Utilisation de splines monotones afin de condenser des tables de mortalité dans un contexte bayésien

Dans ce mémoire, nous cherchons à modéliser des tables à deux entrées monotones en lignes et/ou en colonnes, pour une éventuelle application sur les tables de mortalité. Nous adoptons une approche bayésienne non paramétrique et représentons la forme fonctionnelle des données par splines bidimensionnelles. L’objectif consiste à condenser une table de mortalité, c’est-à-dire de réduire l’espace d’entreposage de la table en minimisant la perte d’information. De même, nous désirons étudier le temps nécessaire pour reconstituer la table. L’approximation doit conserver les mêmes propriétés que la table de référence, en particulier la monotonie des données. Nous travaillons avec une base de fonctions splines monotones afin d’imposer plus facilement la monotonie au modèle. En effet, la structure flexible des splines et leurs dérivées faciles à manipuler favorisent l’imposition de contraintes sur le modèle désiré. Après un rappel sur la modélisation unidimensionnelle de fonctions monotones, nous généralisons l’approche au cas bidimensionnel. Nous décrivons l’intégration des contraintes de monotonie dans le modèle a priori sous l’approche hiérarchique bayésienne. Ensuite, nous indiquons comment obtenir un estimateur a posteriori à l’aide des méthodes de Monte Carlo par chaînes de Markov. Finalement, nous étudions le comportement de notre estimateur en modélisant une table de la loi normale ainsi qu’une table t de distribution de Student. L’estimation de nos données d’intérêt, soit la table de mortalité, s’ensuit afin d’évaluer l’amélioration de leur accessibilité.

Accuracy of genomic predictions in Bos indicus (Nellore) cattle

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Seleção genômica e estudo de associação em um rebanho experimental da raça Nelore

Pós-graduação em Genética e Melhoramento Animal - FCAV

Quantifying uncertainty in citizen weather data

The sheer volume of citizen weather data collected and uploaded to online data hubs is immense. However as with any citizen data it is difficult to assess the accuracy of the measurements. Within this project we quantify just how much data is available, where it comes from, the frequency at which it is collected, and the types of automatic weather stations being used. We also list the numerous possible sources of error and uncertainty within citizen weather observations before showing evidence of such effects in real data. A thorough intercomparison field study was conducted, testing popular models of citizen weather stations. From this study we were able to parameterise key sources of bias. Most significantly the project develops a complete quality control system through which citizen air temperature observations can be passed. The structure of this system was heavily informed by the results of the field study. Using a Bayesian framework the system learns and updates its estimates of the calibration and radiation-induced biases inherent to each station. We then show the benefit of correcting for these learnt biases over using the original uncorrected data. The system also attaches an uncertainty estimate to each observation, which would provide real world applications that choose to incorporate such observations with a measure on which they may base their confidence in the data. The system relies on interpolated temperature and radiation observations from neighbouring professional weather stations for which a Bayesian regression model is used. We recognise some of the assumptions and flaws of the developed system and suggest further work that needs to be done to bring it to an operational setting. Such a system will hopefully allow applications to leverage the additional value citizen weather data brings to longstanding professional observing networks.

Host gene expression classifiers diagnose acute respiratory illness etiology.

Acute respiratory infections caused by bacterial or viral pathogens are among the most common reasons for seeking medical care. Despite improvements in pathogen-based diagnostics, most patients receive inappropriate antibiotics. Host response biomarkers offer an alternative diagnostic approach to direct antimicrobial use. This observational cohort study determined whether host gene expression patterns discriminate noninfectious from infectious illness and bacterial from viral causes of acute respiratory infection in the acute care setting. Peripheral whole blood gene expression from 273 subjects with community-onset acute respiratory infection (ARI) or noninfectious illness, as well as 44 healthy controls, was measured using microarrays. Sparse logistic regression was used to develop classifiers for bacterial ARI (71 probes), viral ARI (33 probes), or a noninfectious cause of illness (26 probes). Overall accuracy was 87% (238 of 273 concordant with clinical adjudication), which was more accurate than procalcitonin (78%, P < 0.03) and three published classifiers of bacterial versus viral infection (78 to 83%). The classifiers developed here externally validated in five publicly available data sets (AUC, 0.90 to 0.99). A sixth publicly available data set included 25 patients with co-identification of bacterial and viral pathogens. Applying the ARI classifiers defined four distinct groups: a host response to bacterial ARI, viral ARI, coinfection, and neither a bacterial nor a viral response. These findings create an opportunity to develop and use host gene expression classifiers as diagnostic platforms to combat inappropriate antibiotic use and emerging antibiotic resistance.

DATA DRIVEN APPROACHES TO IDENTIFY DETERMINANTS OF HEART DISEASES AND CANCER RESISTANCE

Cancer and cardio-vascular diseases are the leading causes of death world-wide. Caused by systemic genetic and molecular disruptions in cells, these disorders are the manifestation of profound disturbance of normal cellular homeostasis. People suffering or at high risk for these disorders need early diagnosis and personalized therapeutic intervention. Successful implementation of such clinical measures can significantly improve global health. However, development of effective therapies is hindered by the challenges in identifying genetic and molecular determinants of the onset of diseases; and in cases where therapies already exist, the main challenge is to identify molecular determinants that drive resistance to the therapies. Due to the progress in sequencing technologies, the access to a large genome-wide biological data is now extended far beyond few experimental labs to the global research community. The unprecedented availability of the data has revolutionized the capabilities of computational researchers, enabling them to collaboratively address the long standing problems from many different perspectives. Likewise, this thesis tackles the two main public health related challenges using data driven approaches. Numerous association studies have been proposed to identify genomic variants that determine disease. However, their clinical utility remains limited due to their inability to distinguish causal variants from associated variants. In the presented thesis, we first propose a simple scheme that improves association studies in supervised fashion and has shown its applicability in identifying genomic regulatory variants associated with hypertension. Next, we propose a coupled Bayesian regression approach -- eQTeL, which leverages epigenetic data to estimate regulatory and gene interaction potential, and identifies combinations of regulatory genomic variants that explain the gene expression variance. On human heart data, eQTeL not only explains a significantly greater proportion of expression variance in samples, but also predicts gene expression more accurately than other methods. We demonstrate that eQTeL accurately detects causal regulatory SNPs by simulation, particularly those with small effect sizes. Using various functional data, we show that SNPs detected by eQTeL are enriched for allele-specific protein binding and histone modifications, which potentially disrupt binding of core cardiac transcription factors and are spatially proximal to their target. eQTeL SNPs capture a substantial proportion of genetic determinants of expression variance and we estimate that 58% of these SNPs are putatively causal. The challenge of identifying molecular determinants of cancer resistance so far could only be dealt with labor intensive and costly experimental studies, and in case of experimental drugs such studies are infeasible. Here we take a fundamentally different data driven approach to understand the evolving landscape of emerging resistance. We introduce a novel class of genetic interactions termed synthetic rescues (SR) in cancer, which denotes a functional interaction between two genes where a change in the activity of one vulnerable gene (which may be a target of a cancer drug) is lethal, but subsequently altered activity of its partner rescuer gene restores cell viability. Next we describe a comprehensive computational framework --termed INCISOR-- for identifying SR underlying cancer resistance. Applying INCISOR to mine The Cancer Genome Atlas (TCGA), a large collection of cancer patient data, we identified the first pan-cancer SR networks, composed of interactions common to many cancer types. We experimentally test and validate a subset of these interactions involving the master regulator gene mTOR. We find that rescuer genes become increasingly activated as breast cancer progresses, testifying to pervasive ongoing rescue processes. We show that SRs can be utilized to successfully predict patients' survival and response to the majority of current cancer drugs, and importantly, for predicting the emergence of drug resistance from the initial tumor biopsy. Our analysis suggests a potential new strategy for enhancing the effectiveness of existing cancer therapies by targeting their rescuer genes to counteract resistance. The thesis provides statistical frameworks that can harness ever increasing high throughput genomic data to address challenges in determining the molecular underpinnings of hypertension, cardiovascular disease and cancer resistance. We discover novel molecular mechanistic insights that will advance the progress in early disease prevention and personalized therapeutics. Our analyses sheds light on the fundamental biological understanding of gene regulation and interaction, and opens up exciting avenues of translational applications in risk prediction and therapeutics.

Multicollinearity and financial constraint in investment decisions: a Bayesian generalized ridge regression

This paper addresses the investment decisions considering the presence of financial constraints of 373 large Brazilian firms from 1997 to 2004, using panel data. A Bayesian econometric model was used considering ridge regression for multicollinearity problems among the variables in the model. Prior distributions are assumed for the parameters, classifying the model into random or fixed effects. We used a Bayesian approach to estimate the parameters, considering normal and Student t distributions for the error and assumed that the initial values for the lagged dependent variable are not fixed, but generated by a random process. The recursive predictive density criterion was used for model comparisons. Twenty models were tested and the results indicated that multicollinearity does influence the value of the estimated parameters. Controlling for capital intensity, financial constraints are found to be more important for capital-intensive firms, probably due to their lower profitability indexes, higher fixed costs and higher degree of property diversification.

Bayesian Model Averaging in the Instrumental Variable Regression Model

This paper considers the instrumental variable regression model when there is uncertainty about the set of instruments, exogeneity restrictions, the validity of identifying restrictions and the set of exogenous regressors. This uncertainty can result in a huge number of models. To avoid statistical problems associated with standard model selection procedures, we develop a reversible jump Markov chain Monte Carlo algorithm that allows us to do Bayesian model averaging. The algorithm is very exible and can be easily adapted to analyze any of the di¤erent priors that have been proposed in the Bayesian instrumental variables literature. We show how to calculate the probability of any relevant restriction (e.g. the posterior probability that over-identifying restrictions hold) and discuss diagnostic checking using the posterior distribution of discrepancy vectors. We illustrate our methods in a returns-to-schooling application.

A sparse kernel density estimation algorithm using forward constrained regression

Using the classical Parzen window (PW) estimate as the target function, the sparse kernel density estimator is constructed in a forward constrained regression manner. The leave-one-out (LOO) test score is used for kernel selection. The jackknife parameter estimator subject to positivity constraint check is used for the parameter estimation of a single parameter at each forward step. As such the proposed approach is simple to implement and the associated computational cost is very low. An illustrative example is employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with comparable accuracy to that of the classical Parzen window estimate.

Sparse kernel density estimator using orthogonal regression based on D-optimality experimental design

A novel sparse kernel density estimator is derived based on a regression approach, which selects a very small subset of significant kernels by means of the D-optimality experimental design criterion using an orthogonal forward selection procedure. The weights of the resulting sparse kernel model are calculated using the multiplicative nonnegative quadratic programming algorithm. The proposed method is computationally attractive, in comparison with many existing kernel density estimation algorithms. Our numerical results also show that the proposed method compares favourably with other existing methods, in terms of both test accuracy and model sparsity, for constructing kernel density estimates.

Sparse kernel density construction using orthogonal forward regression with leave-one-out test score and local regularization

This paper presents an efficient construction algorithm for obtaining sparse kernel density estimates based on a regression approach that directly optimizes model generalization capability. Computational efficiency of the density construction is ensured using an orthogonal forward regression, and the algorithm incrementally minimizes the leave-one-out test score. A local regularization method is incorporated naturally into the density construction process to further enforce sparsity. An additional advantage of the proposed algorithm is that it is fully automatic and the user is not required to specify any criterion to terminate the density construction procedure. This is in contrast to an existing state-of-art kernel density estimation method using the support vector machine (SVM), where the user is required to specify some critical algorithm parameter. Several examples are included to demonstrate the ability of the proposed algorithm to effectively construct a very sparse kernel density estimate with comparable accuracy to that of the full sample optimized Parzen window density estimate. Our experimental results also demonstrate that the proposed algorithm compares favorably with the SVM method, in terms of both test accuracy and sparsity, for constructing kernel density estimates.

An orthogonal forward regression technique for sparse kernel density estimation

Using the classical Parzen window (PW) estimate as the desired response, the kernel density estimation is formulated as a regression problem and the orthogonal forward regression technique is adopted to construct sparse kernel density (SKD) estimates. The proposed algorithm incrementally minimises a leave-one-out test score to select a sparse kernel model, and a local regularisation method is incorporated into the density construction process to further enforce sparsity. The kernel weights of the selected sparse model are finally updated using the multiplicative nonnegative quadratic programming algorithm, which ensures the nonnegative and unity constraints for the kernel weights and has the desired ability to reduce the model size further. Except for the kernel width, the proposed method has no other parameters that need tuning, and the user is not required to specify any additional criterion to terminate the density construction procedure. Several examples demonstrate the ability of this simple regression-based approach to effectively construct a SKID estimate with comparable accuracy to that of the full-sample optimised PW density estimate. (c) 2007 Elsevier B.V. All rights reserved.

Sparse modeling using orthogonal forward regression with PRESS statistic and regularization

The paper introduces an efficient construction algorithm for obtaining sparse linear-in-the-weights regression models based on an approach of directly optimizing model generalization capability. This is achieved by utilizing the delete-1 cross validation concept and the associated leave-one-out test error also known as the predicted residual sums of squares (PRESS) statistic, without resorting to any other validation data set for model evaluation in the model construction process. Computational efficiency is ensured using an orthogonal forward regression, but the algorithm incrementally minimizes the PRESS statistic instead of the usual sum of the squared training errors. A local regularization method can naturally be incorporated into the model selection procedure to further enforce model sparsity. The proposed algorithm is fully automatic, and the user is not required to specify any criterion to terminate the model construction procedure. Comparisons with some of the existing state-of-art modeling methods are given, and several examples are included to demonstrate the ability of the proposed algorithm to effectively construct sparse models that generalize well.

Sparse model identification using orthogonal forward regression with basis pursuit and D-optimality

An efficient model identification algorithm for a large class of linear-in-the-parameters models is introduced that simultaneously optimises the model approximation ability, sparsity and robustness. The derived model parameters in each forward regression step are initially estimated via the orthogonal least squares (OLS), followed by being tuned with a new gradient-descent learning algorithm based on the basis pursuit that minimises the l(1) norm of the parameter estimate vector. The model subset selection cost function includes a D-optimality design criterion that maximises the determinant of the design matrix of the subset to ensure model robustness and to enable the model selection procedure to automatically terminate at a sparse model. The proposed approach is based on the forward OLS algorithm using the modified Gram-Schmidt procedure. Both the parameter tuning procedure, based on basis pursuit, and the model selection criterion, based on the D-optimality that is effective in ensuring model robustness, are integrated with the forward regression. As a consequence the inherent computational efficiency associated with the conventional forward OLS approach is maintained in the proposed algorithm. Examples demonstrate the effectiveness of the new approach.