Recurrent events are very common in a wide range of scientific disciplines. The majority of statistical models developed to characterise recurrent events are derived from either reliability theory or survival analysis. This thesis concentrates on applications that arise from reliability, which in general involve the study about components or devices where the recurring event is failure. Specifically, interest lies in repairable components that experience a number of failures during their lifetime. The goal is to develop statistical models in order to gain a good understanding about the driving force behind the failures. A particular counting process is adopted, the non-homogenous Poisson process (NHPP), where the rate of occurrence (failure rate) depends on time. The primary application considered in the thesis is the prediction of underground water pipe bursts although the methods described have more general scope. First, a Bayesian mixed effects NHPP model is developed and applied to a network of water pipes using MCMC. The model is then extended to a mixture of NHPPs. Further, a special mixture case, the zero-inflated NHPP model is developed to cope with data involving a large number of pipes that have never failed. The zero-inflated model is applied to the same pipe network. Quite often, data involving recurrent failures over time, are aggregated where for instance the times of failures are unknown and only the total number of failures are available. Aggregated versions of the NHPP model and its zero-inflated version are developed to accommodate aggregated data and these are applied to the aggregated version of the earlier data set. Complex devices in random environments often exhibit what may be termed as state changes in their behaviour. These state changes may be caused by unobserved and possibly non-stationary processes such as severe weather changes. A hidden semi-Markov NHPP model is formulated, which is a NHPP process modulated by an unobserved semi-Markov process. An algorithm is developed to evaluate the likelihood of this model and a Metropolis-Hastings sampler is constructed for parameter estimation. Simulation studies are performed to test implementation and finally an illustrative application of the model is presented. The thesis concludes with a general discussion and a list of possible generalisations and extensions as well as possible applications other than the ones considered.

This thesis deals with the estimation of model parameters of the interacting segments process in plane. The motivation is application on the system of stress fibers in human mesenchymal stem cells, which are detected by fluorescent microscopy. The model of segments is defined as a spatial Gibbs point process with marks. We use two methods for parameter estimation: moment method and Takacs-Fiksel method. Further, we implement algorithm for these estimation methods in software Mathematica. Also we are able to simulate the model structure by Markov Chain Monte Carlo, using birth-death process. Numerical results are presented for real and simulated data. Match of model and data is considered by descriptive statistics. Powered by TCPDF (www.tcpdf.org)

Muitos caracteres em plantas e animais são de natureza quantitativa, influenciados por múltiplos genes. Com o advento de novas técnicas moleculares tem sido possível mapear os locos que controlam os caracteres quantitativos, denominados QTLs (Quantitative Trait Loci). Mapear um QTL significa identificar sua posição no genoma, bem como, estimar seus efeitos genéticos. A maior dificuldade para realizar o mapeamento de QTLs, se deve ao fato de que o número de QTLs é desconhecido. Métodos bayesianos juntamente com método Monte Carlo com Cadeias de Markov (MCMC), têm sido implementados para inferir conjuntamente o número de QTLs, suas posições no genoma e os efeitos genéticos . O desafio está em obter a amostra da distribuição conjunta a posteriori desses parâmetros, uma vez que o número de QTLs pode ser considerado desconhecido e a dimensão do espaço paramétrico muda de acordo com o número de QTLs presente no modelo. No presente trabalho foi implementado, utilizando-se o programa estatístico R uma abordagem bayesiana para mapear QTLs em que múltiplos QTLs e os efeitos de epistasia são considerados no modelo. Para tanto foram ajustados modelos com números crescentes de QTLs e o fator de Bayes foi utilizado para selecionar o modelo mais adequado e conseqüentemente, estimar o número de QTLs que controlam os fenótipos de interesse. Para investigar a eficiência da metodologia implementada foi feito um estudo de simulação em que foram considerados duas diferentes populações experimentais: retrocruzamento e F2, sendo que para ambas as populações foi feito o estudo de simulação considerando modelos com e sem epistasia. A abordagem implementada mostrou-se muito eficiente, sendo que para todas as situações consideradas o modelo selecionado foi o modelo contendo o número verdadeiro de QTLs considerado na simulação dos dados. Além disso, foi feito o mapeamento de QTLs de três fenótipos de milho tropical: altura da planta (AP), altura da espiga (AE) e produção de grãos utilizando a metodologia implementada e os resultados obtidos foram comparados com os resultados encontrados pelo método CIM. / Many traits in plants and animals have quantitative nature, influenced by multiple genes. With the new molecular techniques, it has been possible to map the loci, which control the quantitative traits, called QTL (Quantitative Trait Loci). Mapping a QTL means to identify its position in the genome, as well as to estimate its genetics effects. The great difficulty of mapping QTL relates to the fact that the number of QTL is unknown. Bayesian approaches used with Markov Chain Monte Carlo method (MCMC) have been applied to infer QTL number, their positions in the genome and their genetic effects. The challenge is to obtain the sample from the joined distribution posterior of these parameters, since the number of QTL may be considered unknown and hence the dimension of the parametric space changes according to the number of QTL in the model. In this study, a Bayesian approach was applied, using the statistical program R, in order to map QTL, considering multiples QTL and epistasis effects in the model. Models were adjusted with the crescent number of QTL and Bayes factor was used to select the most suitable model and, consequently, to estimate the number of QTL that control interesting phenotype. To evaluate the efficiency of the applied methodology, a simulation study was done, considering two different experimental populations: backcross and F2, accomplishing the simulation study for both populations, considering models with and without epistasis. The applied approach resulted to be very efficient, considering that for all the used situations, the selected model was the one containing the real number of QTL used in the data simulation. Moreover, the QTL mapping of three phenotypes of tropical corn was done: plant height, corn-cob height and grain production, using the applied methodology and the results were compared to the results found by the CIM method.

This paper presents a comprehensive review and comparison of five computational methods for Bayesian model selection, based on MCMC simulations from posterior model parameter distributions. We apply these methods to a well-known and important class of models in financial time series analysis, namely GARCH and GARCH-t models for conditional return distributions (assuming normal and t-distributions). We compare their performance vis--vis the more common maximum likelihood-based model selection on both simulated and real market data. All five MCMC methods proved feasible in both cases, although differing in their computational demands. Results on simulated data show that for large degrees of freedom (where the t-distribution becomes more similar to a normal one), Bayesian model selection results in better decisions in favour of the true model than maximum likelihood. Results on market data show the feasibility of all model selection methods, mainly because the distributions appear to be decisively non-Gaussian. / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

This thesis is concerned with a fundamental unit of the economy: Households. Even in advanced economies, upwards of 70% of the population live in households composed of multiple people. A large number of decisions are taken at the level of the household, that is to say, they are taken jointly by household members: How to raise children, how much and when to work, how many cartons of milk to purchase. How these decisions are made is therefore of great importance for the people who live in them and for their well-being.But precisely because household members make decisions jointly it is hard to know how they come about and to what extent they benefit individual members. This is why households are often viewed as unique decision makers in economics. Even if they contain multiple people, they are treated as though they were a single person with a single set of preferences. This unitary approach is often sufficient and can be a helpful simplification. But in many situations it does not deliver an adequate description of household behavior. For instance, the unitary model does not permit the study of individual wellbeing and inequality inside the household. In addition, implications of the unitary model have been rejected repeatedly in the demand literature.Bargaining models offer an alternative where household members have individual preferences and come to joint decisions in various ways. There are by now a great number of such models, all of which allow for the study of bargaining power, a measure of the influence a member has in decision making. This concept is important because it has implications for the welfare of individuals. If one household member’s bargaining power increases, the household’s choices will be more closely aligned with that member’s preferences, ceteris paribus.The three chapters below can be divided into two parts. The first part consists of Chapter 1, which looks to detect the influence of intra-household bargaining in a specific set of consumption choices: Consumption of the arts. The research in this chapter is designed to measure aspects of the effect of bargaining power in this domain, but does not seek to quantify bargaining power itself or to infer economic well-being of household members.Precisely this last point, however, is the focus of the second part of the thesis, consisting of Chapters 2 and 3. These focus specifically on the recovery of one measure of bargaining power, the resource share. Resource shares have the advantage of being interpretable in terms of economic well-being, which is not true of all such measures. They are estimated as part of structural models of household demand. These models are versions of the collective model of household decision making.Pioneered by Chiappori (1988) and Apps and Rees (1988), the collective model has become the go-to alternative to unitary approaches, where the household is seen as a single decision-making unit with a single well-behaved utility function. Instead, the collective model allows for individual utility functions for each member of the household. The model owes much of its success to the simplicity of its most fundamental assumption: That whatever the structure of the intra-household bargaining process, outcomes are Pareto-efficient. This means that no member can be made better off, without making another worse off. Though the model nests unitary models as special cases, it does have testable implications.The first chapter of the thesis is entitled “Household Decisions on Arts Consumption” and is joint work with Caterina Mauri, who has also collaborated with me on many other projects in her capacity as my girlfriend. In it, we explore the role of intra-household bargaining in arts consumption. We do this by estimating demand for various arts and cultural events such as the opera or dance performances using a large number of explanatory variables. One of these variables plays a special role. This variable is a distribution factor, meaning that it can be reasonably assumed to affect consumption only through the bargaining process, and not by modifying preferences. Such variables play an important role in the household bargaining literature. Here, three such variables are used. Among them is the share of household income that is contributed by the husband, the canonical distribution factor.The chapter fits into a literature on drivers of arts consumption, which has shown that in addition to such factors as age, income and education, spousal preferences and characteristics are important in determining how much and which cultural goods are consumed. Gender differences in preferences in arts consumption have also been shown to be important and to persist after accounting for class, education and other socio-economic factors (Bihagen and Katz-Gerro, 2000).We explore to what extent this difference in preferences can be used to shed light on the decision process in couples’ households. Using three different distribution factors, we infer whether changes in the relative bargaining power of spouses induce changes in arts consumption.Using a large sample from the US Current Population Survey which includes data on the frequency of visits to various categories of cultural activities, we regress atten- dance rates on a range of socio-economic variables using a suitable count data model.We find that attendance by men at events such as the opera, ballet and other dance performances, which are more frequently attended by women than by men, show a significant influence of the distribution factors. This significant effect persists irrespec- tively of which distribution factor is used. We conclude that more influential men tend to participate in these activities less frequently than less influential men, conditionally on a host of controls notably including hours worked.The second chapter centers around the recovery of resource shares. This chapter is joint work with Denni Tommasi, a fellow PhD student at ECARES. It relies on the collective model of the household, which assumes simply that household decisions are Pareto-efficient. From this assumption, a relatively simple household problem can be formulated. Households can be seen as maximizers of weighted sums of their members’ utility functions. Importantly the weights, known as bargaining weights (or bargaining power), may depend on many factors, including prices. The household problem in turn implies structure for household demand, which is observed in survey data.Collective demand systems do not necessarily identify measures of bargaining power however. In fact, the ability to recover such a measure, and especially one that is useful for welfare analysis, was an important milestone in the literature. It was reached by (Browning et al. 2013) (henceforth BCL), with a collective model capable of identi- fying resource shares (also known as a sharing rule). These shares provide a measure of how resources are allocated in the household and so can be used to study intra- household consumption inequality. They also take into account that households gen- erate economies of scale for their members, a phenomenon known as a consumption technology: By sharing goods such as housing, members of households can generate savings that can be used elsewhere.Estimation of these resource shares involves expressing household budget shares functions of preferences, a consumption technology and a sharing rule, each of which is a function of observables, and letting the resulting system loose on the data. But obtaining such a demand system is not free. In addition to the usual empirical speci- fications of the various parts of the system, an identifying assumption has to be made to assure that resource shares can be recovered in estimation. In BCL, this is the assumption that singles and adult members of households share the same preferences. In Chapter 2, however, an alternative assumption is used.In a recent paper, Dunbar et al. (2013) (hereafter DLP) develop a collective model based on BCL that allows to identify resource shares using assumptions on the simi- larity of preferences within and between households. The model uses demand only for assignable goods, a favorite of household economists. These are goods such as mens’ clothing and womens’ clothing for which it is known who in a household consumes them. In this chapter, we show why, especially when the data exhibit relatively flat Engel curves, the model is weakly identified and induces high variability and an im- plausible pattern in least squares estimates.We propose an estimation strategy nested in their framework that greatly reduces this practical impediment to recovery of individual resource shares. To achieve this, we follow an empirical Bayes method that incorporates additional (or out-of-sample) information on singles and relies on mild assumptions on preferences. We show the practical usefulness of this strategy through a series of Monte Carlo simulations and by applying it to Mexican data.The results show that our approach is robust, gives a plausible picture of the house- hold decision process, and is particularly beneficial for the practitioner who wishes to apply the DLP framework. Our welfare analysis of the PROGRESA program in Mexico is the first to include separate poverty rates for men and women in a CCT program.The third Chapter addresses a problem similar to the one discussed in Chapter 2. The goal, again, is to estimate resource shares and to remedy issues of imprecision and instability in the demand systems that can deliver them. Here, the collective model used is based on Lewbel and Pendakur (2008), and uses data on the entire basket of goods that households consume. The identifying assumption is similar to that used by BCL, although I allow for some differences in preferences between singles and married individuals.I set out to improve the precision and stability of the resulting estimates, and so to make the model more useful for welfare analysis. In order to do so, this chapter approaches, for the first time, the estimation of a collective household demand system from a Bayesian perspective. Using prior information on equivalence scales, as well as restrictions implied by theory, tight credible intervals are found for resource shares, a measure of the distribution of economic well-being in a household. A modern MCMC sampling method provides a complete picture of the high-dimensional parameter vec- tor’s posterior distribution and allows for reliable inference.The share of household earnings generated by a household member is estimated to have a positive effect on her share of household resources in a sample of couples from the US Consumer Expenditure survey. An increase in the earnings share of one percentage point is estimated to result in a shift of between 0.05% and 0.14% of household resources in the same direction, meaning that spouses partially insure one another against such shifts. The estimates imply an expected shift of 0.71% of household resources from the average man to the average woman in the same sample between 2008 and 2012, when men lost jobs at a greater rate than women.Both Chapters 2 and 3 explore unconventional ways to achieve gains in estimator precision and reliability at relatively little cost. This represents a valuable contribution to a literature that, for all its merits in complexity and ingenious modeling, has not yet seriously endeavored to make itself empirically useful. / Doctorat en Sciences économiques et de gestion / info:eu-repo/semantics/nonPublished

Biological systems are driven by complex regulatory processes. Graphical models play a crucial role in the analysis and reconstruction of such processes. It is possible to derive regulatory models using network inference algorithms from high-throughput data, for example; from gene or protein expression data. A wide variety of network inference algorithms have been designed and implemented. Our aim is to explore the possibilities of using statistical independence criteria for biological network inference. The contributions of our work can be categorized into four sections. First, we provide a detailed overview of some of the most popular general independence criteria: distance covariance (dCov), kernel canonical variance (KCC), kernel generalized variance (KGV) and the Hilbert-Schmidt Independence Criterion (HSIC). We provide easy to understand geometrical interpretations for these criteria. We also explicitly show the equivalence of dCov, KGV and HSIC. Second, we introduce a new criterion for measuring dependence based on the signal to noise ratio (SNRIC). SNRIC is significantly faster to compute than other popular independence criteria. SNRIC is an approximate criterion but becomes exact under many popular modelling assumptions, for example for data from an additive noise model. Third, we compare the performance of the independence criteria on biological experimental data within the framework of the PC algorithm. Since not all criteria are available in a version that allows for testing conditional independence, we propose and test an approach which relies on residuals and requires only an unconditional version of an independence criterion. Finally we propose a novel method to infer networks with feedback loops. We use an MCMC sampler, which samples using a loss function based on an independence criterion. This allows us to find networks under very general assumptions, such as non-linear relationships, non-Gaussian noise distributions and feedback loops.

Conventional probabilistic models for phylogenetic inference assume that an evolutionary tree,andasinglesetofbranchlengthsandstochasticprocessofDNA evolutionare sufficient to characterise the generating process across an entire DNA alignment. Unfortunately such a simplistic, homogeneous formulation may be a poor description of reality when the data arise from heterogeneous processes. A well-known example is when sites evolve at heterogeneous rates. This thesis is a contribution to the modelling and understanding of heterogeneityin phylogenetic data. Weproposea methodfor the classificationof DNA sites based on Bayesian mixture modelling. Our method not only accounts for heterogeneous data but also identifies the underlying classes and enables their interpretation. We also introduce novel MCMC methodology with the same, or greater, estimation performance than existing algorithms but with lower computational cost. We find that our mixture model can successfully detect evolutionary heterogeneity and demonstrate its direct relevance by applying it to real DNA data. One of these applications is the analysis of sixteen strains of one of the bacterial species that cause Lyme disease. Results from that analysis have helped understanding the evolutionary paths of these bacterial strains and, therefore, the dynamics of the spread of Lyme disease. Our method is discussed in the context of DNA but it may be extendedto othertypesof molecular data. Moreover,the classification scheme thatwe propose is evidence of the breadth of application of mixture modelling and a step forwards in the search for more realistic models of theprocesses that underlie phylogenetic data.

The analysis of big data is now very popular. Big data may be very important for companies, societies or even human beings if we can take full advantage of them. Data scientists defined big data with four Vs: volume, velocity, variety and veracity. In a short, the data have large volume, grow with high velocity, represent with numerous varieties and must have high quality. Here we analyze data from many sources (varieties). In small area estimation, the term ``big data' refers to numerous areas. We want to analyze binary for a large number of small areas. Then standard Markov Chain Monte Carlo methods (MCMC) methods do not work because the time to do the computation is prohibitive. To solve this problem, we use numerical approximations. We set up four methods which are MCMC, method based on Beta-Binomial model, Integrated Nested Normal Approximation Model (INNA) and Empirical Logistic Transform (ELT) method. We compare the processing time and accuracies of these four methods in order to find the fastest and reasonable accurate one. Last but not the least, we combined the empirical logistic transform method, the fastest and accurate method, with time series to explore the sales data over time.

In this thesis we introduce a framework for parallel MCMC methods which we call parallel adaptive importance sampling (PAIS). At each iteration we have an ensemble of particles, from which PAIS builds a kernel density estimate (KDE). We propose a new ensemble, using this KDE, that is weighted according to standard importance sampling rules. A state-of-the art resampling method from the optimal transportation literature, or alternatively our own novel resampling algorithm, can be used to produce an equally weighted ensemble from this weighted ensemble. This equally weighted ensemble is approximately distributed according to the target distribution and is used to progress the algorithm. The PAIS algorithm outputs a weighted sample. We introduce an adaptive scheme for PAIS which automatically tunes the scaling parameters required for efficient sampling. This adaptive tuning converges rapidly for the target distributions we have experimented with and significantly reduces the burn-in period of the algorithm. PAIS has been designed to work well on computers with parallel processing units available, and we have demonstrated that a doubling of the number of processing units available more than halves the number of iterations required to reach the same accuracy. The numerical examples have been implemented on a shared memory system. PAIS is incredibly flexible in terms of the proposal distributions and resampling methods we can use. Throughout the thesis we introduce a number of these proposal schemes, and highlight when they may be of use. Of particular interest is the transport map based proposal scheme introduced in Chapter 7 which, while more expensive than the other schemes, allows us to sample efficiently from a wide range of complex target distributions.

Operational risk losses are heavy tailed and are likely to be asymmetric and extremely dependent among business lines/event types. The analysis of dependence via copula models has been focussed on the bivariate case mainly. In the vast majority of instances symmetric elliptical copulas are employed to model dependence for severities. This thesis proposes a new methodology to assess, in a multivariate way, the asymmetry and extreme dependence between severities, and to calculate the capital for operational risk. This methodology simultaneously uses (i) several parametric distributions and an alternative mixture distribution (the Lognormal for the body of losses and the generalised Pareto Distribution for the tail) using a technique from extreme value theory, (ii) the multivariate skew t-copula applied for the first time across severities and (iii) Bayesian theory. The former to model severities, I test simultaneously several parametric distributions and the mixture distribution for each business line. This procedure enables me to achieve multiple combinations of the severity distribution and to find which fits most closely. The second to effectively model asymmetry and extreme dependence in high dimensions. The third to estimate the copula model, given the high multivariate component (i.e. eight business lines and seven event types) and the incorporation of mixture distributions it is highly difficult to implement maximum likelihood. Therefore, I use a Bayesian inference framework and Markov chain Monte Carlo simulation to evaluate the posterior distribution to estimate and make inferences of the parameters of the skew t-copula model. The research analyses an updated operational loss data set, SAS® Operational Risk Global Data (SAS OpRisk Global Data), to model operational risk at international financial institutions. I then evaluate the impact of this multivariate, asymmetric and extreme dependence on estimating the total regulatory capital, among other established multivariate copulas. My empirical findings are consistent with other studies reporting thin and medium-tailed loss distributions. My approach substantially outperforms symmetric elliptical copulas, demonstrating that modelling dependence via the skew t-copula provides a more efficient allocation of capital charges of up to 56% smaller than that indicated by the standard Basel model.