The FGM bivariate lifetime copula model: a bayesian approach

In this paper, we propose a bivariate distribution for the bivariate survival times based on Farlie-Gumbel-Morgenstern copula to model the dependence on a bivariate survival data. The proposed model allows for the presence of censored data and covariates. For inferential purpose a Bayesian approach via Markov Chain Monte Carlo (MCMC) is considered. Further, some discussions on the model selection criteria are given. In order to examine outlying and influential observations, we present a Bayesian case deletion influence diagnostics based on the Kullback-Leibler divergence. The newly developed procedures are illustrated via a simulation study and a real dataset.

Estudo da viabilidade de implantação do INOVAR-AUTO utilizando o método do fluxo de caixa sob risco

The automobile industry has a growing importance in the Brazilian economic environment. The industry moves a huge chain that encompasses manufacturers, suppliers of raw materials, auto parts dealers, gas stations, insurance companies, repair shops, tire stores, media companies, advertising agencies, among others. Because of this importance in the current economic environment in Brazil, the federal government, through Law No. 12715 of 17 December 2012 established a Program for the Promotion of Innovation and Densification in the Productive Chain of Motor Vehicles called INOVAR-AUTO in order to support technological development, innovation, safety, environmental protection, energy efficiency and quality of cars, trucks, buses and auto parts. The specific purpose of this study, a simulation for discussion of the viability of the program implementation using the Monte Carlo Simulation combined with the Cash-Flow-at-Risk was performed. To this end, an exploratory and documentary literature on the subject was held as well as a case study in a automobile company of Japanese origin

Estudo da viabilidade de implantação do INOVAR-AUTO utilizando o método do fluxo de caixa sob risco

The automobile industry has a growing importance in the Brazilian economic environment. The industry moves a huge chain that encompasses manufacturers, suppliers of raw materials, auto parts dealers, gas stations, insurance companies, repair shops, tire stores, media companies, advertising agencies, among others. Because of this importance in the current economic environment in Brazil, the federal government, through Law No. 12715 of 17 December 2012 established a Program for the Promotion of Innovation and Densification in the Productive Chain of Motor Vehicles called INOVAR-AUTO in order to support technological development, innovation, safety, environmental protection, energy efficiency and quality of cars, trucks, buses and auto parts. The specific purpose of this study, a simulation for discussion of the viability of the program implementation using the Monte Carlo Simulation combined with the Cash-Flow-at-Risk was performed. To this end, an exploratory and documentary literature on the subject was held as well as a case study in a automobile company of Japanese origin

Study of using marker assisted selection on a beef cattle breeding program by model comparison

A data set of a commercial Nellore beef cattle selection program was used to compare breeding models that assumed or not markers effects to estimate the breeding values, when a reduced number of animals have phenotypic, genotypic and pedigree information available. This herd complete data set was composed of 83,404 animals measured for weaning weight (WW), post-weaning gain (PWG), scrotal circumference (SC) and muscle score (MS), corresponding to 116,652 animals in the relationship matrix. Single trait analyses were performed by MTDFREML software to estimate fixed and random effects solutions using this complete data. The additive effects estimated were assumed as the reference breeding values for those animals. The individual observed phenotype of each trait was adjusted for fixed and random effects solutions, except for direct additive effects. The adjusted phenotype composed of the additive and residual parts of observed phenotype was used as dependent variable for models' comparison. Among all measured animals of this herd, only 3160 animals were genotyped for 106 SNP markers. Three models were compared in terms of changes on animals' rank, global fit and predictive ability. Model 1 included only polygenic effects, model 2 included only markers effects and model 3 included both polygenic and markers effects. Bayesian inference via Markov chain Monte Carlo methods performed by TM software was used to analyze the data for model comparison. Two different priors were adopted for markers effects in models 2 and 3, the first prior assumed was a uniform distribution (U) and, as a second prior, was assumed that markers effects were distributed as normal (N). Higher rank correlation coefficients were observed for models 3_U and 3_N, indicating a greater similarity of these models animals' rank and the rank based on the reference breeding values. Model 3_N presented a better global fit, as demonstrated by its low DIC. The best models in terms of predictive ability were models 1 and 3_N. Differences due prior assumed to markers effects in models 2 and 3 could be attributed to the better ability of normal prior in handle with collinear effects. The models 2_U and 2_N presented the worst performance, indicating that this small set of markers should not be used to genetically evaluate animals with no data, since its predictive ability is restricted. In conclusion, model 3_N presented a slight superiority when a reduce number of animals have phenotypic, genotypic and pedigree information. It could be attributed to the variation retained by markers and polygenic effects assumed together and the normal prior assumed to markers effects, that deals better with the collinearity between markers. (C) 2012 Elsevier B.V. All rights reserved.

Weibull and generalised exponential overdispersion models with an application to ozone air pollution

We consider the problem of estimating the mean and variance of the time between occurrences of an event of interest (inter-occurrences times) where some forms of dependence between two consecutive time intervals are allowed. Two basic density functions are taken into account. They are the Weibull and the generalised exponential density functions. In order to capture the dependence between two consecutive inter-occurrences times, we assume that either the shape and/or the scale parameters of the two density functions are given by auto-regressive models. The expressions for the mean and variance of the inter-occurrences times are presented. The models are applied to the ozone data from two regions of Mexico City. The estimation of the parameters is performed using a Bayesian point of view via Markov chain Monte Carlo (MCMC) methods.

Response plateau models fitting via isotonic regression

Within the nutritional context, the supplementation of microminerals in bird food is often made in quantities exceeding those required in the attempt to ensure the proper performance of the animals. The experiments of type dosage x response are very common in the determination of levels of nutrients in optimal food balance and include the use of regression models to achieve this objective. Nevertheless, the regression analysis routine, generally, uses a priori information about a possible relationship between the response variable. The isotonic regression is a method of estimation by least squares that generates estimates which preserves data ordering. In the theory of isotonic regression this information is essential and it is expected to increase fitting efficiency. The objective of this work was to use an isotonic regression methodology, as an alternative way of analyzing data of Zn deposition in tibia of male birds of Hubbard lineage. We considered the models of plateau response of polynomial quadratic and linear exponential forms. In addition to these models, we also proposed the fitting of a logarithmic model to the data and the efficiency of the methodology was evaluated by Monte Carlo simulations, considering different scenarios for the parametric values. The isotonization of the data yielded an improvement in all the fitting quality parameters evaluated. Among the models used, the logarithmic presented estimates of the parameters more consistent with the values reported in literature.

Modeling random corrosion processes via polynomial chaos expansion

Polynomial Chaos Expansion (PCE) is widely recognized as a flexible tool to represent different types of random variables/processes. However, applications to real, experimental data are still limited. In this article, PCE is used to represent the random time-evolution of metal corrosion growth in marine environments. The PCE coefficients are determined in order to represent data of 45 corrosion coupons tested by Jeffrey and Melchers (2001) at Taylors Beach, Australia. Accuracy of the representation and possibilities for model extrapolation are considered in the study. Results show that reasonably accurate smooth representations of the corrosion process can be obtained. The representation is not better because a smooth model is used to represent non-smooth corrosion data. Random corrosion leads to time-variant reliability problems, due to resistance degradation over time. Time variant reliability problems are not trivial to solve, especially under random process loading. Two example problems are solved herein, showing how the developed PCE representations can be employed in reliability analysis of structures subject to marine corrosion. Monte Carlo Simulation is used to solve the resulting time-variant reliability problems. However, an accurate and more computationally efficient solution is also presented.

Constraints on neutrino mass fraction using Redshift Space Distortions

Redshift Space Distortions (RSD) are an apparent anisotropy in the distribution of galaxies due to their peculiar motion. These features are imprinted in the correlation function of galaxies, which describes how these structures distribute around each other. RSD can be represented by a distortions parameter $\beta$, which is strictly related to the growth of cosmic structures. For this reason, measurements of RSD can be exploited to give constraints on the cosmological parameters, such us for example the neutrino mass. Neutrinos are neutral subatomic particles that come with three flavours, the electron, the muon and the tau neutrino. Their mass differences can be measured in the oscillation experiments. Information on the absolute scale of neutrino mass can come from cosmology, since neutrinos leave a characteristic imprint on the large scale structure of the universe. The aim of this thesis is to provide constraints on the accuracy with which neutrino mass can be estimated when expoiting measurements of RSD. In particular we want to describe how the error on the neutrino mass estimate depends on three fundamental parameters of a galaxy redshift survey: the density of the catalogue, the bias of the sample considered and the volume observed. In doing this we make use of the BASICC Simulation from which we extract a series of dark matter halo catalogues, characterized by different value of bias, density and volume. This mock data are analysed via a Markov Chain Monte Carlo procedure, in order to estimate the neutrino mass fraction, using the software package CosmoMC, which has been conveniently modified. In this way we are able to extract a fitting formula describing our measurements, which can be used to forecast the precision reachable in future surveys like Euclid, using this kind of observations.

A BAYESIAN HIERARCHICAL FRAMEWORK FOR SPATIAL MODELING OF fMRI DATA

Functional neuroimaging techniques enable investigations into the neural basis of human cognition, emotions, and behaviors. In practice, applications of functional magnetic resonance imaging (fMRI) have provided novel insights into the neuropathophysiology of major psychiatric,neurological, and substance abuse disorders, as well as into the neural responses to their treatments. Modern activation studies often compare localized task-induced changes in brain activity between experimental groups. One may also extend voxel-level analyses by simultaneously considering the ensemble of voxels constituting an anatomically defined region of interest (ROI) or by considering means or quantiles of the ROI. In this work we present a Bayesian extension of voxel-level analyses that offers several notable benefits. First, it combines whole-brain voxel-by-voxel modeling and ROI analyses within a unified framework. Secondly, an unstructured variance/covariance for regional mean parameters allows for the study of inter-regional functional connectivity, provided enough subjects are available to allow for accurate estimation. Finally, an exchangeable correlation structure within regions allows for the consideration of intra-regional functional connectivity. We perform estimation for our model using Markov Chain Monte Carlo (MCMC) techniques implemented via Gibbs sampling which, despite the high throughput nature of the data, can be executed quickly (less than 30 minutes). We apply our Bayesian hierarchical model to two novel fMRI data sets: one considering inhibitory control in cocaine-dependent men and the second considering verbal memory in subjects at high risk for Alzheimer’s disease. The unifying hierarchical model presented in this manuscript is shown to enhance the interpretation content of these data sets.

Bayesian generalized linear models for meta-analysis of diagnostic tests

With the recognition of the importance of evidence-based medicine, there is an emerging need for methods to systematically synthesize available data. Specifically, methods to provide accurate estimates of test characteristics for diagnostic tests are needed to help physicians make better clinical decisions. To provide more flexible approaches for meta-analysis of diagnostic tests, we developed three Bayesian generalized linear models. Two of these models, a bivariate normal and a binomial model, analyzed pairs of sensitivity and specificity values while incorporating the correlation between these two outcome variables. Noninformative independent uniform priors were used for the variance of sensitivity, specificity and correlation. We also applied an inverse Wishart prior to check the sensitivity of the results. The third model was a multinomial model where the test results were modeled as multinomial random variables. All three models can include specific imaging techniques as covariates in order to compare performance. Vague normal priors were assigned to the coefficients of the covariates. The computations were carried out using the 'Bayesian inference using Gibbs sampling' implementation of Markov chain Monte Carlo techniques. We investigated the properties of the three proposed models through extensive simulation studies. We also applied these models to a previously published meta-analysis dataset on cervical cancer as well as to an unpublished melanoma dataset. In general, our findings show that the point estimates of sensitivity and specificity were consistent among Bayesian and frequentist bivariate normal and binomial models. However, in the simulation studies, the estimates of the correlation coefficient from Bayesian bivariate models are not as good as those obtained from frequentist estimation regardless of which prior distribution was used for the covariance matrix. The Bayesian multinomial model consistently underestimated the sensitivity and specificity regardless of the sample size and correlation coefficient. In conclusion, the Bayesian bivariate binomial model provides the most flexible framework for future applications because of its following strengths: (1) it facilitates direct comparison between different tests; (2) it captures the variability in both sensitivity and specificity simultaneously as well as the intercorrelation between the two; and (3) it can be directly applied to sparse data without ad hoc correction. ^

A multivariate frailty model for disease recurrences and survival

A multivariate frailty hazard model is developed for joint-modeling of three correlated time-to-event outcomes: (1) local recurrence, (2) distant recurrence, and (3) overall survival. The term frailty is introduced to model population heterogeneity. The dependence is modeled by conditioning on a shared frailty that is included in the three hazard functions. Independent variables can be included in the model as covariates. The Markov chain Monte Carlo methods are used to estimate the posterior distributions of model parameters. The algorithm used in present application is the hybrid Metropolis-Hastings algorithm, which simultaneously updates all parameters with evaluations of gradient of log posterior density. The performance of this approach is examined based on simulation studies using Exponential and Weibull distributions. We apply the proposed methods to a study of patients with soft tissue sarcoma, which motivated this research. Our results indicate that patients with chemotherapy had better overall survival with hazard ratio of 0.242 (95% CI: 0.094 - 0.564) and lower risk of distant recurrence with hazard ratio of 0.636 (95% CI: 0.487 - 0.860), but not significantly better in local recurrence with hazard ratio of 0.799 (95% CI: 0.575 - 1.054). The advantages and limitations of the proposed models, and future research directions are discussed. ^

A Bayesian approach to estimating the regression coefficients of a multinomial logit model

A Bayesian approach to estimation of the regression coefficients of a multinominal logit model with ordinal scale response categories is presented. A Monte Carlo method is used to construct the posterior distribution of the link function. The link function is treated as an arbitrary scalar function. Then the Gauss-Markov theorem is used to determine a function of the link which produces a random vector of coefficients. The posterior distribution of the random vector of coefficients is used to estimate the regression coefficients. The method described is referred to as a Bayesian generalized least square (BGLS) analysis. Two cases involving multinominal logit models are described. Case I involves a cumulative logit model and Case II involves a proportional-odds model. All inferences about the coefficients for both cases are described in terms of the posterior distribution of the regression coefficients. The results from the BGLS method are compared to maximum likelihood estimates of the regression coefficients. The BGLS method avoids the nonlinear problems encountered when estimating the regression coefficients of a generalized linear model. The method is not complex or computationally intensive. The BGLS method offers several advantages over Bayesian approaches. ^

A Bayesian analysis for spatial processes with application to mapping

In geographical epidemiology, maps of disease rates and disease risk provide a spatial perspective for researching disease etiology. For rare diseases or when the population base is small, the rate and risk estimates may be unstable. Empirical Bayesian (EB) methods have been used to spatially smooth the estimates by permitting an area estimate to "borrow strength" from its neighbors. Such EB methods include the use of a Gamma model, of a James-Stein estimator, and of a conditional autoregressive (CAR) process. A fully Bayesian analysis of the CAR process is proposed. One advantage of this fully Bayesian analysis is that it can be implemented simply by using repeated sampling from the posterior densities. Use of a Markov chain Monte Carlo technique such as Gibbs sampler was not necessary. Direct resampling from the posterior densities provides exact small sample inferences instead of the approximate asymptotic analyses of maximum likelihood methods (Clayton & Kaldor, 1987). Further, the proposed CAR model provides for covariates to be included in the model. A simulation demonstrates the effect of sample size on the fully Bayesian analysis of the CAR process. The methods are applied to lip cancer data from Scotland, and the results are compared. ^

Bayesian and survival model for tumor relapse status and disease-specific survival, with applications to breast cancer

Breast cancer is the most common non-skin cancer and the second leading cause of cancer-related death in women in the United States. Studies on ipsilateral breast tumor relapse (IBTR) status and disease-specific survival will help guide clinic treatment and predict patient prognosis.^ After breast conservation therapy, patients with breast cancer may experience breast tumor relapse. This relapse is classified into two distinct types: true local recurrence (TR) and new ipsilateral primary tumor (NP). However, the methods used to classify the relapse types are imperfect and are prone to misclassification. In addition, some observed survival data (e.g., time to relapse and time from relapse to death)are strongly correlated with relapse types. The first part of this dissertation presents a Bayesian approach to (1) modeling the potentially misclassified relapse status and the correlated survival information, (2) estimating the sensitivity and specificity of the diagnostic methods, and (3) quantify the covariate effects on event probabilities. A shared frailty was used to account for the within-subject correlation between survival times. The inference was conducted using a Bayesian framework via Markov Chain Monte Carlo simulation implemented in softwareWinBUGS. Simulation was used to validate the Bayesian method and assess its frequentist properties. The new model has two important innovations: (1) it utilizes the additional survival times correlated with the relapse status to improve the parameter estimation, and (2) it provides tools to address the correlation between the two diagnostic methods conditional to the true relapse types.^ Prediction of patients at highest risk for IBTR after local excision of ductal carcinoma in situ (DCIS) remains a clinical concern. The goals of the second part of this dissertation were to evaluate a published nomogram from Memorial Sloan-Kettering Cancer Center, to determine the risk of IBTR in patients with DCIS treated with local excision, and to determine whether there is a subset of patients at low risk of IBTR. Patients who had undergone local excision from 1990 through 2007 at MD Anderson Cancer Center with a final diagnosis of DCIS (n=794) were included in this part. Clinicopathologic factors and the performance of the Memorial Sloan-Kettering Cancer Center nomogram for prediction of IBTR were assessed for 734 patients with complete data. Nomogram for prediction of 5- and 10-year IBTR probabilities were found to demonstrate imperfect calibration and discrimination, with an area under the receiver operating characteristic curve of .63 and a concordance index of .63. In conclusion, predictive models for IBTR in DCIS patients treated with local excision are imperfect. Our current ability to accurately predict recurrence based on clinical parameters is limited.^ The American Joint Committee on Cancer (AJCC) staging of breast cancer is widely used to determine prognosis, yet survival within each AJCC stage shows wide variation and remains unpredictable. For the third part of this dissertation, biologic markers were hypothesized to be responsible for some of this variation, and the addition of biologic markers to current AJCC staging were examined for possibly provide improved prognostication. The initial cohort included patients treated with surgery as first intervention at MDACC from 1997 to 2006. Cox proportional hazards models were used to create prognostic scoring systems. AJCC pathologic staging parameters and biologic tumor markers were investigated to devise the scoring systems. Surveillance Epidemiology and End Results (SEER) data was used as the external cohort to validate the scoring systems. Binary indicators for pathologic stage (PS), estrogen receptor status (E), and tumor grade (G) were summed to create PS+EG scoring systems devised to predict 5-year patient outcomes. These scoring systems facilitated separation of the study population into more refined subgroups than the current AJCC staging system. The ability of the PS+EG score to stratify outcomes was confirmed in both internal and external validation cohorts. The current study proposes and validates a new staging system by incorporating tumor grade and ER status into current AJCC staging. We recommend that biologic markers be incorporating into revised versions of the AJCC staging system for patients receiving surgery as the first intervention.^ Chapter 1 focuses on developing a Bayesian method to solve misclassified relapse status and application to breast cancer data. Chapter 2 focuses on evaluation of a breast cancer nomogram for predicting risk of IBTR in patients with DCIS after local excision gives the statement of the problem in the clinical research. Chapter 3 focuses on validation of a novel staging system for disease-specific survival in patients with breast cancer treated with surgery as the first intervention. ^

Vision-based vehicle detection and tracking with a mobile camera using a statistical framework

En esta tesis se aborda la detección y el seguimiento automático de vehículos mediante técnicas de visión artificial con una cámara monocular embarcada. Este problema ha suscitado un gran interés por parte de la industria automovilística y de la comunidad científica ya que supone el primer paso en aras de la ayuda a la conducción, la prevención de accidentes y, en última instancia, la conducción automática. A pesar de que se le ha dedicado mucho esfuerzo en los últimos años, de momento no se ha encontrado ninguna solución completamente satisfactoria y por lo tanto continúa siendo un tema de investigación abierto. Los principales problemas que plantean la detección y seguimiento mediante visión artificial son la gran variabilidad entre vehículos, un fondo que cambia dinámicamente debido al movimiento de la cámara, y la necesidad de operar en tiempo real. En este contexto, esta tesis propone un marco unificado para la detección y seguimiento de vehículos que afronta los problemas descritos mediante un enfoque estadístico. El marco se compone de tres grandes bloques, i.e., generación de hipótesis, verificación de hipótesis, y seguimiento de vehículos, que se llevan a cabo de manera secuencial. No obstante, se potencia el intercambio de información entre los diferentes bloques con objeto de obtener el máximo grado posible de adaptación a cambios en el entorno y de reducir el coste computacional. Para abordar la primera tarea de generación de hipótesis, se proponen dos métodos complementarios basados respectivamente en el análisis de la apariencia y la geometría de la escena. Para ello resulta especialmente interesante el uso de un dominio transformado en el que se elimina la perspectiva de la imagen original, puesto que este dominio permite una búsqueda rápida dentro de la imagen y por tanto una generación eficiente de hipótesis de localización de los vehículos. Los candidatos finales se obtienen por medio de un marco colaborativo entre el dominio original y el dominio transformado. Para la verificación de hipótesis se adopta un método de aprendizaje supervisado. Así, se evalúan algunos de los métodos de extracción de características más populares y se proponen nuevos descriptores con arreglo al conocimiento de la apariencia de los vehículos. Para evaluar la efectividad en la tarea de clasificación de estos descriptores, y dado que no existen bases de datos públicas que se adapten al problema descrito, se ha generado una nueva base de datos sobre la que se han realizado pruebas masivas. Finalmente, se presenta una metodología para la fusión de los diferentes clasificadores y se plantea una discusión sobre las combinaciones que ofrecen los mejores resultados. El núcleo del marco propuesto está constituido por un método Bayesiano de seguimiento basado en filtros de partículas. Se plantean contribuciones en los tres elementos fundamentales de estos filtros: el algoritmo de inferencia, el modelo dinámico y el modelo de observación. En concreto, se propone el uso de un método de muestreo basado en MCMC que evita el elevado coste computacional de los filtros de partículas tradicionales y por consiguiente permite que el modelado conjunto de múltiples vehículos sea computacionalmente viable. Por otra parte, el dominio transformado mencionado anteriormente permite la definición de un modelo dinámico de velocidad constante ya que se preserva el movimiento suave de los vehículos en autopistas. Por último, se propone un modelo de observación que integra diferentes características. En particular, además de la apariencia de los vehículos, el modelo tiene en cuenta también toda la información recibida de los bloques de procesamiento previos. El método propuesto se ejecuta en tiempo real en un ordenador de propósito general y da unos resultados sobresalientes en comparación con los métodos tradicionales. ABSTRACT This thesis addresses on-road vehicle detection and tracking with a monocular vision system. This problem has attracted the attention of the automotive industry and the research community as it is the first step for driver assistance and collision avoidance systems and for eventual autonomous driving. Although many effort has been devoted to address it in recent years, no satisfactory solution has yet been devised and thus it is an active research issue. The main challenges for vision-based vehicle detection and tracking are the high variability among vehicles, the dynamically changing background due to camera motion and the real-time processing requirement. In this thesis, a unified approach using statistical methods is presented for vehicle detection and tracking that tackles these issues. The approach is divided into three primary tasks, i.e., vehicle hypothesis generation, hypothesis verification, and vehicle tracking, which are performed sequentially. Nevertheless, the exchange of information between processing blocks is fostered so that the maximum degree of adaptation to changes in the environment can be achieved and the computational cost is alleviated. Two complementary strategies are proposed to address the first task, i.e., hypothesis generation, based respectively on appearance and geometry analysis. To this end, the use of a rectified domain in which the perspective is removed from the original image is especially interesting, as it allows for fast image scanning and coarse hypothesis generation. The final vehicle candidates are produced using a collaborative framework between the original and the rectified domains. A supervised classification strategy is adopted for the verification of the hypothesized vehicle locations. In particular, state-of-the-art methods for feature extraction are evaluated and new descriptors are proposed by exploiting the knowledge on vehicle appearance. Due to the lack of appropriate public databases, a new database is generated and the classification performance of the descriptors is extensively tested on it. Finally, a methodology for the fusion of the different classifiers is presented and the best combinations are discussed. The core of the proposed approach is a Bayesian tracking framework using particle filters. Contributions are made on its three key elements: the inference algorithm, the dynamic model and the observation model. In particular, the use of a Markov chain Monte Carlo method is proposed for sampling, which circumvents the exponential complexity increase of traditional particle filters thus making joint multiple vehicle tracking affordable. On the other hand, the aforementioned rectified domain allows for the definition of a constant-velocity dynamic model since it preserves the smooth motion of vehicles in highways. Finally, a multiple-cue observation model is proposed that not only accounts for vehicle appearance but also integrates the available information from the analysis in the previous blocks. The proposed approach is proven to run near real-time in a general purpose PC and to deliver outstanding results compared to traditional methods.