Dissertations / Theses on the topic 'The hierarchical model'

In this thesis, we study the spectral properties of the hierarchical Anderson model. This model is an approximation of the Anderson tight-binding model on Zd , with the usual discrete Laplacian replaced by a hierarchical long-range interaction operator. In the hierarchical Anderson model, we are given a countable set X endowed with a hierarchical structure. The free hierarchical Laplacian is a self-adjoint operator Delta acting on the Hilbert space l 2( X ). The spectrum of Delta consists of isolated infinitely degenerate eigenvalues. We look at small random perturbations of the operator Delta. The disorder is modeled by a random potential Vo, (Vopsi)(x) = o( x)psi(x) for psi ∈ l 2( X ). The numbers o(x) are identically distributed independent random variables with a bounded density. The hierarchical Anderson model is the random self-adjoint operator Ho = Delta + Vo. We prove the following two results. If the model has a spectral dimension dsp ≤ 4 then, almost surely, the spectrum of Ho is dense pure-point. The second result is on eigenvalue statistics. For dsp < 1, the energy levels for Ho are asymptotically a Poisson point process in the thermodynamic limit, after a proper rescaling.

Flexible Manufacturing Systems (FMSs) are usually composed of general purpose machines with automatic tool changing capability and integrated material handling. FMSs offer the advantages of high utilization levels and simultaneous production of a variety of part types with minimal changeover time. The complexity of FMSs however requires sophisticated control. In this dissertation a four level control hierarchy along with computationally feasible control algorithms for each level is presented. Decisions are made at each level utilizing the flexibility inherent in FMSs. The proposed scheme has the advantages of ensuring satisfaction of higher level decisions as lower level operating decisions are made, and allows performance and status data collected at lower levels to be fed back and influence future high level decisions. The top level is concerned with the choice of part types and volumes to be assigned to the FMS over the next several months. Within this horizon, production volumes are planned for each period, a period typically being between a week and a month in length. A linear programming model is used for planning at this level. The second level plans daily or shift production. Advantage is taken of the FMSs ability to be configured to respond to different part mixes to allocate tools to machines so as to minimize holding costs. Separate mathematical programming models are formulated to match various FMS environments. A heuristic for solution of a model of an automated production flexible environment is detailed. Computational results are presented. Extensions of this heuristic to other environments are outlined. The third level determines process routes for each part type in order to minimize material handling. Additional tools are loaded on machines when possible to maximize alternate routings, and using the flexibility offered by FMSs to process parts along alternate routes, routing assignments are made to minimize workload assignment. These routing assignments are used by level four for actual routing, sequencing and material handling path control. The level three model is formulated as a linear program and heuristics are used for level four. An example is provided to illustrate the completeness of the decision hierarchy and the relationships between levels.

A model is considered for the dynamics of a size-structured population in which the birth, death and growth rates of an individual of size s are functions of the total population biomass of all individuals of size larger or smaller than s. The dynamics of the size distribution is governed by the McKendrick equations. An existence/uniqueness theorem for this equation is proved using an equivalent pair of partial and ordinary differential equations. The asymptotic dynamics of the density function is studied and some applications of the model to intraspecific predation and certain types of intraspecific competitions are given.

CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
Esta dissertação investiga a utilização de sistemas Neuro- Fuzzy Hierárquicos BSP (Binary Space Partitioning) para aplicações em classificação de padrões, previsão, sistemas de controle e extração de regras fuzzy. O objetivo é criar um modelo Neuro-Fuzzy Hierárquico BSP do tipo Mamdani a partir do modelo Neuro-Fuzzy Hierárquico BSP Class (NFHB-Class) que é capaz de criar a sua própria estrutura automaticamente e extrair conhecimento de uma base de dados através de regras fuzzy, lingüisticamente interpretáveis, que explicam a estrutura dos dados. Esta dissertação consiste de quatros etapas principais: estudo dos principais sistemas hierárquicos; análise do sistema Neuro-Fuzzy Hierárquico BSP Class, definição e implementação do modelo NFHB-Mamdani e estudo de casos. No estudo dos principais sistemas hierárquicos é efetuado um levantamento bibliográfico na área. São investigados, também, os principais modelos neuro-fuzzy utilizados em sistemas de controle - Falcon e o Nefcon. Na análise do sistema NFHB- Class, é verificado o aprendizado da estrutura, o particionamento recursivo, a possibilidade de se ter um maior número de entrada - em comparação com outros sistemas neuro-fuzzy - e regras fuzzy recursivas. O sistema NFHB- Class é um modelo desenvolvido especificamente para classificação de padrões, como possui várias saídas, não é possível utilizá-lo em aplicações em controle e em previsão. Para suprir esta deficiência, é criado um novo modelo que contém uma única saída. Na terceira etapa é definido um novo modelo Neuro-Fuzzy Hierárquico BSP com conseqüentes fuzzy (NFHB-Mamdani), cuja implementação utiliza a arquitetura do NFHBClass para a fase do aprendizado, teste e validação, porém, com os conseqüentes diferentes, modificando a estratégia de definição dos conseqüentes das regras. Além de sua utilização em classificação de padrões, previsão e controle, o sistema NFHB-Mamdani é capaz de extrair conhecimento de uma base de dados em forma de regras do tipo SE ENTÃO. No estudo de casos são utilizadas duas bases de dados típicas para aplicações em classificação: Wine e o Iris. Para previsão são utilizadas séries de cargas elétricas de seis companhias brasileiras diferentes: Copel, Cemig, Light, Cerj, Eletropaulo e Furnas. Finalmente, para testar o desempenho do sistema em controle faz-se uso de uma planta de terceira ordem como processo a controlar. Os resultados obtidos para classificação, na maioria dos casos, são superiores aos melhores resultados encontrados pelos outros modelos e algoritmos aos quais foram comparados. Para previsão de cargas elétricas, os resultados obtidos estão sempre entre os melhores resultados fornecidos por outros modelos aos quais formam comparados. Quanto à aplicação em controle, o modelo NFHB-Mamdani consegue controlar, de forma satisfatória, o processo utilizado para teste.
This paper investigates the use of Binary Space Partitioning (BSP) Hierarchical Neuro-Fuzzy Systems for applications in pattern classification, forecast, control systems and obtaining of fuzzy rules. The goal is to create a BSP Hierarchical Neuro-Fuzzy Model of the Mamdani type from the BSP Hierarchical Neuro-Fuzzy Class (NFHB-Class) which is able to create its own structure automatically and obtain knowledge from a data base through fuzzy rule, interpreted linguistically, that explain the data structure. This paper is made up of four main parts: study of the main Hierarchical Systems; analysis of the BSP Hierarchical Neuro-Fuzzy Class System, definition and implementation of the NFHB-Mamdani model, and case studies. A bibliographical survey is made in the study of the main Hierarchical Systems. The main Neuro-Fuzzy Models used in control systems - Falcon and Nefcon -are also investigated. In the NFHB-Class System, the learning of the structure is verified, as well as, the recursive partitioning, the possibility of having a greater number of inputs in comparison to other Neuro-Fuzzy systems and recursive fuzzy rules. The NFHB-Class System is a model developed specifically for pattern classification, since it has various outputs, it is not possible to use it in control application and forecast. To make up for this deficiency, a new unique output model is developed. In the third part, a new BSP Hierarchical Neuro-Fuzzy model is defined with fuzzy consequents (NFHB-Mamdani), whose implementation uses the NFHB-Class architecture for the learning, test, and validation phase, yet with the different consequents, modifying the definition strategy of the consequents of the rules. Aside from its use in pattern classification, forecast, and control, the NFHB-Mamdani system is capable of obtaining knowledge from a data base in the form of rules of the type IF THEN. Two typical data base for application in classification are used in the case studies: Wine and Iris. Electric charge series of six different Brazilian companies are used for forecasting: Copel, Cemig, Light, Cerj, Eletropaulo and Furnas. Finally, to test the performance of the system in control, a third order plant is used as a process to be controlled. The obtained results for classification, in most cases, are better than the best results found by other models and algorithms to which they were compared. For forecast of electric charges, the obtained results are always among the best supplied by other models to which they were compared. Concerning its application in control, the NFHB-Mamdani model is able to control, reasonably, the process used for test.

Hierarchical task decompositions play an essential role in the design of complex simulation and decision systems, such as the ones that arise in video games. Game designers find it very natural to adopt a divide-and-conquer philosophy of specifying hierarchical policies, where decision modules can be constructed somewhat independently. The process of choosing the parameters of these modules manually is typically lengthy and tedious. The hierarchical reinforcement learning (HRL) field has produced elegant ways of decomposing policies and value functions using semi-Markov decision processes. However, there is still a lack of demonstrations in larger nonlinear systems with discrete and continuous variables. To narrow this gap between industrial practices and academic ideas, we address the problem of designing efficient algorithms to facilitate the deployment of HRL ideas in more realistic settings. In particular, we propose Bayesian active learning methods to learn the relevant aspects of either policies or value functions by focusing on the most relevant parts of the parameter and state spaces respectively. To demonstrate the scalability of our solution, we have applied it to The Open Racing Car Simulator (TORCS), a 3D game engine that implements complex vehicle dynamics. The environment is a large topological map roughly based on downtown Vancouver, British Columbia. Higher level abstract tasks are also learned in this process using a model-based extension of the MAXQ algorithm. Our solution demonstrates how HRL can be scaled to large applications with complex, discrete and continuous non-linear dynamics.

COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
Este trabalho tem por objetivo criar um novo sistema de inferência fuzzy intervalar do tipo 2 para tratamento de incertezas com aprendizado automático e que proporcione um intervalo de confiança para as suas saídas defuzzificadas através do cálculo dos conjuntos tipo-reduzidos correspondentes. Para viabilizar este objetivo, este novo modelo combina os paradigmas de modelagem dos sistemas de inferência fuzzy do tipo 2 e redes neurais com técnicas de particionamento recursivo BSP. Este modelo possui principalmente a capacidade de modelar e manipular a maioria dos tipos de incertezas existentes em situações reais, minimizando os efeitos destas para produzir um melhor desempenho. Além disso, tem a capacidade autônoma de criar e expandir automaticamente a sua própria estrutura, de reduzir a limitação quanto ao número de entradas e de extrair regras de conhecimento a partir de um conjunto de dados. Este novo modelo fornece um intervalo de confiança, que se constitui em uma informação importante para aplicações reais. Neste contexto, este modelo supera as limitações dos sistemas de inferência fuzzy do tipo 2 - complexidade computacional, reduzido número de entradas permissíveis e forma limitada, ou inexistente, de criarem a sua própria estrutura e regras - e dos sistemas de inferência fuzzy do tipo 1 - adaptação incompleta a incertezas e não fornecimento de um intervalo de confiança para a saída. Os sistemas de inferência fuzzy do tipo1 também apresentam limitações quanto ao reduzido número de entradas permissíveis, mas o uso de particionamentos recursivos, já explorado com excelentes resultados [SOUZ99], reduz significativamente estas limitações. O trabalho constitui-se fundamentalmente em quatro partes: um estudo sobre os diferentes sistemas de inferência fuzzy do tipo 2 existentes, análise dos sistemas neuro-fuzzy hierárquicos que usam conjuntos fuzzy do tipo 1, modelagem e implementação do novo modelo neuro-fuzzy hierárquico BSP do tipo 2 e estudo de casos. O novo modelo, denominado modelo neuro-fuzzy hierárquico BSP do tipo 2 (NFHB-T2), foi definido a partir do estudo das características desejáveis e das limitações dos sistemas de inferência fuzzy do tipo 2 e do tipo 1 e dos sistemas neuro-fuzzy hierárquicos que usam conjuntos fuzzy do tipo 1 existentes. Desta forma, o NFHB-T2 é modelado e implementado com os atributos de interpretabilidade e autonomia, a partir da concepção de sistemas de inferência fuzzy do tipo 2, de redes neurais e do particionamento recursivo BSP. O modelo desenvolvido é avaliado em diversas bases de dados benchmark e aplicações reais de previsão e aproximação de funções. São feitas comparações com outros modelos. Os resultados encontrados mostram que o modelo NFHB-T2 fornece, em previsão e aproximação de funções, resultados próximos e em vários casos superiores aos melhores resultados proporcionados pelos modelos utilizados para comparação. Em termos de tempo computacional, o seu desempenho também é muito bom. Em previsão e aproximação de funções, os intervalos de confiança obtidos para as saídas defuzzificadas mostram-se sempre coerentes e oferecem maior credibilidade na maioria dos casos quando comparados a intervalos de confiança obtidos por métodos tradicionais usando as saídas previstas pelos outros modelos e pelo próprio NFHB-T2 .
The objective of this thesis is to create a new type-2 fuzzy inference system for the treatment of uncertainties with automatic learning and that provides an interval of confidence for its defuzzified output through the calculation of corresponding type-reduced sets. In order to attain this objective, this new model combines the paradigms of the modelling of the type-2 fuzzy inference systems and neural networks with techniques of recursive BSP partitioning. This model mainly has the capacity to model and to manipulate most of the types of existing uncertainties in real situations, diminishing the effects of these to produce a better performance. In addition, it has the independent capacity to create and to expand its own structure automatically, to reduce the limitation referred to the number of inputs and to extract rules of knowledge from a data set. This new model provides a confidence interval, that constitutes an important information for real applications. In this context, this model surpasses the limitations of the type-2 fuzzy inference systems - complexity computational, small number of inputs allowed and limited form, or nonexistent, to create its own structure and rules - and of the type-1 fuzzy inference systems - incomplete adaptation to uncertainties and not to give an interval of confidence for the output. The type-1 fuzzy inference systems also present limitations with regard to the small number of inputs allowed, but the use of recursive partitioning, already explored with excellent results [SOUZ99], reduce significantly these limitations. This work constitutes fundamentally of four parts: a study on the different existing type-2 fuzzy inference systems, analysis of the hierarchical neuro- fuzzy systems that use type-1 fuzzy sets, modelling and implementation of the new type-2 hierarchical neuro-fuzzy BSP model and study of cases. The new model, denominated type-2 hierarchical neuro-fuzzy BSP model (T2-HNFB) was defined from the study of the desirable characteristics and the limitations of the type-2 and type-1 fuzzy inference systems and the existing hierarchical neuro-fuzzy systems that use type- 1 fuzzy sets. Of this form, the T2-HNFB model is modelling and implemented with the attributes of interpretability and autonomy, from the conception of type-2 fuzzy inference systems, neural networks and recursive BSP partitioning. The developed model is evaluated in different benchmark databases and real applications of forecast and approximation of functions. Comparisons with other models are done. The results obtained show that T2-HNFB model provides, in forecast and approximation of functions, next results and in several cases superior to the best results provided by the models used for comparison. In terms of computational time, its performance also is very good. In forecast and approximation of functions, the intervals of confidence obtained for the defuzzified outputs are always coherent and offer greater credibility in most of cases when compared with intervals of confidence obtained through traditional methods using the forecast outputs by the other models and the own T2-HNFB model.

Master of Science
Department of Computing and Information Sciences
William H. Hsu
(Higgins, Savje, & Sekhon, 2016) Provides us with a sampling blocking algorithm that enables large and complex experiments to run in polynomial time without sacrificing the precision of estimates on a covariate dataset. The goal of this project is to run the different clustering algorithms on top of clusters formed from above mentioned blocking algorithm and analyze the performance and compatibility of the clustering algorithms. We first start with applying the blocking algorithm on a covariate dataset and once the clusters are formed, we then apply our clustering algorithm HAC (Hierarchical Agglomerative Clustering) or PAM (Partitioning Around Medoids) on the seeds of the clusters. This will help us to generate more similar clusters. We compare our performance and precision of our hybridized clustering techniques with the pure clustering techniques to identify a suitable hybridized blocking model.

Hierarchical models provide a flexible way of modeling complex behavior. However, the complicated interdependencies among the parameters in the hierarchy make training such models difficult. MCMC methods have been widely used for this purpose, but can often only approximate the necessary distributions. Acceptance-rejection sampling allows for perfect simulation from these often unnormalized distributions by drawing from another distribution over the same support. The efficacy of acceptance-rejection sampling is explored through application to a small dataset which has been widely used for evaluating different methods for inference on hierarchical models. A particular algorithm is developed to draw variates from the posterior distribution. The algorithm is both verified and validated, and then finally applied to the given data, with comparisons to the results of different methods.

Nowadays, model-driven engineering (MDE) promises to ease software development by decreasing the inherent complexity of classical software development. In order to deliver on this promise, MDE increases the level of abstraction and automation, through a consideration of domain-specific models (DSMs) and model operations (e.g. model transformations or code generations). DSMs conform to domain-specific modeling languages (DSMLs), which increase the level of abstraction, and model operations are first-class entities of software development because they increase the level of automation. Nevertheless, MDE has to deal with at least two new dimensions of complexity, which are basically caused by the increased linguistic and technological heterogeneity. The first dimension of complexity is setting up an MDE environment, an activity comprised of the implementation or selection of DSMLs and model operations. Setting up an MDE environment is both time-consuming and error-prone because of the implementation or adaptation of model operations. The second dimension of complexity is concerned with applying MDE for actual software development. Applying MDE is challenging because a collection of DSMs, which conform to potentially heterogeneous DSMLs, are required to completely specify a complex software system. A single DSML can only be used to describe a specific aspect of a software system at a certain level of abstraction and from a certain perspective. Additionally, DSMs are usually not independent but instead have inherent interdependencies, reflecting (partial) similar aspects of a software system at different levels of abstraction or from different perspectives. A subset of these dependencies are applications of various model operations, which are necessary to keep the degree of automation high. This becomes even worse when addressing the first dimension of complexity. Due to continuous changes, all kinds of dependencies, including the applications of model operations, must also be managed continuously. This comprises maintaining the existence of these dependencies and the appropriate (re-)application of model operations. The contribution of this thesis is an approach that combines traceability and model management to address the aforementioned challenges of configuring and applying MDE for software development. The approach is considered as a traceability approach because it supports capturing and automatically maintaining dependencies between DSMs. The approach is considered as a model management approach because it supports managing the automated (re-)application of heterogeneous model operations. In addition, the approach is considered as a comprehensive model management. Since the decomposition of model operations is encouraged to alleviate the first dimension of complexity, the subsequent composition of model operations is required to counteract their fragmentation. A significant portion of this thesis concerns itself with providing a method for the specification of decoupled yet still highly cohesive complex compositions of heterogeneous model operations. The approach supports two different kinds of compositions - data-flow compositions and context compositions. Data-flow composition is used to define a network of heterogeneous model operations coupled by sharing input and output DSMs alone. Context composition is related to a concept used in declarative model transformation approaches to compose individual model transformation rules (units) at any level of detail. In this thesis, context composition provides the ability to use a collection of dependencies as context for the composition of other dependencies, including model operations. In addition, the actual implementation of model operations, which are going to be composed, do not need to implement any composition concerns. The approach is realized by means of a formalism called an executable and dynamic hierarchical megamodel, based on the original idea of megamodels. This formalism supports specifying compositions of dependencies (traceability and model operations). On top of this formalism, traceability is realized by means of a localization concept, and model management by means of an execution concept.
Die modellgetriebene Softwareentwicklung (MDE) verspricht heutzutage, durch das Verringern der inhärenten Komplexität der klassischen Softwareentwicklung, das Entwickeln von Software zu vereinfachen. Um dies zu erreichen, erhöht MDE das Abstraktions- und Automationsniveau durch die Einbindung domänenspezifischer Modelle (DSMs) und Modelloperationen (z.B. Modelltransformationen oder Codegenerierungen). DSMs sind konform zu domänenspezifischen Modellierungssprachen (DSMLs), die dazu dienen das Abstraktionsniveau der Softwareentwicklung zu erhöhen. Modelloperationen sind essentiell für die Softwareentwicklung da diese den Grad der Automatisierung erhöhen. Dennoch muss MDE mit Komplexitätsdimensionen umgehen die sich grundsätzlich aus der erhöhten sprachlichen und technologischen Heterogenität ergeben. Die erste Komplexitätsdimension ist das Konfigurieren einer Umgebung für MDE. Diese Aktivität setzt sich aus der Implementierung und Selektion von DSMLs sowie Modelloperationen zusammen. Eine solche Aktivität ist gerade durch die Implementierung und Anpassung von Modelloperationen zeitintensiv sowie fehleranfällig. Die zweite Komplexitätsdimension hängt mit der Anwendung von MDE für die eigentliche Softwareentwicklung zusammen. Das Anwenden von MDE ist eine Herausforderung weil eine Menge von heterogenen DSMs, die unterschiedlichen DSMLs unterliegen, erforderlich sind um ein komplexes Softwaresystem zu spezifizieren. Individuelle DSMLs werden verwendet um spezifische Aspekte eines Softwaresystems auf bestimmten Abstraktionsniveaus und aus bestimmten Perspektiven zu beschreiben. Hinzu kommt, dass DSMs sowie DSMLs grundsätzlich nicht unabhängig sind, sondern inhärente Abhängigkeiten besitzen. Diese Abhängigkeiten reflektieren äquivalente Aspekte eines Softwaresystems. Eine Teilmenge dieser Abhängigkeiten reflektieren Anwendungen diverser Modelloperationen, die notwendig sind um den Grad der Automatisierung hoch zu halten. Dies wird erschwert wenn man die erste Komplexitätsdimension hinzuzieht. Aufgrund kontinuierlicher Änderungen der DSMs, müssen alle Arten von Abhängigkeiten, inklusive die Anwendung von Modelloperationen, kontinuierlich verwaltet werden. Dies beinhaltet die Wartung dieser Abhängigkeiten und das sachgerechte (wiederholte) Anwenden von Modelloperationen. Der Beitrag dieser Arbeit ist ein Ansatz, der die Bereiche Traceability und Model Management vereint. Das Erfassen und die automatische Verwaltung von Abhängigkeiten zwischen DSMs unterstützt Traceability, während das (automatische) wiederholte Anwenden von heterogenen Modelloperationen Model Management ermöglicht. Dadurch werden die zuvor erwähnten Herausforderungen der Konfiguration und Anwendung von MDE überwunden. Die negativen Auswirkungen der ersten Komplexitätsdimension können gelindert werden indem Modelloperationen in atomare Einheiten zerlegt werden. Um der implizierten Fragmentierung entgegenzuwirken, erfordert dies allerdings eine nachfolgende Komposition der Modelloperationen. Der Ansatz wird als erweitertes Model Management betrachtet, da ein signifikanter Anteil dieser Arbeit die Kompositionen von heterogenen Modelloperationen behandelt. Unterstützt werden zwei unterschiedliche Arten von Kompositionen. Datenfluss-Kompositionen werden verwendet, um Netzwerke von heterogenen Modelloperationen zu beschreiben, die nur durch das Teilen von Ein- und Ausgabe DSMs komponiert werden. Kontext-Kompositionen bedienen sich eines Konzepts, das von deklarativen Modelltransformationen bekannt ist. Dies ermöglicht die Komposition von unabhängigen Transformationsregeln auf unterschiedlichsten Detailebenen. Die in dieser Arbeit eingeführten Kontext-Kompositionen bieten die Möglichkeit eine Menge von unterschiedlichsten Abhängigkeiten als Kontext für eine Komposition zu verwenden -- unabhängig davon ob diese Abhängigkeit eine Modelloperation repräsentiert. Zusätzlich müssen die Modelloperationen, die komponiert werden, selber keine Kompositionsaspekte implementieren, was deren Wiederverwendbarkeit erhöht. Realisiert wird dieser Ansatz durch einen Formalismus der Executable and Dynamic Hierarchical Megamodel genannt wird und auf der originalen Idee der Megamodelle basiert. Auf Basis dieses Formalismus' sind die Konzepte Traceability (hier Localization) und Model Management (hier Execution) umgesetzt.

Pathway is a set of genes which are predefined and serve a particular celluar or physiological function. Ranking pathways relevant to a particular phenotype can help researchers focus on a few sets of genes in pathways. In this thesis, a Bayesian hierarchical latent model was proposed using generalized linear random effects model. The advantage of the approach was that it can easily incorporate prior knowledges when the sample size was small and the number of genes was large. For the covariance matrix of a set of random variables, two Gaussian random processes were considered to construct the dependencies among genes in a pathway. One was based on the polynomial kernel and the other was based on the Gaussian kernel. Then these two kernels were compared with constant covariance matrix of the random effect by using the ratio, which was based on the joint posterior distribution with respect to each model. For mixture models, log-likelihood values were computed at different values of the mixture proportion, compared among mixtures of selected kernels and point-mass density (or constant covariance matrix). The approach was applied to a data set (Mootha et al., 2003) containing the expression profiles of type II diabetes where the motivation was to identify pathways that can discriminate between normal patients and patients with type II diabetes.
Master of Science

In this dissertation, we develop a model selection and estimation methodology for nonstationary spatial fields. Large, spatially correlated data often cover a vast geographical area. However, local spatial regions may have different mean and covariance structures. Our methodology accomplishes three goals: (1) cluster locations into small regions with distinct, stationary models, (2) perform Bayesian model selection within each cluster, and (3) correlate the model selection and estimation in nearby clusters. We utilize the Conditional Autoregressive (CAR) model and Ising distribution to provide intra-cluster correlation on the linear effects and model inclusion indicators, while modeling inter-cluster correlation with separate Gaussian processes. We apply our model selection methodology to a dataset involving the prediction of Brook trout presence in subwatersheds across Pennsylvania. We find that our methodology outperforms the stationary spatial model and that different regions in Pennsylvania are governed by separate Gaussian process regression models.
Ph. D.

One challenge that faces hydrologists in water resources planning is to predict the catchment???s response to a given rainfall. Estimation of parameter uncertainty (and model uncertainty) allows assessment of the risk in likely applications of hydrological models. Bayesian statistical inference, with computations carried out via Markov Chain Monte Carlo (MCMC) methods, offers an attractive approach to model specification, allowing for the combination of any pre-existing knowledge about individual models and their respective parameters with the available catchment data to assess both parameter and model uncertainty. This thesis develops and applies Bayesian statistical tools for parameter estimation, comparison of model performance and hierarchical model aggregation. The work presented has three main sections. The first area of research compares four MCMC algorithms for simplicity, ease of use, efficiency and speed of implementation in the context of conceptual rainfall-runoff modelling. Included is an adaptive Metropolis algorithm that has characteristics that are well suited to hydrological applications. The utility of the proposed adaptive algorithm is further expanded by the second area of research in which a probabilistic regime for comparing selected models is developed and applied. The final area of research introduces a methodology for hydrologic model aggregation that is flexible and dynamic. Rigidity in the model structure limits representation of the variability in the flow generation mechanism, which becomes a limitation when the flow processes are not clearly understood. The proposed Hierarchical Mixtures of Experts (HME) model architecture is designed to do away with this limitation by selecting individual models probabilistically based on predefined catchment indicators. In addition, the approach allows a more flexible specification of the model error to better assess the risk of likely outcomes based on the model simulations. Application of the approach to lumped and distributed rainfall runoff models for a variety of catchments shows that by assessing different catchment predictors the method can be a useful tool for prediction of catchment response.

A main objective of Departments of Transportation is to improve the safety of the roadways over which they have jurisdiction. Safety projects, such as cable barriers and raised medians, are utilized to reduce both crash frequency and crash severity. The efficacy of these projects must be evaluated in order to use resources in the best way possible. Five models are proposed for the evaluation of traffic projects: (1) a Bayesian Poisson regression model; (2) a hierarchical Poisson regression model building on model (1) by adding hyperpriors; (3) a similar model correcting for overdispersion; (4) a dynamic linear model; and (5) a traditional before-after study model. Evaluation of these models is discussed using various metrics including DIC. Using the models selected for analysis, it was determined that cable barriers are quite effective at reducing severe crashes and cross-median crashes on Utah highways. Raised medians are also largely effective at reducing severe crashes. The results of before and after analyses are highly valuable to Departments of Transportation in identifying effective projects and in determining which roadway segments will benefit most from their implementation.

The mammalian brain is, with its numerous neural elements and structured complex connectivity, one of the most complex systems in nature. Recently, large-scale corticocortical connectivities, both structural and functional, have received a great deal of research attention, especially using the approach of complex networks. Here, we try to shed some light on the relationship between structural and functional connectivities by studying synchronization dynamics in a realistic anatomical network of cat cortical connectivity. We model the cortical areas by a subnetwork of interacting excitable neurons (multilevel model) and by a neural mass model (population model). With weak couplings, the multilevel model displays biologically plausible dynamics and the synchronization patterns reveal a hierarchical cluster organization in the network structure. We can identify a group of brain areas involved in multifunctional tasks by comparing the dynamical clusters to the topological communities of the network. With strong couplings of multilevel model and by using neural mass model, the dynamics are characterized by well-defined oscillations. The synchronization patterns are mainly determined by the node intensity (total input strengths of a node); the detailed network topology is of secondary importance. The biologically improved multilevel model exhibits similar dynamical patterns in the two regimes. Thus, the study of synchronization in a multilevel complex network model of cortex can provide insights into the relationship between network topology and functional organization of complex brain networks.
Das Gehirn von Säugetieren stellt mit seinen zahlreichen, hochgradig vernetzten Neuronen ein natürliches Netzwerk von immenser Komplexität dar. In der jüngsten Vergangenheit sind die großflächige kortikale Konnektivitäten, sowohl unter strukturellen wie auch funktionalen Gesichtspunkten, in den Fokus der Forschung getreten. Die Verwendung von komplexe Netzwerke spielt hierbei eine entscheidende Rolle. In der vorliegenden Dissertation versuchen wir, das Verhältnis von struktureller und funktionaler Konnektivität durch Untersuchung der Synchronisationsdynamik anhand eines realistischen Modells der Konnektivität im Kortex einer Katze näher zu beleuchten. Wir modellieren die Kortexareale durch ein Subnetzwerk interagierender, erregbarer Neuronen (multilevel model) und durch ein Modell von Neuronenensembles (population model). Bei schwacher Kopplung zeigt das multilevel model eine biologisch plausible Dynamik und die Synchronisationsmuster lassen eine hierarchische Organisation der Netzwerkstruktur erkennen. Indem wir die dynamischen Cluster mit den topologischen Einheiten des Netzwerks vergleichen, sind wir in der Lage die Hirnareale, die an der Bewältigung komplexer Aufgaben beteiligt sind, zu identifizieren. Bei starker Kopplung im multilevel model und unter Verwendung des Ensemblemodells weist die Dynamik klare Oszillationen auf. Die Synchronisationsmuster werden hauptsächlich durch die Eingangsstärke an den einzelnen Knoten bestimmt, während die genaue Netzwerktopologie zweitrangig ist. Eine Erweiterung des Modells auf andere biologisch relevante Faktoren bestätigt die vorherigen Ergebnisse. Die Untersuchung der Synchronisation in einem multilevel model des Kortex ermöglicht daher tiefere Einblicke in die Zusammenhänge zwischen Netzwerktopologie und funktionaler Organisation in komplexen Hirn-Netzwerken.

The objective of this research is to establish consistency thresholds linked to alpha (α) levels for HDM’s (Hierarchical Decision Model) judgment quantification method. Measuring consistency in order to control it is a crucial and inseparable part of any AHP/HDM experiment. The researchers on the subject recommend establishing thresholds that are statistically based on hypothesis testing, and are linked to the number of decision variables and (α) level. Such thresholds provide the means with which to evaluate the soundness and validity of an AHP/HDM decision. The linkage of thresholds to (α) levels allows the decision makers to set an appropriate inconsistency tolerance compatible with the situation at hand. The measurements of judgments are unreliable in the absence of an inconsistency measure that includes acceptable limits. All of this is essential to the credibility of the entire decision making process and hence is extremely useful for practitioners and researchers alike. This research includes distribution fitting for the inconsistencies. It is a valuable and interesting part of the research results and adds usefulness, practicality and insight. The superb fits obtained give confidence that all the statistical inferences based on the fitted distributions accurately reflect the HDM’s inconsistency measure.

Le pisé est une technique constructive vernaculaire consistant à compacter successivement des couches de terre humide entre des coffrages. Cette technique, présente dans le monde entier, l'est en particulier en France dans la région Auvergne-Rhône-Alpes. Comme il n'existe pas de réglementation attachée à cette technique constructive, il est très difficile pour des propriétaires de réparer leur bien. Le développement de cette technique pour de nouveaux projets souffre aussi de cette absence alors qu'elle répond à certains enjeux posés par le Développement Durable. Le travail présenté ici fait partie intégrante du projet national PRIMATERRE dédié à l'étude des constructions impliquant de la terre. Une loi de comportement élasto-plastique est développée dans ce travail pour modéliser le comportement du pisé. Elle s'appuie sur une approche hiérarchisée de la modélisation en lien avec le nombre d'essais disponibles pour identifier les paramètres de modèle mais aussi en lien avec la complexité de phénomènes à prendre en compte. Ce modèle s'inspire d'un modèle pré-existant, CJS, développé en géotechnique pour modéliser le comportement mécanique des matériaux granulaires. Une adaptation s'est imposée pour prendre en compte les spécificités du comportement mécanique du pisé qui possède de nombreuses similitudes avec celui des matériaux quasi-fragiles. Deux niveaux de modélisation pour le modèle de comportement appelé CJS-RE sont présentés, pouvant être utilisés dans un contexte de sollicitation monotone. Le premier niveau CJS-RE1 est un modèle élastique parfaitement plastique alors que le second niveau CJS-RE2 est un modèle élasto-plastique à écrouissage isotrope. Deux mécanismes de déformation plastique sont présents, l'un lié aux phénomènes purement déviatoires et l'autre aux phénomènes de traction. La validation du modèle a été entreprise sur la base de la simulation d'essais en laboratoire de compression diagonale et de chargement latéral (pushover) sur des murets, issus de la littérature. Le niveau CJS-RE1 a été capable de capturer les phénomènes essentiels issus de ces deux tests et peut être utilisé comme une première approches des problèmes. Le niveau CJS-RE2 a permis de retrouver plus précisément le comportement non linéaire du pisé sur une large gamme de déformations, que ce soit dans l'essai de compression diagonale ou dans le pushover. Enfin, la prise en compte d'interfaces entre les couches dans la modélisation semble constituer une approche surdimensionnée lorsque seule la résistance d'un système constitué en pisé est recherchée. Cependant, parce qu'elles apportent une certaine ductilité au système dans la modélisation, elles peuvent être utilisées lorsque des résultats plus détaillés sont attendus
Rammed earth is a vernacular building technique consisting in compacting successively layers of moist earth within formworks. This technique is present worldwide and in particular in the region Auvergne-Rhône-Alpes in France. As no regulation exists for rammed earth structures in France, the owners of such structures are helpless at the time when repairing damages appearing in any aging heritage structures. Moreover, this lack of regulation tends to slow down the development of such a constructive solution in new projects though this technique answers many of the issues raised by the sustainable development. The work presented herein is part of the national research project PRIMATERRE devoted to the study of construction building involving earth. Herein, an elasto-plastic constitutive law is developed for modeling the behavior of rammed earth. It is based on a hierarchical approach of the modeling in relation to the information available to identify the set of model parameters and the refinement of phenomena to be modelled. This model was adapted from a pre-existing CJS model used in advanced foundation engineering for the modelling of granular soils. The necessary adaptation of some mechanisms of the model in the context of rammed earth material which holds the characteristics of a quasi-brittle material is highlighted. Two levels for the model denoted CJS-RE which can be used in the context of monotonous loadings are presented herein. The first level is a simple elastic perfectly plastic model (CJS-RE1) and the second model is an elasto-plastic model with an isotropic hardening (CJS-RE2). Two mechanisms of plastic deformation are involved, one related to purely deviatoric phenomena and one related to tensile phenomena. The validation of the model was performed based on different sets of actual tests including diagonal compression tests and pushover tests on wallets. The simple elasto-plastic model CJS-RE1 was able to capture some basic features for these two tests and may be used for a first estimate of the system resistance. The more sophisticated model CJS-RE2 was found better to retrieve the nonlinear behavior of rammed earth over a larger range of deformations throughout both a diagonal compression test and a pushover test. Finally, the modelling of interfaces between layers of earth seems oversized when the resistance of the system is investigated. However, since they may influence the simulated ductility of the system, they may be used to model the behavior of rammed earth system more precisely

Water quality and river/stream ecosystems are important for all living creatures. To protect human health, aquatic life and the surrounding ecosystem, a considerable amount of time and money has been spent on sampling and monitoring streams and rivers. Water quality monitoring and analysis can help researchers predict and learn from natural processes in the environment and determine human impacts on an ecosystem. Measurements such as temperature, pH, nitrogen concentration, algae and fish count collected along the network are all important factors in water quality analysis. The main purposes of the statistical analysis in this thesis are (1) to assess the relationship between the variable measured in the water (response variable) and other variables that describe either the locations on/along the stream network or certain characteristics at each location (explanatory variable), and (2) to assess the degree of similarity between the response variable values measured at different locations of the stream, i.e. spatial dependence structure. It is commonly accepted that measurements taken at two locations close to each other should have more similarity than locations far away. However, this is not always true for observations from stream networks. Observations from two sites that do not share water flow could be independent of each other even if they are very close in terms of stream distance, especially those observations taken on objects that move passively with the water flow. To model stream network data correctly, it is important to quantify the strength of association between observations from sites that do not share water.

In this thesis, a dynamic spatial model for the spread of Chronic Wasting Disease in Colorado mule deer is derived from a system of differential equations that captures the qualitative spatial and temporal behaviour of the disease. These differential equations are incorporated into an empirical Bayesian hierarchical model through the unusual step of deterministic autoregressive updates. Spatial effects in the model are described directly in the differential equations rather than through the use of correlations in the data. The use of deterministic updates is a simplification that reduces the number of parameters that must be estimated, yet still provides a flexible model that gives reasonable predictions for the disease. The posterior distribution generated by the data model hierarchy possesses characteristics that are atypical for many Markov chain Monte Carlo simulation techniques. To address these difficulties, a new MCMC technique is developed that has qualities similar to recently introduced tempered Langevin type algorithms. The methodology is used to fit the CWD model, and posterior parameter estimates are then used to obtain predictions about Chronic Wasting Disease.

Dual response surface methodology (Vining and Myers (1990)) has been successfully used as a cost-effective approach to improve the quality of products and processes since Taguchi (Tauchi (1985)) introduced the idea of robust parameter design on the quality improvement in the United States in mid-1980s. The original procedure is to use the mean and the standard deviation of the characteristic to form a dual response system in linear model structure, and to estimate the model coefficients using least squares methods. In this dissertation, a Bayesian hierarchical approach is proposed to model the dual response system so that the inherent hierarchical variance structure of the response can be modeled naturally. The Bayesian model is developed for both univariate and multivariate dual response surfaces, and for both fully replicated and partially replicated dual response surface designs. To evaluate its performance, the Bayesian method has been compared with the original method under a wide range of scenarios, and it shows higher efficiency and more robustness. In applications, the Bayesian approach retains all the advantages provided by the original dual response surface modelling method. Moreover, the Bayesian analysis allows inference on the uncertainty of the model parameters, and thus can give practitioners complete information on the distribution of the characteristic of interest.
Ph. D.

An important objective in statistical risk assessment is estimation of minimum exposure levels, called Benchmark Doses (BMDs) that induce a pre-specified Benchmark Response (BMR) in a target population. Established inferential approaches for BMD analysis typically involve one-sided, frequentist confidence limits, leading in practice to what are called Benchmark Dose Lower Limits (BMDLs). Appeal to hierarchical Bayesian modeling and credible limits for building BMDLs is far less developed, however. Indeed, for the few existing forms of Bayesian BMDs, informative prior information is seldom incorporated. Here, a new method is developed by using reparameterized quantal-response models that explicitly describe the BMD as a target parameter. This potentially improves the BMD/BMDL estimation by combining elicited prior belief with the observed data in the Bayesian hierarchy. Besides this, the large variety of candidate quantal-response models available for applying these methods, however, lead to questions of model adequacy and uncertainty. Facing this issue, the Bayesian estimation technique here is further enhanced by applying Bayesian model averaging to produce point estimates and (lower) credible bounds. Implementation is facilitated via a Monte Carlo-based adaptive Metropolis (AM) algorithm to approximate the posterior distribution. Performance of the method is evaluated via a simulation study. An example from carcinogenicity testing illustrates the calculations.

En la ingeniería estructural, uno de los desafíos constantes es encontrar nuevas formas de proteger las estructuras de las fuerzas medioambientales. El aislamiento sísmico se ha mostrado como una forma efectiva de reducir la respuesta de la estructura principal y de mitigar el daño de equipos o elementos secundarios. Una desventaja de la mayoría de los sistemas de aislamiento se hace evidente en el caso de estructuras sometidas a terremotos cercanos. Estos suelen producir grandes deformaciones en los aisladores que pueden llegar a poner en peligro la estabilidad de la estructura. Para evitar esto se ha sugerido combinar aisladores con dispositivos adicionales de disipación de energía (sistema hibrido). En este contexto, se ha potenciado significativamente el interés por incorporar dispositivos cuyas propiedades se pueden ajustar en tiempo real durante un terremoto. Este tipo de sistemas se denominan semi-activos. Las fuerzas de control en los sistemas semi-activos se aplican como resultado del movimiento propio de la estructura. La fuerza en cuestión puede modificarse únicamente mediante el ajuste de ciertas propiedades mecánicas de los actuadores semi-activos. Además, las fuerzas de control actúan siempre en el sentido de oponerse al movimiento del sistema estructural y por tanto garantizan la estabilidad global de la estructura. Específicamente, los amortiguadores magnetoreològicos (MR) parecen tener un buen potencial para avanzar en la aceptación del control estructural como una forma viable de atenuar el riesgo de las estructuras frente a cargas dinámicas. Sin embargo, debido a la inherente no linealidad de los amortiguadores MR, el primer paso en el diseño de una estrategia de control semi-activo es el desarrollo de un modelo matemático adecuado. Aquí, la identificación de sistemas juega un papel clave. La naturaleza de esta investigación es multidisciplinar porque trata con dos conceptos, la identificación de un dispositivo mecánico (amortiguador MR) y la solución de un problema de control estructural en una perspectiva de ingeniera civil. Como primer paso, se ha desarrollado un nuevo modelo, basado en el modelo Bouc-Wen normalizado, para describir el comportamiento de una gama más amplia de amortiguadores MR, de manera especial los que pueden ser más eficaces en el control de estructuras de ingeniería civil (amortiguadores MR de gran escala). Basado en este modelo, se ha extendido un método de identificación de los parámetros. La validación del método de identificación se ha llevado a cabo sobre un modelo caja negra de un amortiguador MR que es parte de un modelo numérico de edificio muy utilizado como banco de pruebas en la comunidad de investigadores en control estructural. La versatilidad del método se ha probado utilizando el amortiguador de MR en forma semi-activa, con un voltaje variable y operando en el edificio bajo la excitación de terremotos. Posteriormente, basado en el modelo Bouc-Wen extendido, se ha propuesto un nuevo modelo inverso para amortiguadores MR, el cual permite calcular el voltaje requerido para manipular los amortiguadores. Finalmente, se ha presentado una estrategia jerárquica de control semi-activo Esta estrategia consta de cuatro pasos aplicados en tiempo real en cada instante de control: 1. Calcular la fuerza de control deseada global para ser aplicada en la base de la estructura. 2. Determinar la fuerza total que se está aplicando en instante de control actual por el conjunto de amortiguadores MR. Si esta fuerza es más pequeña que la fuerza deseada y tienen el mismo signo, esto significa que los amortiguadores MR necesitan aplicar más fuerza de amortiguamiento y entonces se va al paso 3. De lo contrario el voltaje de los amortiguadores MR se pone en 0. 3. Determinar el número de amortiguadores MR que están aplicando fuerza en la misma dirección que la fuerza de control deseada. 4. Calcular el voltaje a aplicar a cada amortiguador MR usando el modelo inverso. El método (algoritmo) completo se ha simulado en el edificio tridimensional de pruebas utilizado por la comunidad de control estructural como modelo realista para experimentos numéricos de control de la respuesta sísmica. Los índices de rendimiento obtenidos muestran que el método semi-activo propuesto puede mejorar eficazmente el rendimiento del edificio bajo diferentes terremotos.
In structural engineering, one of the constant challenges is to find new better means of protecting structures from destructive environmental forces. One approach is seismic isolation, which has shown to not only reduce the response of the primary structure, but also reduce damage to equipment and other non-structural secondary elements. A drawback of most isolation systems appears when one considers the response of isolated structures subjected to earthquakes characterized by near-field motions. Such motions are likely to produce large isolation deformations, which may lead to buckling or rupture of isolators. To control these large deformations one way is to utilize supplemental dampers together with the isolation system (a hybrid system). However the benefits of isolation system may be significantly reduced for both moderate and strong earthquakes due to the transfer of energy into higher modes which can result in increased interstory drift and floor accelerations. One approach to improve the performance of an isolation system is to incorporate devices within the isolation system whose properties can be adjusted in real-time during earthquakes. Such devices are referred to as semi-active. The control forces in semi-active systems are developed as a result of the motion of the structure itself. They can only be modified through appropriate adjustment of mechanical properties of semi-active devices. Furthermore, the control forces act to oppose the motion of the structural system and therefore promote the global stability of the structure. Specifically the MR dampers appear to have significant potential to advance the acceptance of structural control as a viable means for dynamic hazard mitigation. However, because of the inherent nonlinearity of MR dampers, the first step in the design of a semiactive control is the development of an accurate model of the MR device. The system-identification issue plays a key role in control problems. The nature of this research is multidisciplinary because it deals with two concepts, identification of a mechanical device (MR damper) as well as a structural control problem in a civil engineering perspective. As a first step, a new Bouc-Wen based normalized model has been developed to study the behavior of a wider range of MR dampers, specially the devices which can be more effective in the vibration control of real civil engineering structures (large-scale MR dampers). Based on this new model, an extension of a parameter identification method for MR dampers has been proposed. This extension allows to identify a larger class of MR dampers more accurately. The validation of the parameter identification method has been carried out using a black-box model of an MR damper that is a part of a smart base-isolated benchmark building model available in the community of researchers in structural control. The versatility of the parameter identification method has been tested using the MR damper as a semi-active device under time-varying voltage and earthquake excitation. Then, based on the proposed extended Bouc-Wen based normalized model, a new inverse model for MR dampers has been proposed. If two additional practical physical constraints are satisfied, then the voltage of the MR dampers can be manipulated by the inverse model. Finally, a hierarchical semi-active control strategy for the control of the vibration response of the isolated buildings equipped with a set of parallel MR dampers has been presented. This strategy consists of four steps applied in real time at each control instant: 1. Compute the overall desired control force to be applied at the base of the structure. 2. Determine the total force applied at the current control instant by the set of MR dampers. If this force is smaller than the desired force and they have the same sign, this means that the MR dampers need to apply more damping force and go to step 3. Otherwise the voltage of the MR dampers is set to 0. 3. Determine the number of dampers that are applying force in the same direction as the desired control force. 4. Compute the corresponding command voltage for each MR damper using the inverse model. The whole method is simulated by considering the three-dimensional smart base isolated benchmark building which is also used by the structural control community as a state-of-the-art model for numerical experiments of seismic control attenuation. The resulted performance indices demonstrate that the proposed semi-active method can effectively improve the performance of the building under earthquake loading

Himesis is a complete yet minimal kernel for meta-modelling and model transformation, which consists of a specification of hierarchical graphs and in a highly efficient matching algorithm. Himesis graphs encode the essence of models: nodes, edges, containment, attributes, names and labels. There is a defined set of events which transform the graphs. Above all Himesis introduces an explicit notion of hierarchy, which allows the specification of formalisms which were very hard to meta-model in the past, such as graph grammars. Moreover, with containment, it is possible to couple and reuse existing formalisms.
Himesis implements HVF, a new matching algorithm based on the VF2 approach. HVF extends VF2 with hierarchy and with several optimization strategies. It was designed to support advanced features that are required for graph rewriting, such as matching from a context as well as negative application conditions. We show that HVF is a faster algorithm than VF2 for matching of flat graphs. HVF is particularly efficient when matching irregular graphs.

In this thesis, we have given out a comprehensive approach to estimate the pairwise interaction in a bivariate additive model when the additive assumption is untenable. A new "nested backfilling' model fitting approach has been proposed and compared with some earlier approaches. The explicit estimators of each individual term were derived for the hierarchical bivariate additive model fitted by this "nested backfilling' approach. The convergence of the "nested backfilling" approach and the existence of these estimators have been shown depending on the ratio of the bandwidths that were used in the estimation of the effect of the same variable but in different terms. The mean average square error properties of these proposed explicit estimators were investigated. A discussion the pattern left in this bias and variance expressions derived for these estimators, such as mean corrected, Gauss-Seidel style etc., were provided to facilitate the understanding these properties. Unlike in the pure additive model case, the mean average square error of our model cannot be attributed to each individual variable. The four optimal bandwidths used need to be selected simultaneously to minimize the mean average square error. These estimators were shown worked reasonably well in simulated datasets, regardless of the level of dependence of the covariates.

Approved for public release; distribution unlimited.
Combat models often involve target detection times which may vary with different observers due to characteristics of personnel, or detection systems. They may also be affected by different environmental factors such as visual levels, sea states, terrains, etc. There is often interest in quantifying the effects of different observer characteristics and environmental factors on detection times. A hierarchical gammaWeibull regression model is considered which can incorporate observer characteristics and environmental effects which may influence the time to detect targets. Numerical procedures for the estimation of parameters of the hierarchical gammaWeibull model based on maximum likelihood are described. Results of simulation experiments to study small sample behavior of the estimates are reported.

This thesis focusses on how the behaviour of consumers can be predicted within the Behavioural Perspective Model’s (BPM) theoretical framework. The study focuses on three specific area. First, a complex functional form is created, utilizing the BPM’s Informational and Utilitarian reinforcement in combination with behavioural economic, consumer psychology, marketing and seasonal variables. Second, the text introduces a hierarchical framework to the model. The data are structured as purchases within household and hence the assumption of independence within household purchase is questioned. The hierarchical framework allows the removal of this assumption. Therefore, hierarchical and non-hierarchical models are constructed and compared to investigate this. Third, the text discusses the Bayesian paradigm and the differences this brings to model estimation versus the more traditional frequentist methods of calculation. The debate between the Bayesian and frequentist paradigms has been prevalent within mathematical and statistical literature for some time and this text is not meant to directly contribute to this literature. However, the text does explore the potential advantages to the subject matter through the exploration of a Bayesian framework for model estimation. Hence, model estimation through a Bayesian framework is employed employing both vague and informed prior distribution, with the informed priors calibrated from frequentist estimates.

In this paper, we propose a Bayesian hierarchical model for predicting accident counts in future years at sites within a pool of potential road safety hotspots. The aim is to inform road safety practitioners of the location of likely future hotspots to enable a proactive, rather than reactive, approach to road safety scheme implementation. A feature of our model is the ability to rank sites according to their potential to exceed, in some future time period, a threshold accident count which may be used as a criterion for scheme implementation. Our model specification enables the classical empirical Bayes formulation – commonly used in before-and-after studies, wherein accident counts from a single before period are used to estimate counterfactual counts in the after period – to be extended to incorporate counts from multiple time periods. This allows site-specific variations in historical accident counts (e.g. locally-observed trends) to offset estimates of safety generated by a global accident prediction model (APM), which itself is used to help account for the effects of global trend and regression-to-mean (RTM). The Bayesian posterior predictive distribution is exploited to formulate predictions and to properly quantify our uncertainty in these predictions. The main contributions of our model include (i) the ability to allow accident counts from multiple time-points to inform predictions, with counts in more recent years lending more weight to predictions than counts from time-points further in the past; (ii) where appropriate, the ability to offset global estimates of trend by variations in accident counts observed locally, at a site-specific level; and (iii) the ability to account for unknown/unobserved site-specific factors which may affect accident counts. We illustrate our model with an application to accident counts at 734 potential hotspots in the German city of Halle; we also propose some simple diagnostics to validate the predictive capability of our model. We conclude that our model accurately predicts future accident counts, with point estimates from the predictive distribution matching observed counts extremely well.

The practice of simulating real world systems on computers is widespread and forms an important aspect of many different disciplines. A simulation model provides a simplified view of a real world system facilitating interaction with key aspects of a system without the distraction of unnecessary detail. This thesis is concerned with the role of simulation in computer architecture design. It is recognised that use of simulation in the design lifecycle is expensive and has tended to focus upon the register transfer (RT) level of design. The majority of design projects have no need for fully articulated models in the initial stages: the designer is more involved with fundamental decisions typically based upon choice of algorithm and high-level performance analysis. However, it has been shown that representation of systems in a more abstract form than that found at the RT level can be problematic in terms of reusability. Following an overview of current simulation techniques and software, extensions to the HASE simulation environment are proposed that classify simulation components according to their communication interfaces. This facilitates the loose coupling of simulation entities and consequently promotes component reuse. In addition, the problem of allowing entities represented at different levels of architectural abstraction to communicate was examined and a technique developed to allow entities to negotiate a level of service. The MEDL and EDL languages were developed to enhance HASE's component library and project storage facilities; other software tools allowing the visualisation of a hierarchical model in terms of communication and abstraction were also developed. Various model libraries were developed to investigate the trade-offs between model accuracy, runtime and flexibility afforded by the new techniques. It was demonstrated that the developed techniques facilitate component reuse and offer potential runtime reduction.

The ever-growing size and complexity of molecular network models makes them difficult to construct and understand. Modifying a model that consists of tens of reactions is no easy task. Attempting the same on a model containing hundreds of reactions can seem nearly impossible. We present the JigCell Model Connector, a software tool that supports large-scale molecular network modeling. Our approach to developing large models is to combine together smaller models, making the result easier to comprehend. At the base, the smaller models (called modules) are defined by small collections of reactions. Modules connect together to form larger modules through clearly defined interfaces, called ports. In this work, we enhance the port concept by defining different types of ports. Not all modules connect together the same way, therefore multiple connection options need to exist.
Master of Science

A set of elementary building blocks undergoes self-assembly if local interactions govern how this set forms intricate structures. Self-assembly has been widely observed in nature, ranging from the field of crystallography to the study of viruses and multicellular organisms. A natural question is whether a model of self-assembly can capture the hierarchical growth seen in nature or in other fields of mathematics. In this work, we consider hierarchical growth in substitution rules; informally, a substitution rule describes the iterated process by which the polygons of a given set are individually enlarged and dissected. We develop the Polygonal Two-Handed Assembly Model (p-2HAM) where building blocks, or tiles, are polygons and growth occurs when tiles bind to one another via matching, complementary bonds on adjacent sides; the resulting assemblies can then be used to construct new, larger structures. The p-2HAM is based on a handful of well-studied models, notably the Two-Handed Assembly Model and the polygonal free-body Tile Assembly Model. The primary focus of our work is to provide conditions which are either necessary or sufficient for the ``bordered simulation'' substitution rules. By this, we mean that a border made up of tiles is allowed to form around an assembly which then coordinates how the assembly interacts with other assemblies. In our main result, we provide a construction which gives a sufficient condition for bordered simulation. This condition is presented in graph theoretic terms and considers the adjacency of the polygons in the tilings associated to a given substitution rule. Alongside our results, we consider a collection of over one hundred substitution rules from various sources. We show that only the substitution rules in this collection which satisfy our sufficient condition admit bordered simulation. We conclude by considering open questions related to simulating substitution rules and to hierarchical growth in general.

With the development of modern data collection approaches, researchers may collect hundreds to millions of variables, yet may not need to utilize all explanatory variables available in predictive models. Hence, choosing models that consist of a subset of variables often becomes a crucial step. In linear regression, variable selection not only reduces model complexity, but also prevents over-fitting. From a Bayesian perspective, prior specification of model parameters plays an important role in model selection as well as parameter estimation, and often prevents over-fitting through shrinkage and model averaging.

We develop two novel hierarchical priors for selection and model averaging, for Generalized Linear Models (GLMs) and normal linear regression, respectively. They can be considered as "spike-and-slab" prior distributions or more appropriately "spike- and-bell" distributions. Under these priors we achieve dimension reduction, since their point masses at zero allow predictors to be excluded with positive posterior probability. In addition, these hierarchical priors have heavy tails to provide robust- ness when MLE's are far from zero.

Zellner's g-prior is widely used in linear models. It preserves correlation structure among predictors in its prior covariance, and yields closed-form marginal likelihoods which leads to huge computational savings by avoiding sampling in the parameter space. Mixtures of g-priors avoid fixing g in advance, and can resolve consistency problems that arise with fixed g. For GLMs, we show that the mixture of g-priors using a Compound Confluent Hypergeometric distribution unifies existing choices in the literature and maintains their good properties such as tractable (approximate) marginal likelihoods and asymptotic consistency for model selection and parameter estimation under specific values of the hyper parameters.

While the g-prior is invariant under rotation within a model, a potential problem with the g-prior is that it inherits the instability of ordinary least squares (OLS) estimates when predictors are highly correlated. We build a hierarchical prior based on scale mixtures of independent normals, which incorporates invariance under rotations within models like ridge regression and the g-prior, but has heavy tails like the Zeller-Siow Cauchy prior. We find this method out-performs the gold standard mixture of g-priors and other methods in the case of highly correlated predictors in Gaussian linear models. We incorporate a non-parametric structure, the Dirichlet Process (DP) as a hyper prior, to allow more flexibility and adaptivity to the data.

Dissertation

碩士
國立臺灣大學
資訊工程學研究所
94
In this thesis we propose a motor control model inspired by organizational priciples of the cerebral cortex. Specifically the model is based on cortical maps and functional hierarchy in sensory and motor areas of the brain. We introduce observed properties of the F5 area in the macaque monkey brain, an area which combines sensory and motor information, producing actions without high processing information. The properties here observed can be quickly summarized to mdularity and hierarchical processing. These form the basis for the model we propose. We make use of well known computational tools, to put together a biology imitating model, for action learning and motor control. The Self-Organizing Maps (SOM) have proven to be useful in modeling cortical topological maps. A hierarchical SOM provides a natural way to extract hierarchical information from the environment, which we propose may in turn be used to select actions hierarchically. We use a neighborhood update version of the Q-learning algorithm, so the final model maps a continuous input space to a continuous action space in a hierarchical, topology preserving manner. The model is called the Hierarchical Map Forming model (HMF) due to the way in which it forms maps in both the input and output spaces in a hierarchical manner.

In recent years the simulation of gas flow on networks attracts increasing interest. Since natural sources of energy, like wind and solar power, might lack of continuity, some demands in energy are compensated by gas. Therefore, accurate simulations for gas transport are essential. However, a highly detailed simulation suffers from great computational costs. Consequently, it becomes natural to use models with less physical detail in pipes with lower activity, while for pipes with greater dynamics, models with higher physical detail are used. In the analytical part of this work, we consider a network, with one single junction and a given model hierarchy. It appears the question how these models are coupled at the junction and which kind of coupling conditions have to be posed such that a resulting solution is unique and physically correct, as far as it even exists. In order to answer the above questions, we propose mass-, energy- and entropy- preserving coupling conditions at the junction. By introducing, a so called generalized Riemann problem at the junction, i.e., piecewise constant initial data, all models are connectible to each other through the coupling conditions. Afterwards, we show well-posedness of the generalized Riemann problem, i.e., there exists a unique physically correct solution. The well-posedness above creates a foundation for a more general setting, the so called Cauchy problem, in which initial data needs to be integrable with small total variation only. Here, well-posedness is shown as well. Based on these results, even existence of an optimal control can be proven. In the second part of this work, we like to give some numerical illustrations, built on our analytical results.