The genealogy of a random sample of a population of organisms can be represented as a rooted binary tree. Population dynamics determine a distribution over sample genealogies. For large populations of constant size and in the absence of selection effects, the coalescent process of Kingman determines a suitable distribution. Neuhauser and Krone gave a stochastic model generalising the Kingman coalescent in a natural way to include the effects of selection. The model of Neuhauser and Krone determines a distribution over a class of graphs of randomly variable vertex number, known as ancestral selection graphs. Because vertices have associated scalar ages, realisations of the ancestral selection graph process have randomly variable dimensions. A Markov chain Monte Carlo method is used to simulate the posterior distribution for population parameters of interest. The state of the Markov chain Monte Carlo is a random graph, with random dimension and equilibrium distribution equal to the posterior distribution. The aim of the project is to determine if the data is informative of the selection parameter by fitting the model to synthetic data. / Foundation for Research Science and Technology Top Achiever Doctoral Scolarship

The field of Machine Learning is concerned with the development of algorithms, models and techniques that solve challenging computational problems by learning from data representative of the problem (e.g. given a set of medical images previously classified by a human expert, build a model to predict unseen images as either benign or malignant). Many important real-world problems have been formulated as supervised learning problems. The assumption is that a data set is available containing the correct output (e.g. class label or target value) for each given data point. In many application domains, obtaining the correct outputs (labels) for data points is a costly and time-consuming task. This has provided the motivation for the development of Machine Learning techniques that attempt to minimize the number of labeled data points while maintaining good generalization performance on a given problem. Active Learning is one such class of techniques and is the focus of this thesis. Active Learning algorithms select or generate unlabeled data points to be labeled and use these points for learning. If successful, an Active Learning algorithm should be able to produce learning performance (e.g test set error) comparable to an equivalent supervised learner using fewer labeled data points. Theoretical, algorithmic and experimental Active Learning research has been conducted and a number of successful applications have been demonstrated. However, the scope of many of the experimental studies on Active Learning has been relatively small and there are very few large-scale experimental evaluations of Active Learning techniques. A significant amount of performance variability exists across Active Learning experimental results in the literature. Furthermore, the implementation details and effects of experimental factors have not been closely examined in empirical Active Learning research, creating some doubt over the strength and generality of conclusions that can be drawn from such results. The Active Learning model/system used in this thesis is the Optimal Active Learning algorithm framework with Gaussian Processes for regression problems (however, most of the research questions are of general interest in many other Active Learning scenarios). Experimental and implementation details of the Active Learning system used are described in detail, using a number of regression problems and datasets of different types. It is shown that the experimental results of the system are subject to significant variability across problem datasets. The hypothesis that experimental factors can account for this variability is then investigated. The results show the impact of sampling and sizes of the datasets used when generating experimental results. Furthermore, preliminary experimental results expose performance variability across various real-world regression problems. The results suggest that these experimental factors can (to a large extent) account for the variability observed in experimental results. A novel resampling technique for Optimal Active Learning, called '3-Sets Cross-Validation', is proposed as a practical solution to reduce experimental performance variability. Further results confirm the usefulness of the technique. The thesis then proposes an extension to the Optimal Active Learning framework, to perform learning via membership queries via a novel algorithm named MQOAL. The MQOAL algorithm employs the Metropolis-Hastings Markov chain Monte Carlo (MCMC) method to sample data points for query selection. Experimental results show that MQOAL provides comparable performance to the pool-based OAL learner, using a very generic, simple MCMC technique, and is robust to experimental factors related to the MCMC implementation. The possibility of making queries in batches is also explored experimentally, with results showing that while some performance degradation does occur, it is minimal for learning in small batch sizes, which is likely to be valuable in some real-world problem domains.

Στην παρούσα διατριβή επεκτείνουμε και γενικεύουμε γνωστές κατανομές ροών. Για το σκοπό αυτό μελετούμε κατανομές απλών σχηματισμών χρησιμοποιώντας τη μέθοδο εμφύτευσης σε Μαρκοβιανή αλυσίδα. Με την ίδια μεθοδολογική προσέγγιση μελετούμε τόσο τις μεταβλητές διωνυμικού τύπου, όσο και τις αντίστοιχες χρόνου αναμονής. Στο Πρώτο Κεφάλαιο παρουσιάζουμε μια ανασκόπηση της ερευνητικής δουλειάς των τελευταίων δεκαετιών σε κατανομές ροών. Στο Δεύτερο Κεφάλαιο μελετούμε κατανομές απλών σχηματισμών, οι οποίες αποτελούν επεκτάσεις και γενικεύσεις κατανομές ροών. Η μελέτη αυτή γίνεται στην περίπτωση που οι δοκιμές είναι ανεξάρτητες. Η υπόθεση αυτή αντικαθίσταται στο Τρίτο Κεφάλαιο από τη γενικότερη υπόθεση δοκιμών που παρουσιάζουν Μαρκοβιανή εξάρτηση πρώτης τάξης και κάτω από αυτό το νέο πλαίσιο μελετούνται κατανομές χρόνου αναμονής. Στο Τέταρτο Κεφάλαιο παρουσιάζεται μια ανασκόπηση των συνεχόμενων συστημάτων στη Θεωρία Αξιοπιστίας. Στη συνέχεια εισάγονται και μελετούνται δύο νέα συστήματα, τα αποία οποία επεκτείνουν και γενικεύουν γνωστά συνεχόμενα συστήματα. Στο Πέμπτο Κεφάλαιο γενικεύεται ένα κλασικό πρόβλημα περιορισμένης χωρητικότητας, το οποίο αναφέρεται συχνά στη Θεωρία Ροών και μας απασχολεί συχνά στο Πρώτο Κεφάλαιο. Νέα αποτελέσματα της διατριβής αυτής δημοσιεύονται στις εργασίες των Dafnis et al. (2007), Dafnis and Philippou (2010), Dafnis et al. (2010a), Dafnis et al. (2010b) και Dafnis et al. (2010c). / In the present Ph.D. thesis we extend and generalize well-known runs' distributions. For this purpose, we study exact distributions of simple patterns using the Markov chain embedding technique. Both binomial-type and waiting-time random variables are treated. In Chapter 1, we review known results on distributions of runs presented over the last decades. In Chapter 2, we study distributions of simple patterns, which extend and generalize distributions of runs. The trials are considered to be independent. This assumption is replaced by the more general one of first order dependence. Under this new framework, waiting time distributions are studied in chapter 3. In Chapter 4, we first review the research on consecutive systems in Reliability Theory. Then, we introduce and study two new systems which are generalizations of consecutive systems extensively studied in literature. Finally, in Chapter 5, a well-known restricted occupancy problem, applicable to the Theory of Runs and often met in Chapter 1, is generalized. New results of the thesis are published in the papers of Dafnis et al. (2007), Dafnis and Philippou (2010), Dafnis et al. (2010a), Dafnis et al. (2010b) and Dafnis et al. (2010c).

Submitted by Thaís Saes Giuliani null (thais_saes@hotmail.com) on 2017-12-13T20:19:43Z No. of bitstreams: 1 Dissertação Thaís Saes Giuliani Ribeiro.pdf: 1429513 bytes, checksum: 6145616464ae520fc8e8d6211d5e63d2 (MD5) / Submitted by Thaís Saes Giuliani Ribeiro (thais_saes@hotmail.com) on 2017-12-14T11:25:03Z No. of bitstreams: 1 Dissertação Thaís Saes Giuliani Ribeiro.pdf: 1429513 bytes, checksum: 6145616464ae520fc8e8d6211d5e63d2 (MD5) / Approved for entry into archive by Elza Mitiko Sato null (elzasato@ibilce.unesp.br) on 2017-12-14T12:31:48Z (GMT) No. of bitstreams: 1 ribeiro_tsg_me_sjrp.pdf: 1429513 bytes, checksum: 6145616464ae520fc8e8d6211d5e63d2 (MD5) / Made available in DSpace on 2017-12-14T12:31:48Z (GMT). No. of bitstreams: 1 ribeiro_tsg_me_sjrp.pdf: 1429513 bytes, checksum: 6145616464ae520fc8e8d6211d5e63d2 (MD5) Previous issue date: 2017-11-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho, mostramos como construir um processo estocástico de Markov e seu espaço de probabilidade a partir das probabilidades de transição e da distribuição inicial. Além disso, mostramos a convergência das matrizes de transição utilizando como ferramenta conhecimentos de Álgebra Linear. A aplicação das cadeias de Markov num contexto voltado para o Ensino Médio é mostrado no último capítulo, onde procuramos oferecer aos alunos a oportunidade de ter uma visão mais ampla de como a Matemática pode ser aplicada em outras áreas do conhecimento. / In this work, we show how to construct a stochastic Markov process and its probability space from the transition probabilities and the initial distribution. In addition, we show to investigate the convergence of the transition matrices using Linear Algebra knowledge as a tool. Application of Markov chains in a context focused on High School, it is shown in the last chapter, where we try to offer the students the opportunity to have a view of how mathematics can be applied in other areas of knowledge.

This thesis studies numerical methods for integrating the master equations describing Markov chain models of cardiac ion channels. Such models describe the time evolution of the probability that ion channels are in a particular state. Numerical simulations of such models are often computationally demanding because many solvers require relatively small time steps to ensure numerical stability. The aim of this project is to analyse selected Markov chains and develop more efficient and accurate solvers. We separate a Markov chain model into fast and slow time-scales based on the speed of transitions between states. Eliminating the fast transitions, we find an asymptotic reduction of zeroth-order and first-order in a small parameter describing the time-scales separation. We apply the theory to a Markov chain model of the fast sodium channel INa. We consider several variants for classifying some transitions as fast in order to find reduced systems that yield a good accuracy. However, the time step size is still restricted by numerical instabilities. We adapt the Rush-Larsen technique originally developed for gate models. Assuming that a transition matrix can be considered constant during each time step, we solve the Markov chain model analytically. The solution provides a recipe for a stable exponential solver, which we call "Matrix Rush-Larsen" (MRL). Using operator splitting we design an even more flexible "hybrid" method that combines the MRL with other solvers. The resulting improvement in stability allows a large increase in the time step size. In some models, we obtain reasonably accurate results 27 times faster using a hybrid method than with the forward Euler method, even with the maximal time step allowed by the stability constraint. Finally, we extend the cardiac simulation package BeatBox by the developed exponential solvers. We upgrade a format of "ionic" modules which describe a cardiac cell, in order to allow for a specific definition of Markov chain models. We also modify a particular integrator for ionic modules to include the MRL and the hybrid method. To test the functionality of the code, we have converted a number of cellular models into the ionic format. The documented code is available in the official BeatBox package distribution.

Esta pesquisa investiga o comportamento não-linear do pass-through de taxa de câmbio na economia brasileira, durante o período de câmbio flutuante (2000-2015), a partir de um modelo de equilíbrio geral dinâmico estocástico com mudança de regime Markoviana (MS-DSGE). Para isso, utilizamos a metodologia proposta por Baele et al. (2015) e um modelo Novo-Keynesiano básico, sobre o qual incluímos novos elementos na curva de oferta agregada e uma nova equação para a dinâmica cambial. Encontramos evidências de existência de dois regimes distintos para o repasse cambial e para a variância dos choques sobre a inflação. No regime denominado de “Normal”, o pass-through de longo prazo é estimado em 0.0092 pontos percentuais para inflação, dado um choque cambial de 1%, contra 0.1302 pontos percentuais no regime de “Crise”. A superioridade do modelo MS-DSGE sobre o modelo com parâmetros fixos é constatada de acordo com diversos critérios comparativos. / This research investigates the non-linearity of exchange rate pass-through on the Brazilian economy during the floating exchange rate period (2000-2015) in a Markov-switching dynamic stochastic general equilibrium framework (MS-DSGE). We apply methods proposed by Baele et al. (2015) in a basic New Keynesian model, with the addition of new elements to the aggregate supply curve and a new equation for the exchange rate dynamics. We find evidence of two distinct regimes for the exchange rate pass-through and for the volatility of shocks to inflation. During the regime named “Normal”, the long run pass-through is estimated as 0.0092 percent points to inflation, given a 1% exchange rate shock, in contrast to 0.1302 percent points during the “Crisis” regime. The MS-DSGE model appears superior to the fixed parameters model according to various comparison criteria.

Climate change is a global concern as it may affect many aspects of life, including water supply. A tool used to model climate change’s impacts is called a General Circulation Model (GCM). GCMs project future scenarios including temperature and precipitation, but these are designed at a coarse resolution and require downscaling for employment for regional hydrologic modeling. There is a vast amount of research on downscaling and bias-correcting GCMs data, but it is unknown whether these techniques alter precipitation signals embedded in these models or reproduce climate states that are viable for water resource planning and management. Using the Tampa, Florida region for the case study, the first part of the research investigated 1) whether GCM and the downscaled, bias-corrected data were able to replicate important historical climate states; and 2) if climate state and/or transition probabilities in raw GCMs were preserved or lost in translation in the corrected downscaled data. This has an important implication in understanding the limitations of bias-correction methods and shortcomings of future projection scenarios. Results showed that the GCM, and downscaled and bias-corrected data did a poor job in capturing historical climate states for wet or dry states as well as the variability in precipitation including some extremes associated with El Niño events. Additionally, the corrected products ended up creating different cycles compared to the original GCMs. Since the corrected products did not preserve GCMs historical transition probabilities, more than likely similar types of deviations will occur for “future” predictions and therefore another correction could be applied if desired to reproduce the degree of spatial persistence of atmospheric features and climatic states that are hydrologically important. Furthermore, understanding the sustainability of water supply systems in a changing climate is required for undertaking adaptation measures. Many water suppliers employ GCMs to examine climate change’s effect on hydrologic variables such as precipitation, but little is known on the propagation of mismatch errors in downscaled products through cascade of hydrologic and systems models. The second study examined how deviations in downscaled GCMs precipitation propagated into streamflow and reservoir simulation models by using key performance metrics. Findings exhibited that simulations better reproduced the resilience metric, but failed to capture reliability, vulnerability and sustainability metrics. Discrepancies were attributed to multiple factors including variances in GCMs precipitation and streamflow cumulative distribution functions, and divergences in serial correlation and system memory. Finally, the last study examined multiple models, emission scenarios and an ensemble to obtain a range of possible implications on reservation operations for time periods 2030-2053, 2054-2077 and 2077-2100 since the future emission trajectory is uncertain. Currently there are four Representative Concentration Pathways (RCPs) as defined by the IPCC’s fifth Assessment Report which provides time-dependent projections based on different forecasted greenhouse gas emission and land use changes. For this research Representative Concentration Pathways (RCPs) 4.0, 6.0 and 8.5 were examined. Scenarios were evaluated utilizing reliability, resilience, vulnerability and sustainability performance metrics and compared to a historical baseline. Findings exhibited that RCP 4.5, the lower end of emission scenario, improved reservoir reliability and resilience over time. Conversely, RCP 8.5, highest emissions, resulted in a steady decline of all metrics by 2100. Although vulnerability increased by 2100 for all emission scenarios, on average RCP 4.5 was less vulnerable. Investigation of permits and adjustments to capture extreme flows might be necessary to combat climate changes and precipitation inputs along with improvements to atmospheric emissions, which correlated with system recuperation with time.

We discuss efficient Bayesian estimation of dynamic covariance matrices in multivariate time series through a factor stochastic volatility model. In particular, we propose two interweaving strategies (Yu and Meng, Journal of Computational and Graphical Statistics, 20(3), 531-570, 2011) to substantially accelerate convergence and mixing of standard MCMC approaches. Similar to marginal data augmentation techniques, the proposed acceleration procedures exploit non-identifiability issues which frequently arise in factor models. Our new interweaving strategies are easy to implement and come at almost no extra computational cost; nevertheless, they can boost estimation efficiency by several orders of magnitude as is shown in extensive simulation studies. To conclude, the application of our algorithm to a 26-dimensional exchange rate data set illustrates the superior performance of the new approach for real-world data. / Series: Research Report Series / Department of Statistics and Mathematics

Esta pesquisa investiga o comportamento não-linear do pass-through de taxa de câmbio na economia brasileira, durante o período de câmbio flutuante (2000-2015), a partir de um modelo de equilíbrio geral dinâmico estocástico com mudança de regime Markoviana (MS-DSGE). Para isso, utilizamos a metodologia proposta por Baele et al. (2015) e um modelo Novo-Keynesiano básico, sobre o qual incluímos novos elementos na curva de oferta agregada e uma nova equação para a dinâmica cambial. Encontramos evidências de existência de dois regimes distintos para o repasse cambial e para a variância dos choques sobre a inflação. No regime denominado de “Normal”, o pass-through de longo prazo é estimado em 0.0092 pontos percentuais para inflação, dado um choque cambial de 1%, contra 0.1302 pontos percentuais no regime de “Crise”. A superioridade do modelo MS-DSGE sobre o modelo com parâmetros fixos é constatada de acordo com diversos critérios comparativos. / This research investigates the non-linearity of exchange rate pass-through on the Brazilian economy during the floating exchange rate period (2000-2015) in a Markov-switching dynamic stochastic general equilibrium framework (MS-DSGE). We apply methods proposed by Baele et al. (2015) in a basic New Keynesian model, with the addition of new elements to the aggregate supply curve and a new equation for the exchange rate dynamics. We find evidence of two distinct regimes for the exchange rate pass-through and for the volatility of shocks to inflation. During the regime named “Normal”, the long run pass-through is estimated as 0.0092 percent points to inflation, given a 1% exchange rate shock, in contrast to 0.1302 percent points during the “Crisis” regime. The MS-DSGE model appears superior to the fixed parameters model according to various comparison criteria.

Submitted by Joseane Gregório Gomes (joseane.gregomes@gmail.com) on 2018-10-02T15:21:14Z No. of bitstreams: 1 DissertacaoJoseaneGregorioGomes_RepositorioUnesp.pdf: 8742420 bytes, checksum: 34e7536942ba5c06f74cde6d224bbab1 (MD5) / Approved for entry into archive by Elza Mitiko Sato null (elzasato@ibilce.unesp.br) on 2018-10-02T18:47:36Z (GMT) No. of bitstreams: 1 gomes_jg_me_sjrp.pdf: 8742420 bytes, checksum: 34e7536942ba5c06f74cde6d224bbab1 (MD5) / Made available in DSpace on 2018-10-02T18:47:36Z (GMT). No. of bitstreams: 1 gomes_jg_me_sjrp.pdf: 8742420 bytes, checksum: 34e7536942ba5c06f74cde6d224bbab1 (MD5) Previous issue date: 2018-09-05 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho apresentamos uma introdução aos processos estocásticos de Markov dis­cretos e suas propriedades, e como uma aplicação, estudamos um modelo probabilístico para o problema da irreversibilidade dos gases, ou modelo da urna de Ehrenfest. Por fim, apresentamos uma modificação deste modelo, cuja abordagem é adaptada para o Ensino Médio. / ln this work we present an introducion to discrete Markov stochastic processes and their properties, and as an application, we study a probabilistic model for the problem of irre­versibility of gases, or model of Ehrenfest um. Finally, we present a modification of this model, whose approach is adapted for High School. / CAPES: 1115211/001