Hierarchical GTM: constructing localized non-linear projection manifolds in a principled way

It has been argued that a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex data sets, and therefore a hierarchical visualization system is desirable. In this paper we extend an existing locally linear hierarchical visualization system PhiVis ¸iteBishop98a in several directions: bf(1) We allow for em non-linear projection manifolds. The basic building block is the Generative Topographic Mapping (GTM). bf(2) We introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree. General training equations are derived, regardless of the position of the model in the tree. bf(3) Using tools from differential geometry we derive expressions for local directional curvatures of the projection manifold. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. It enables the user to interactively highlight those data in the ancestor visualization plots which are captured by a child model. We also incorporate into our system a hierarchical, locally selective representation of magnification factors and directional curvatures of the projection manifolds. Such information is important for further refinement of the hierarchical visualization plot, as well as for controlling the amount of regularization imposed on the local models. We demonstrate the principle of the approach on a toy data set and apply our system to two more complex 12- and 18-dimensional data sets.

A principled approach to interactive hierarchical non-linear visualization of high-dimensional data

Hierarchical visualization systems are desirable because a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex high-dimensional data sets. We extend an existing locally linear hierarchical visualization system PhiVis [1] in several directions: bf(1) we allow for em non-linear projection manifolds (the basic building block is the Generative Topographic Mapping -- GTM), bf(2) we introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree, bf(3) we describe folding patterns of low-dimensional projection manifold in high-dimensional data space by computing and visualizing the manifold's local directional curvatures. Quantities such as magnification factors [3] and directional curvatures are helpful for understanding the layout of the nonlinear projection manifold in the data space and for further refinement of the hierarchical visualization plot. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. We demonstrate the visualization system principle of the approach on a complex 12-dimensional data set and mention possible applications in the pharmaceutical industry.

Constructing localized non-linear projection manifolds in a principled way:hierarchical generative topographic mapping

It has been argued that a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex data sets, and therefore a hierarchical visualization system is desirable. In this paper we extend an existing locally linear hierarchical visualization system PhiVis (Bishop98a) in several directions: 1. We allow for em non-linear projection manifolds. The basic building block is the Generative Topographic Mapping. 2. We introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree. General training equations are derived, regardless of the position of the model in the tree. 3. Using tools from differential geometry we derive expressions for local directionalcurvatures of the projection manifold. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. It enables the user to interactively highlight those data in the parent visualization plot which are captured by a child model.We also incorporate into our system a hierarchical, locally selective representation of magnification factors and directional curvatures of the projection manifolds. Such information is important for further refinement of the hierarchical visualization plot, as well as for controlling the amount of regularization imposed on the local models. We demonstrate the principle of the approach on a toy data set andapply our system to two more complex 12- and 19-dimensional data sets.

Neural network enhanced self tuning adaptive control application for non-linear control of dynamic systems

The main theme of research of this project concerns the study of neutral networks to control uncertain and non-linear control systems. This involves the control of continuous time, discrete time, hybrid and stochastic systems with input, state or output constraints by ensuring good performances. A great part of this project is devoted to the opening of frontiers between several mathematical and engineering approaches in order to tackle complex but very common non-linear control problems. The objectives are: 1. Design and develop procedures for neutral network enhanced self-tuning adaptive non-linear control systems; 2. To design, as a general procedure, neural network generalised minimum variance self-tuning controller for non-linear dynamic plants (Integration of neural network mapping with generalised minimum variance self-tuning controller strategies); 3. To develop a software package to evaluate control system performances using Matlab, Simulink and Neural Network toolbox. An adaptive control algorithm utilising a recurrent network as a model of a partial unknown non-linear plant with unmeasurable state is proposed. Appropriately, it appears that structured recurrent neural networks can provide conveniently parameterised dynamic models for many non-linear systems for use in adaptive control. Properties of static neural networks, which enabled successful design of stable adaptive control in the state feedback case, are also identified. A survey of the existing results is presented which puts them in a systematic framework showing their relation to classical self-tuning adaptive control application of neural control to a SISO/MIMO control. Simulation results demonstrate that the self-tuning design methods may be practically applicable to a reasonably large class of unknown linear and non-linear dynamic control systems.

Advances in Dynamic Modeling and Computation for Count Data

A class of multi-process models is developed for collections of time indexed count data. Autocorrelation in counts is achieved with dynamic models for the natural parameter of the binomial distribution. In addition to modeling binomial time series, the framework includes dynamic models for multinomial and Poisson time series. Markov chain Monte Carlo (MCMC) and Po ́lya-Gamma data augmentation (Polson et al., 2013) are critical for fitting multi-process models of counts. To facilitate computation when the counts are high, a Gaussian approximation to the P ́olya- Gamma random variable is developed.

Three applied analyses are presented to explore the utility and versatility of the framework. The first analysis develops a model for complex dynamic behavior of themes in collections of text documents. Documents are modeled as a “bag of words”, and the multinomial distribution is used to characterize uncertainty in the vocabulary terms appearing in each document. State-space models for the natural parameters of the multinomial distribution induce autocorrelation in themes and their proportional representation in the corpus over time.

The second analysis develops a dynamic mixed membership model for Poisson counts. The model is applied to a collection of time series which record neuron level firing patterns in rhesus monkeys. The monkey is exposed to two sounds simultaneously, and Gaussian processes are used to smoothly model the time-varying rate at which the neuron’s firing pattern fluctuates between features associated with each sound in isolation.

The third analysis presents a switching dynamic generalized linear model for the time-varying home run totals of professional baseball players. The model endows each player with an age specific latent natural ability class and a performance enhancing drug (PED) use indicator. As players age, they randomly transition through a sequence of ability classes in a manner consistent with traditional aging patterns. When the performance of the player significantly deviates from the expected aging pattern, he is identified as a player whose performance is consistent with PED use.

All three models provide a mechanism for sharing information across related series locally in time. The models are fit with variations on the P ́olya-Gamma Gibbs sampler, MCMC convergence diagnostics are developed, and reproducible inference is emphasized throughout the dissertation.

Explaining dinophysis cf. acuminata abundance in Antifer (Normandy, France) using dynamic linear regression

Classical regression analysis can be used to model time series. However, the assumption that model parameters are constant over time is not necessarily adapted to the data. In phytoplankton ecology, the relevance of time-varying parameter values has been shown using a dynamic linear regression model (DLRM). DLRMs, belonging to the class of Bayesian dynamic models, assume the existence of a non-observable time series of model parameters, which are estimated on-line, i.e. after each observation. The aim of this paper was to show how DLRM results could be used to explain variation of a time series of phytoplankton abundance. We applied DLRM to daily concentrations of Dinophysis cf. acuminata, determined in Antifer harbour (French coast of the English Channel), along with physical and chemical covariates (e.g. wind velocity, nutrient concentrations). A single model was built using 1989 and 1990 data, and then applied separately to each year. Equivalent static regression models were investigated for the purpose of comparison. Results showed that most of the Dinophysis cf. acuminata concentration variability was explained by the configuration of the sampling site, the wind regime and tide residual flow. Moreover, the relationships of these factors with the concentration of the microalga varied with time, a fact that could not be detected with static regression. Application of dynamic models to phytoplankton time series, especially in a monitoring context, is discussed.

Assessing mackerel scad, Decapterus macarellus, in Cape Verde: using a Bayesian approach to biomass dynamic modelling in a data-limited situation

The fisheries for mackerel scad, Decapterus macarellus, are particularly important in Cape Verde, constituting almost 40% of total catches at the peak of the fishery in 1997 and 1998 ( 3700 tonnes). Catches have been stable at a much lower level of about 2 100 tonnes in recent years. Given the importance of mackerel scad in terms of catch weight and local food security, there is an urgent need for updated assessment. Stock assessment was carried out using a Bayesian approach to biomass dynamic modelling. In order to tackle the problem of a non-informative CPUE series, the intrinsic rate of increase, r, was estimated separately, and the ratio B-0/X, initial biomass relative to carrying capacity, was assumed based on available information. The results indicated that the current level of fishing is sustainable. The probability of collapse is low, particularly in the short-term, and it is likely that biomass may increase further above B-msy, indicating a healthy stock level. It would appear that it is relatively safe to increase catches even up to 4000 tonnes. However, the marginal posterior of r was almost identical to the prior, indicating that there is relatively low information content in CPUE. This was also the case in relation to B-0/X There have been substantial increases in fishing efficiency, which have not been adequately captured by the measure used for effort (days or trips), implying that the results may be overly optimistic and should be considered preliminary. (c) 2006 Elsevier B.V. All rights reserved.

Dynamic Modeling and Seasonal Performance Evaluation of Air-to-Water Heat Pump Systems

In this Thesis a series of numerical models for the evaluation of the seasonal performance of reversible air-to-water heat pump systems coupled to residential and non-residential buildings are presented. The exploitation of the energy saving potential linked to the adoption of heat pumps is a hard task for designers due to the influence on their energy performance of several factors, like the external climate variability, the heat pump modulation capacity, the system control strategy and the hydronic loop configuration. The aim of this work is to study in detail all these aspects. In the first part of this Thesis a series of models which use a temperature class approach for the prediction of the seasonal performance of reversible air source heat pumps are shown. An innovative methodology for the calculation of the seasonal performance of an air-to-water heat pump has been proposed as an extension of the procedure reported by the European standard EN 14825. This methodology can be applied not only to air-to-water single-stage heat pumps (On-off HPs) but also to multi-stage (MSHPs) and inverter-driven units (IDHPs). In the second part, dynamic simulation has been used with the aim to optimize the control systems of the heat pump and of the HVAC plant. A series of dynamic models, developed by means of TRNSYS, are presented to study the behavior of On-off HPs, MSHPs and IDHPs. The main goal of these dynamic simulations is to show the influence of the heat pump control strategies and of the lay-out of the hydronic loop used to couple the heat pump to the emitters on the seasonal performance of the system. A particular focus is given to the modeling of the energy losses linked to on-off cycling.

Pricing farm-level agricultural insurance: a Bayesian approach

This paper applies Hierarchical Bayesian Models to price farm-level yield insurance contracts. This methodology considers the temporal effect, the spatial dependence and spatio-temporal models. One of the major advantages of this framework is that an estimate of the premium rate is obtained directly from the posterior distribution. These methods were applied to a farm-level data set of soybean in the State of the Parana (Brazil), for the period between 1994 and 2003. The model selection was based on a posterior predictive criterion. This study improves considerably the estimation of the fair premium rates considering the small number of observations.

Spatio-temporal modeling of agricultural yield data with an application to pricing crop insurance contracts

This article presents a statistical model of agricultural yield data based on a set of hierarchical Bayesian models that allows joint modeling of temporal and spatial autocorrelation. This method captures a comprehensive range of the various uncertainties involved in predicting crop insurance premium rates as opposed to the more traditional ad hoc, two-stage methods that are typically based on independent estimation and prediction. A panel data set of county-average yield data was analyzed for 290 counties in the State of Parana (Brazil) for the period of 1990 through 2002. Posterior predictive criteria are used to evaluate different model specifications. This article provides substantial improvements in the statistical and actuarial methods often applied to the calculation of insurance premium rates. These improvements are especially relevant to situations where data are limited.

A method for setting the size of plant conservation target areas

Realistic time frames in which management decisions are made often preclude the completion of the detailed analyses necessary for conservation planning. Under these circumstances, efficient alternatives may assist in approximating the results of more thorough studies that require extensive resources and time. We outline a set of concepts and formulas that may be used in lieu of detailed population viability analyses and habitat modeling exercises to estimate the protected areas required to provide desirable conservation outcomes for a suite of threatened plant species. We used expert judgment of parameters and assessment of a population size that results in a specified quasiextinction risk based on simple dynamic models The area required to support a population of this size is adjusted to take into account deterministic and stochastic human influences, including small-scale disturbance deterministic trends such as habitat loss, and changes in population density through processes such as predation and competition. We set targets for different disturbance regimes and geographic regions. We applied our methods to Banksia cuneata, Boronia keysii, and Parsonsia dorrigoensis, resulting in target areas for conservation of 1102, 733, and 1084 ha, respectively. These results provide guidance on target areas and priorities for conservation strategies.

A 2D numerical model for simulating the physics of fault systems

Simulations provide a powerful means to help gain the understanding of crustal fault system physics required to progress towards the goal of earthquake forecasting. Cellular Automata are efficient enough to probe system dynamics but their simplifications render interpretations questionable. In contrast, sophisticated elasto-dynamic models yield more convincing results but are too computationally demanding to explore phase space. To help bridge this gap, we develop a simple 2D elastodynamic model of parallel fault systems. The model is discretised onto a triangular lattice and faults are specified as split nodes along horizontal rows in the lattice. A simple numerical approach is presented for calculating the forces at medium and split nodes such that general nonlinear frictional constitutive relations can be modeled along faults. Single and multi-fault simulation examples are presented using a nonlinear frictional relation that is slip and slip-rate dependent in order to illustrate the model.

Remuneração executiva e desempenho: evidências empíricas no mercado de capitais brasileiro

O objetivo desta dissertação é analisar a relação existente entre remuneração executiva e desempenho em companhias brasileiras de capital aberto listadas na BM&FBOVESPA. A linha teórica parte do pressuposto que o contrato de incentivos corrobora com o alinhamento de interesses entre acionistas e executivos e atua como um mecanismo de governança corporativa a fim de direcionar os esforços dos executivos para maximização de valor da companhia. A amostra foi composta pelas 100 companhias mais líquidas listadas em quantidade de negociações de ações na BM&FBOVESPA durante o período 2010-2012, totalizando 296 observações. Os dados foram extraídos dos Formulários de Referência disponibilizados pela CVM e a partir dos softwares Economática® e Thomson Reuters ®. Foram estabelecidas oito hipóteses de pesquisa e estimados modelos de regressão linear múltipla com a técnica de dados em painel desbalanceado, empregando como variável dependente a remuneração total e a remuneração média individual e como regressores variáveis concernentes ao desempenho operacional, valor de mercado, tamanho, estrutura de propriedade, governança corporativa, além de variáveis de controle. Para verificar os fatores que explicam a utilização de stock options, programa de bônus e maior percentual de remuneração variável foram estimados modelos de regressão logit. Os resultados demonstram que, na amostra selecionada, existe relação positiva entre remuneração executiva e valor de mercado. Verificou-se também que os setores de mineração, química, petróleo e gás exercem influência positiva na remuneração executiva. Não obstante, exerce relação inversa com a remuneração total à concentração acionária, o controle acionário público e o fato da companhia pertencer ao nível 2 ou novo mercado conforme classificação da BMF&BOVESPA. O maior valor de mercado influencia na utilização de stock options, assim como no emprego de bônus, sendo que este também é impactado pelo maior desempenho contábil. Foram empregados também testes de robustez com estimações por efeitos aleatórios, regressões com erros-padrão robustos clusterizados, modelos dinâmicos e os resultados foram similares. Conclui-se que a remuneração executiva está relacionada com o valor corporativo gerando riqueza aos acionistas, mas que a ausência de relação com o desempenho operacional sugere falhas no sistema remuneratório que ainda depende de maior transparência e outros mecanismos de governança para alinhar os interesses entre executivos e acionistas.

Comportamento dinâmico da rede eléctrica da ilha de São Vicente em Cabo Verde: estabilidade de tensão

Neste trabalho é efectuado, não só o diagnóstico em regime permanente, mas também o estudo, simulação e análise do comportamento dinâmico da rede eléctrica da ilha de São Vicente em Cabo Verde. Os estudos de estabilidade transitória desempenham um importante papel, tanto no planeamento como na operação dos sistemas de potência. Tais estudos são realizados, em grande parte, através de simulação digital no domínio do tempo, utilizando integração numérica para resolver as equações não-lineares que modelam a dinâmica do sistema e dependem da existência de registos reais de perturbação (ex: osciloperturbografia). O objectivo do trabalho será também verificar a aplicabilidade dos requisitos técnicos que as unidades geradoras devem ter, no que concerne ao controlo de tensão, estabelecidos na futura regulamentação europeia desenvolvida pela ENTSO-E (European Network Transmission System Operator for Electricity). De entre os requisitos analisou-se a capacidade das máquinas existentes suportarem cavas de tensão decorrentes de curto-circuitos trifásicos simétricos, Fault Ride Through, no ponto de ligação à rede. Identificaram-se para o efeito os factores que influenciam a estabilidade desta rede, em regime perturbado nomeadamente: (i) duração do defeito, (ii) caracterização da carga, com e sem a presença do sistema de controlo de tensão (AVR) em unidades de geração síncronas. Na ausência de registos reais sobre o comportamento do sistema, conclui-se que este é sensível à elasticidade das cargas em particular do tipo potência constante, existindo risco de perda de estabilidade, neste caso, para defeitos superiores a 5ms sem AVR. A existência de AVR nesta rede afigura-se como indispensável para garantir estabilidade de tensão sendo contudo necessário proceder a uma correcta parametrização.

Grid Integration of Offshore Wind Farms Using Modular Marx Multilevel Converters

This paper proposes the use of a Modular Marx Multilevel Converter, as a solution for energy integration between an offshore Wind Farm and the power grid network. The Marx modular multilevel converter is based on the Marx generator, and solves two typical problems in this type of multilevel topologies: modularity and dc capacitor voltage balancing. This paper details the strategy for dc capacitor voltage equalization. The dynamic models of the converter and power grid are presented in order to design the converter ac output voltages and the dc capacitor voltage controller. The average current control is presented and used for power flow control, harmonics and reactive power compensation. Simulation results are presented in order to show the effectiveness of the proposed (MC)-C-3 topology.