and unique environmental contributions to variation in the age at onset of melanoma. Two complementary approaches for analyzing correlated time-to-onset family data were considered: the generalized estimating equations (GEE) method in which one can estimate relationship-specific dependence simultaneously with regression coefficients that describe the average population response to changing covariates; and a subject-specific Bayesian mixed model in which heterogeneity in regression parameters is explicitly modeled and the different components of variation may be estimated directly. The proportional hazards and Weibull models were utilized, as both produce natural frameworks for estimating relative risks while adjusting for simultaneous effects of other covariates. A simple Markov Chain Monte Carlo method for covariate imputation of missing data was used and the actual implementation of the Bayesian model was based on Gibbs sampling using the free ware package BUGS. In addition, we also used a Bayesian model to investigate the relative contribution of genetic and environmental effects on the expression of naevi and freckles, which are known risk factors for melanoma.

Random field models and priors on wind

This report seeks to make concrete some of the ideas we have been discussing about sensible priors for winds over the ocean. In particular, random field models are reviewed, as are permissible covariance functions. The criteria which these covariance functions must satisfy in order that vorticity and divergence exist and are continuous are defined. The use of Helmholtz theorem is discussed, and possible choices for the covariances are suggested.

Random graph coloring:Statistical physics approach

The problem of vertex coloring in random graphs is studied using methods of statistical physics and probability. Our analytical results are compared to those obtained by exact enumeration and Monte Carlo simulations. We critically discuss the merits and shortcomings of the various methods, and interpret the results obtained. We present an exact analytical expression for the two-coloring problem as well as general replica symmetric approximated solutions for the thermodynamics of the graph coloring problem with p colors and K-body edges. ©2002 The American Physical Society.

On Multi-Dimensional Random Walk Models Approximating Symmetric Space-Fractional Diffusion Processes

Mathematics Subject Classification: 26A33, 47B06, 47G30, 60G50, 60G52, 60G60.

Parameterized Link Functions in Generalized Linear Random Effect Models: a Case Study on Breast Cancer Treatment

In non-linear random effects some attention has been very recently devoted to the analysis ofsuitable transformation of the response variables separately (Taylor 1996) or not (Oberg and Davidian 2000) from the transformations of the covariates and, as far as we know, no investigation has been carried out on the choice of link function in such models. In our study we consider the use of a random effect model when a parameterized family of links (Aranda-Ordaz 1981, Prentice 1996, Pregibon 1980, Stukel 1988 and Czado 1997) is introduced. We point out the advantages and the drawbacks associated with the choice of this data-driven kind of modeling. Difficulties in the interpretation of regression parameters, and therefore in understanding the influence of covariates, as well as problems related to loss of efficiency of estimates and overfitting, are discussed. A case study on radiotherapy usage in breast cancer treatment is discussed.

Efectividad en redes Inter-Organizacionales : una aproximación al concepto y su medición

El concepto de efectividad en Redes Inter-organizacionales se ha investigado poco a pesar de la gran importancia en el desarrollo y sostenibilidad de la red. Es muy importante entender este concepto ya que cuando hablamos de Red, nos referimos a un grupo de más de tres organizaciones que trabajan juntas para alcanzar un objetivo colectivo que beneficia a cada miembro de la red. Esto nos demuestra la importancia de evaluar y analizar este fenómeno “Red Inter-organizacional” de forma más detallada para poder analizar que estructura, formas de gobierno, relaciones entre los miembros y entre otros factores, influyen en la efectividad y perdurabilidad de la Red Inter-organizacional. Esta investigación se desarrolla con el fin de plantear una aproximación al concepto de medición de la efectividad en Redes Inter-organizacionales. El trabajo se centrara en la recopilación de información y en la investigación documental, la cual se realizará por fases para brindarle al lector una mayor claridad y entendimiento sobre qué es Red, Red Inter-Organizacional, Efectividad. Y para finalizar se estudiara Efectividad en una Red Inter-organizacional.

Network Dynamics in Natural Resource Governance: A Case Study of Swiss Landscape Management

Structural characteristics of social networks have been recognized as important factors of effective natural resource governance. However, network analyses of natural resource governance most often remain static, even though governance is an inherently dynamic process. In this article, we investigate the evolution of a social network of organizational actors involved in the governance of natural resources in a regional nature park project in Switzerland. We ask how the maturation of a governance network affects bonding social capital and centralization in the network. Applying separable temporal exponential random graph modeling (STERGM), we test two hypotheses based on the risk hypothesis by Berardo and Scholz (2010) in a longitudinal setting. Results show that network dynamics clearly follow the expected trend toward generating bonding social capital but do not imply a shift toward less hierarchical and more decentralized structures over time. We investigate how these structural processes may contribute to network effectiveness over time.

An enforced cooperation : understanding scientific assessments in adversarial polities through Quebec shale gas policymaking, 2010-2014

Les biotechnologies, le réchauffement climatique, les ressources naturelles et la gestion des écosystèmes sont tous représentatifs de la “nouvelle politique de la nature” (Hajer 2003), un terme englobant les enjeux marqués par une grande incertitude scientifique et un encadrement réglementaire inadapté aux nouvelles réalités, suscitant de fait un conflit politique hors du commun. Dans l'espoir de diminuer ces tensions et de générer un savoir consensuel, de nombreux gouvernements se tournent vers des institutions scientifiques ad hoc pour documenter l'élaboration des politiques et répondre aux préoccupations des partie-prenantes. Mais ces évaluations scientifiques permettent-elles réellement de créer une compréhension commune partagée par ces acteurs politiques polarisés? Alors que l'on pourrait croire que celles-ci génèrent un climat d'apprentissage collectif rassembleur, un environnement politique conflictuel rend l'apprentissage entre opposant extrêmement improbable. Ainsi, cette recherche documente le potentiel conciliateur des évaluation scientifique en utilisant le cas des gaz de schiste québécois (2010-2014). Ce faisant, elle mobilise la littérature sur les dimensions politiques du savoir et de la science afin de conceptualiser le rôle des évaluations scientifiques au sein d'une théorie de la médiation scientifique (scientific brokerage). Une analyse de réseau (SNA) des 5751 références contenues dans les documents déposés par 268 organisations participant aux consultations publiques de 2010 et 2014 constitue le corps de la démonstration empirique. Précisément, il y est démontré comment un médiateur scientifique peut rediriger le flux d'information afin de contrer l'incompatibilité entre apprentissage collectif et conflit politique. L'argument mobilise les mécanismes cognitifs traditionnellement présents dans la théorie des médiateurs de politique (policy broker), mais introduit aussi les jeux de pouvoir fondamentaux à la circulation de la connaissance entre acteurs politiques.

An enforced cooperation : understanding scientific assessments in adversarial polities through Quebec shale gas policymaking, 2010-2014

Les biotechnologies, le réchauffement climatique, les ressources naturelles et la gestion des écosystèmes sont tous représentatifs de la “nouvelle politique de la nature” (Hajer 2003), un terme englobant les enjeux marqués par une grande incertitude scientifique et un encadrement réglementaire inadapté aux nouvelles réalités, suscitant de fait un conflit politique hors du commun. Dans l'espoir de diminuer ces tensions et de générer un savoir consensuel, de nombreux gouvernements se tournent vers des institutions scientifiques ad hoc pour documenter l'élaboration des politiques et répondre aux préoccupations des partie-prenantes. Mais ces évaluations scientifiques permettent-elles réellement de créer une compréhension commune partagée par ces acteurs politiques polarisés? Alors que l'on pourrait croire que celles-ci génèrent un climat d'apprentissage collectif rassembleur, un environnement politique conflictuel rend l'apprentissage entre opposant extrêmement improbable. Ainsi, cette recherche documente le potentiel conciliateur des évaluation scientifique en utilisant le cas des gaz de schiste québécois (2010-2014). Ce faisant, elle mobilise la littérature sur les dimensions politiques du savoir et de la science afin de conceptualiser le rôle des évaluations scientifiques au sein d'une théorie de la médiation scientifique (scientific brokerage). Une analyse de réseau (SNA) des 5751 références contenues dans les documents déposés par 268 organisations participant aux consultations publiques de 2010 et 2014 constitue le corps de la démonstration empirique. Précisément, il y est démontré comment un médiateur scientifique peut rediriger le flux d'information afin de contrer l'incompatibilité entre apprentissage collectif et conflit politique. L'argument mobilise les mécanismes cognitifs traditionnellement présents dans la théorie des médiateurs de politique (policy broker), mais introduit aussi les jeux de pouvoir fondamentaux à la circulation de la connaissance entre acteurs politiques.

Bayesian parameter estimation for latent Markov random fields and social networks

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the calculation of an intractable normalising constant. This problem has received much attention, but very little of this has focussed on the important practical case where the data consists of noisy or incomplete observations of the underlying hidden structure. This paper specifically addresses this problem, comparing two alternative methodologies. In the first of these approaches particle Markov chain Monte Carlo (Andrieu et al., 2010) is used to efficiently explore the parameter space, combined with the exchange algorithm (Murray et al., 2006) for avoiding the calculation of the intractable normalising constant (a proof showing that this combination targets the correct distribution in found in a supplementary appendix online). This approach is compared with approximate Bayesian computation (Pritchard et al., 1999). Applications to estimating the parameters of Ising models and exponential random graphs from noisy data are presented. Each algorithm used in the paper targets an approximation to the true posterior due to the use of MCMC to simulate from the latent graphical model, in lieu of being able to do this exactly in general. The supplementary appendix also describes the nature of the resulting approximation.

Breeding value accuracy estimates for growth traits using random regression and multi-trait models in Nelore cattle

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Essays on Bayesian Inference for Social Networks

This thesis presents Bayesian solutions to inference problems for three types of social network data structures: a single observation of a social network, repeated observations on the same social network, and repeated observations on a social network developing through time. A social network is conceived as being a structure consisting of actors and their social interaction with each other. A common conceptualisation of social networks is to let the actors be represented by nodes in a graph with edges between pairs of nodes that are relationally tied to each other according to some definition. Statistical analysis of social networks is to a large extent concerned with modelling of these relational ties, which lends itself to empirical evaluation. The first paper deals with a family of statistical models for social networks called exponential random graphs that takes various structural features of the network into account. In general, the likelihood functions of exponential random graphs are only known up to a constant of proportionality. A procedure for performing Bayesian inference using Markov chain Monte Carlo (MCMC) methods is presented. The algorithm consists of two basic steps, one in which an ordinary Metropolis-Hastings up-dating step is used, and another in which an importance sampling scheme is used to calculate the acceptance probability of the Metropolis-Hastings step. In paper number two a method for modelling reports given by actors (or other informants) on their social interaction with others is investigated in a Bayesian framework. The model contains two basic ingredients: the unknown network structure and functions that link this unknown network structure to the reports given by the actors. These functions take the form of probit link functions. An intrinsic problem is that the model is not identified, meaning that there are combinations of values on the unknown structure and the parameters in the probit link functions that are observationally equivalent. Instead of using restrictions for achieving identification, it is proposed that the different observationally equivalent combinations of parameters and unknown structure be investigated a posteriori. Estimation of parameters is carried out using Gibbs sampling with a switching devise that enables transitions between posterior modal regions. The main goal of the procedures is to provide tools for comparisons of different model specifications. Papers 3 and 4, propose Bayesian methods for longitudinal social networks. The premise of the models investigated is that overall change in social networks occurs as a consequence of sequences of incremental changes. Models for the evolution of social networks using continuos-time Markov chains are meant to capture these dynamics. Paper 3 presents an MCMC algorithm for exploring the posteriors of parameters for such Markov chains. More specifically, the unobserved evolution of the network in-between observations is explicitly modelled thereby avoiding the need to deal with explicit formulas for the transition probabilities. This enables likelihood based parameter inference in a wider class of network evolution models than has been available before. Paper 4 builds on the proposed inference procedure of Paper 3 and demonstrates how to perform model selection for a class of network evolution models.