A Fully Bayesian Approach for Combining Multilevel Failure Information in Fault Tree Quantification and Corresponding Optimal Resource Allocation

This paper presents a fully Bayesian approach that simultaneously combines basic event and statistically independent higher event-level failure data in fault tree quantification. Such higher-level data could correspond to train, sub-system or system failure events. The full Bayesian approach also allows the highest-level data that are usually available for existing facilities to be automatically propagated to lower levels. A simple example illustrates the proposed approach. The optimal allocation of resources for collecting additional data from a choice of different level events is also presented. The optimization is achieved using a genetic algorithm.

Bayesian Markov chain Monte Carlo inversion of geophysical data for the purpose of estimating the hydraulic properties of the unsaturated zone

Ground-penetrating radar (GPR) has the potential to provide valuable information on hydrological properties of the vadose zone because of their strong sensitivity to soil water content. In particular, recent evidence has suggested that the stochastic inversion of crosshole GPR data within a coupled geophysical-hydrological framework may allow for effective estimation of subsurface van-Genuchten-Mualem (VGM) parameters and their corresponding uncertainties. An important and still unresolved issue, however, is how to best integrate GPR data into a stochastic inversion in order to estimate the VGM parameters and their uncertainties, thus improving hydrological predictions. Recognizing the importance of this issue, the aim of the research presented in this thesis was to first introduce a fully Bayesian inversion called Markov-chain-Monte-carlo (MCMC) strategy to perform the stochastic inversion of steady-state GPR data to estimate the VGM parameters and their uncertainties. Within this study, the choice of the prior parameter probability distributions from which potential model configurations are drawn and tested against observed data was also investigated. Analysis of both synthetic and field data collected at the Eggborough (UK) site indicates that the geophysical data alone contain valuable information regarding the VGM parameters. However, significantly better results are obtained when these data are combined with a realistic, informative prior. A subsequent study explore in detail the dynamic infiltration case, specifically to what extent time-lapse ZOP GPR data, collected during a forced infiltration experiment at the Arrenaes field site (Denmark), can help to quantify VGM parameters and their uncertainties using the MCMC inversion strategy. The findings indicate that the stochastic inversion of time-lapse GPR data does indeed allow for a substantial refinement in the inferred posterior VGM parameter distributions. In turn, this significantly improves knowledge of the hydraulic properties, which are required to predict hydraulic behaviour. Finally, another aspect that needed to be addressed involved the comparison of time-lapse GPR data collected under different infiltration conditions (i.e., natural loading and forced infiltration conditions) to estimate the VGM parameters using the MCMC inversion strategy. The results show that for the synthetic example, considering data collected during a forced infiltration test helps to better refine soil hydraulic properties compared to data collected under natural infiltration conditions. When investigating data collected at the Arrenaes field site, further complications arised due to model error and showed the importance of also including a rigorous analysis of the propagation of model error with time and depth when considering time-lapse data. Although the efforts in this thesis were focused on GPR data, the corresponding findings are likely to have general applicability to other types of geophysical data and field environments. Moreover, the obtained results allow to have confidence for future developments in integration of geophysical data with stochastic inversions to improve the characterization of the unsaturated zone but also reveal important issues linked with stochastic inversions, namely model errors, that should definitely be addressed in future research.

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. ^

The population pharmacokinetics of citalopram after deliberate self-poisoning: A Bayesian approach

Defining the pharmacokinetics of drugs in overdose is complicated. Deliberate self-poisoning is generally impulsive and associated with poor accuracy in dose history. In addition, early blood samples are rarely collected to characterize the whole plasma-concentration time profile and the effect of decontamination on the pharmacokinetics is uncertain. The aim of this study was to explore a fully Bayesian methodology for population pharmacokinetic analysis of data that arose from deliberate self-poisoning with citalopram. Prior information on the pharmacokinetic parameters was elicited from 14 published studies on citalopram when taken in therapeutic doses. The data set included concentration-time data from 53 patients studied after 63 citalopram overdose events (dose range: 20-1700 mg). Activated charcoal was administered between 0.5 and 4 h after 17 overdose events. The clinical investigator graded the veracity of the patients' dosing history on a 5-point ordinal scale. Inclusion of informative priors stabilised the pharmacokinetic model and the population mean values could be estimated well. There were no indications of non-linear clearance after excessive doses. The final model included an estimated uncertainty of the dose amount which in a simulation study was shown to not affect the model's ability to characterise the effects of activated charcoal. The effect of activated charcoal on clearance and bioavailability was pronounced and resulted in a 72% increase and 22% decrease, respectively. These findings suggest charcoal administration is potentially beneficial after citalopram overdose. The methodology explored seems promising for exploring the dose-exposure relationship in the toxicological settings.

Bayesian population pharmacokinetic analysis of sirolimus

Objective: It is usual that data collected from routine clinical care is sparse and unable to support the more complex pharmacokinetic (PK) models that may have been reported in previous rich data studies. Informative priors may be a pre-requisite for model development. The aim of this study was to estimate the population PK parameters of sirolimus using a fully Bayesian approach with informative priors. Methods: Informative priors including prior mean and precision of the prior mean were elicited from previous published studies using a meta-analytic technique. Precision of between-subject variability was determined by simulations from a Wishart distribution using MATLAB (version 6.5). Concentration-time data of sirolimus retrospectively collected from kidney transplant patients were analysed using WinBUGS (version 1.3). The candidate models were either one- or two-compartment with first order absorption and first order elimination. Model discrimination was based on computation of the posterior odds supporting the model. Results: A total of 315 concentration-time points were obtained from 25 patients. Most data were clustered at trough concentrations with range of 1.6 to 77 hours post-dose. Using informative priors, either a one- or two-compartment model could be used to describe the data. When a one-compartment model was applied, information was gained from the data for the value of apparent clearance (CL/F = 18.5 L/h), and apparent volume of distribution (V/F = 1406 L) but no information was gained about the absorption rate constant (ka). When a two-compartment model was fitted to the data, the data were informative about CL/F, apparent inter-compartmental clearance, and apparent volume of distribution of the peripheral compartment (13.2 L/h, 20.8 L/h, and 579 L, respectively). The posterior distribution of the volume distribution of central compartment and ka were the same as priors. The posterior odds for the two-compartment model was 8.1, indicating the data supported the two-compartment model. Conclusion: The use of informative priors supported the choice of a more complex and informative model that would otherwise have not been supported by the sparse data.

Determinação da prevalência de fibrilhação auricular na população portuguesa ao nível da NUTS III usando modelos hierárquicos bayesianos

A Fibrilhação Auricular é uma alteração do ritmo cardíaco designada por arritmia. Esta patologia é considerada a forma de arritmia mais frequentemente observada na prática clínica e que constitui uma importante causa de morbilidade pelo risco inerente de desenvolvimento de AVC. Em 2010 foi realizado um estudo epidemiológico na população Portuguesa com o objectivo determinar a prevalência de Fibrilhação Auricular na população portuguesa com idade igual ou superior a 40 anos, sob o acrónimo de FAMA. Os dados publicados indicaram uma estimativa de prevalência de 2,5%, com um aumento da prevalência em função da classe etária. A nível regional não foram observadas diferenças na taxa de prevalência. Estudos de mapeamento de doenças mostraram que a determinação de taxas de prevalência por região, quando o número de casos observados é relativamente baixo, apresentam sobredispersão e, consequentemente, uma falta de precisão nas estimativas obtidas através um método frequencista clássico. A utilização de modelos Bayesianos hierárquicos no mapeamento de doenças tem apresentado vantagem na estimação de valores de risco da doença comparativamente à abordagem clássica. Assim, é objectivo deste trabalho determinar a prevalência de Fibrilhação Auricular na população Portuguesa por região, ao nível da NUTS III, usando modelos hierárquicos Bayesianos. Os dados utilizados neste estudo são os dados referentes ao estudo FAMA, pós-estratificados para correcção dos ponderadores. O modelo Bayesiano proposto por Besag, York e Mollié (1991) foi usado para modelar os dados, covariando para a idade e índice de massa corporal. A revisão do desenho do estudo e o recálculo dos ponderadores foi realizado com recurso ao software R, survey, e a análise Bayesiana efectuada através do WinBugs. iii Os resultados deste estudo demonstram que o uso de modelos Bayesianos são uma melhor opção para a estimação de valores risco relativo e prevalência da doença. Contudo, a utilização de covariáveis não resultou numa melhoria considerável ao contrário do que seria esperado. Conclui-se que a Fibrilhação Auricular apresenta variações regionais significativas, a nível de NUTS III, que não devem ser desvalorizadas na determinação de políticas de saúde pública para controle da doença.

From Empirical Bayes to Full Bayes: Methods for Analysing Traffice Safety Data, October 25, 2004

Traffic safety engineers are among the early adopters of Bayesian statistical tools for analyzing crash data. As in many other areas of application, empirical Bayes methods were their first choice, perhaps because they represent an intuitively appealing, yet relatively easy to implement alternative to purely classical approaches. With the enormous progress in numerical methods made in recent years and with the availability of free, easy to use software that permits implementing a fully Bayesian approach, however, there is now ample justification to progress towards fully Bayesian analyses of crash data. The fully Bayesian approach, in particular as implemented via multi-level hierarchical models, has many advantages over the empirical Bayes approach. In a full Bayesian analysis, prior information and all available data are seamlessly integrated into posterior distributions on which practitioners can base their inferences. All uncertainties are thus accounted for in the analyses and there is no need to pre-process data to obtain Safety Performance Functions and other such prior estimates of the effect of covariates on the outcome of interest. In this slight, fully Bayesian methods may well be less costly to implement and may result in safety estimates with more realistic standard errors. In this manuscript, we present the full Bayesian approach to analyzing traffic safety data and focus on highlighting the differences between the empirical Bayes and the full Bayes approaches. We use an illustrative example to discuss a step-by-step Bayesian analysis of the data and to show some of the types of inferences that are possible within the full Bayesian framework.

From Empirical Bayes to Full Bayes: Methods for Analyzubg Traffic Safey Data, October 25, 2004

Traffic safety engineers are among the early adopters of Bayesian statistical tools for analyzing crash data. As in many other areas of application, empirical Bayes methods were their first choice, perhaps because they represent an intuitively appealing, yet relatively easy to implement alternative to purely classical approaches. With the enormous progress in numerical methods made in recent years and with the availability of free, easy to use software that permits implementing a fully Bayesian approach, however, there is now ample justification to progress towards fully Bayesian analyses of crash data. The fully Bayesian approach, in particular as implemented via multi-level hierarchical models, has many advantages over the empirical Bayes approach. In a full Bayesian analysis, prior information and all available data are seamlessly integrated into posterior distributions on which practitioners can base their inferences. All uncertainties are thus accounted for in the analyses and there is no need to pre-process data to obtain Safety Performance Functions and other such prior estimates of the effect of covariates on the outcome of interest. In this light, fully Bayesian methods may well be less costly to implement and may result in safety estimates with more realistic standard errors. In this manuscript, we present the full Bayesian approach to analyzing traffic safety data and focus on highlighting the differences between the empirical Bayes and the full Bayes approaches. We use an illustrative example to discuss a step-by-step Bayesian analysis of the data and to show some of the types of inferences that are possible within the full Bayesian framework.

Estimation of population growth or decline in genetically monitored populations

This article introduces a new general method for genealogical inference that samples independent genealogical histories using importance sampling (IS) and then samples other parameters with Markov chain Monte Carlo (MCMC). It is then possible to more easily utilize the advantages of importance sampling in a fully Bayesian framework. The method is applied to the problem of estimating recent changes in effective population size from temporally spaced gene frequency data. The method gives the posterior distribution of effective population size at the time of the oldest sample and at the time of the most recent sample, assuming a model of exponential growth or decline during the interval. The effect of changes in number of alleles, number of loci, and sample size on the accuracy of the method is described using test simulations, and it is concluded that these have an approximately equivalent effect. The method is used on three example data sets and problems in interpreting the posterior densities are highlighted and discussed.

Modelos dinâmicos e simulação estocástica

This paper presents new methodology for making Bayesian inference about dy~ o!s for exponential famiIy observations. The approach is simulation-based _~t> use of ~vlarkov chain Monte Carlo techniques. A yletropolis-Hastings i:U~UnLlllll 1::; combined with the Gibbs sampler in repeated use of an adjusted version of normal dynamic linear models. Different alternative schemes are derived and compared. The approach is fully Bayesian in obtaining posterior samples for state parameters and unknown hyperparameters. Illustrations to real data sets with sparse counts and missing values are presented. Extensions to accommodate for general distributions for observations and disturbances. intervention. non-linear models and rnultivariate time series are outlined.

A new snowfall detection algorithm for high latitude regions based on a combination of active and passive sensors

Precipitation retrieval over high latitudes, particularly snowfall retrieval over ice and snow, using satellite-based passive microwave spectrometers, is currently an unsolved problem. The challenge results from the large variability of microwave emissivity spectra for snow and ice surfaces, which can mimic, to some degree, the spectral characteristics of snowfall. This work focuses on the investigation of a new snowfall detection algorithm specific for high latitude regions, based on a combination of active and passive sensors able to discriminate between snowing and non snowing areas. The space-borne Cloud Profiling Radar (on CloudSat), the Advanced Microwave Sensor units A and B (on NOAA-16) and the infrared spectrometer MODIS (on AQUA) have been co-located for 365 days, from October 1st 2006 to September 30th, 2007. CloudSat products have been used as truth to calibrate and validate all the proposed algorithms. The methodological approach followed can be summarised into two different steps. In a first step, an empirical search for a threshold, aimed at discriminating the case of no snow, was performed, following Kongoli et al. [2003]. This single-channel approach has not produced appropriate results, a more statistically sound approach was attempted. Two different techniques, which allow to compute the probability above and below a Brightness Temperature (BT) threshold, have been used on the available data. The first technique is based upon a Logistic Distribution to represent the probability of Snow given the predictors. The second technique, defined Bayesian Multivariate Binary Predictor (BMBP), is a fully Bayesian technique not requiring any hypothesis on the shape of the probabilistic model (such as for instance the Logistic), which only requires the estimation of the BT thresholds. The results obtained show that both methods proposed are able to discriminate snowing and non snowing condition over the Polar regions with a probability of correct detection larger than 0.5, highlighting the importance of a multispectral approach.

HHV-8 seroprevalence: a global view

BACKGROUND Human herpes virus 8 (HHV-8) is the underlying infectious cause of Kaposi sarcoma (KS) and other proliferative diseases; that is, primary effusion lymphoma and multicentric Castleman disease. In regions with high HHV-8 seroprevalence in the general population, KS accounts for a major burden of disease. Outside these endemic regions, HHV-8 prevalence is high in men who have sex with men (MSM) and in migrants from endemic regions. We aim to conduct a systematic literature review and meta-analysis in order 1) to define the global distribution of HHV-8 seroprevalence (primary objective) and 2) to identify risk factors for HHV-8 infection, with a focus on HIV status (secondary objective). METHODS/DESIGN We will include observational studies reporting data on seroprevalence of HHV-8 in children and/or adults from any region in the world. Case reports and case series as well as any studies with fewer than 50 participants will be excluded. We will search MEDLINE, EMBASE, and relevant conference proceedings without language restriction. Two reviewers will independently screen the identified studies and extract data on study characteristics and quality, study population, risk factors, and reported outcomes, using a standardized form. For the primary objective we will pool the data using a fully bayesian approach for meta-analysis, with random effects at the study level. For the secondary objective (association of HIV and HHV-8) we aim to pool odds ratios for the association of HIV and HHV-8 using a fully bayesian approach for meta-analysis, with random effects at the study level. Sub-group analyses and meta-regression analyses will be used to explore sources of heterogeneity, including factors such as geographical region, calendar years of recruitment, age, gender, ethnicity, socioeconomic status, different risk groups for sexually and parenterally transmitted infections (MSM, sex workers, hemophiliacs, intravenous drug users), comorbidities such as organ transplantation and malaria, test(s) used to measure HHV-8 infection, study design, and study quality. DISCUSSION Using the proposed systematic review and meta-analysis, we aim to better define the global seroprevalence of HHV-8 and its associated risk factors. This will improve the current understanding of HHV-8 epidemiology, and could suggest measures to prevent HHV-8 infection and to reduce its associated cancer burden.

SURVIVAL PREDICTION FOR BRAIN TUMOR PATIENTS USING GENE EXPRESSION DATA

Brain tumor is one of the most aggressive types of cancer in humans, with an estimated median survival time of 12 months and only 4% of the patients surviving more than 5 years after disease diagnosis. Until recently, brain tumor prognosis has been based only on clinical information such as tumor grade and patient age, but there are reports indicating that molecular profiling of gliomas can reveal subgroups of patients with distinct survival rates. We hypothesize that coupling molecular profiling of brain tumors with clinical information might improve predictions of patient survival time and, consequently, better guide future treatment decisions. In order to evaluate this hypothesis, the general goal of this research is to build models for survival prediction of glioma patients using DNA molecular profiles (U133 Affymetrix gene expression microarrays) along with clinical information. First, a predictive Random Forest model is built for binary outcomes (i.e. short vs. long-term survival) and a small subset of genes whose expression values can be used to predict survival time is selected. Following, a new statistical methodology is developed for predicting time-to-death outcomes using Bayesian ensemble trees. Due to a large heterogeneity observed within prognostic classes obtained by the Random Forest model, prediction can be improved by relating time-to-death with gene expression profile directly. We propose a Bayesian ensemble model for survival prediction which is appropriate for high-dimensional data such as gene expression data. Our approach is based on the ensemble "sum-of-trees" model which is flexible to incorporate additive and interaction effects between genes. We specify a fully Bayesian hierarchical approach and illustrate our methodology for the CPH, Weibull, and AFT survival models. We overcome the lack of conjugacy using a latent variable formulation to model the covariate effects which decreases computation time for model fitting. Also, our proposed models provides a model-free way to select important predictive prognostic markers based on controlling false discovery rates. We compare the performance of our methods with baseline reference survival methods and apply our methodology to an unpublished data set of brain tumor survival times and gene expression data, selecting genes potentially related to the development of the disease under study. A closing discussion compares results obtained by Random Forest and Bayesian ensemble methods under the biological/clinical perspectives and highlights the statistical advantages and disadvantages of the new methodology in the context of DNA microarray data analysis.

Representation via Probabilities: Models of Probabilistic Modeling

How do probabilistic models represent their targets and how do they allow us to learn about them? The answer to this question depends on a number of details, in particular on the meaning of the probabilities involved. To classify the options, a minimalist conception of representation (Su\'arez 2004) is adopted: Modelers devise substitutes (``sources'') of their targets and investigate them to infer something about the target. Probabilistic models allow us to infer probabilities about the target from probabilities about the source. This leads to a framework in which we can systematically distinguish between different models of probabilistic modeling. I develop a fully Bayesian view of probabilistic modeling, but I argue that, as an alternative, Bayesian degrees of belief about the target may be derived from ontic probabilities about the source. Remarkably, some accounts of ontic probabilities can avoid problems if they are supposed to apply to sources only.

Analysis of population pharmacokinetic data using NONMEM and WinBUGS

The aim of this report is to describe the use of WinBUGS for two datasets that arise from typical population pharmacokinetic studies. The first dataset relates to gentamicin concentration-time data that arose as part of routine clinical care of 55 neonates. The second dataset incorporated data from 96 patients receiving enoxaparin. Both datasets were originally analyzed by using NONMEM. In the first instance, although NONMEM provided reasonable estimates of the fixed effects parameters it was unable to provide satisfactory estimates of the between-subject variance. In the second instance, the use of NONMEM resulted in the development of a successful model, albeit with limited available information on the between-subject variability of the pharmacokinetic parameters. WinBUGS was used to develop a model for both of these datasets. Model comparison for the enoxaparin dataset was performed by using the posterior distribution of the log-likelihood and a posterior predictive check. The use of WinBUGS supported the same structural models tried in NONMEM. For the gentamicin dataset a one-compartment model with intravenous infusion was developed, and the population parameters including the full between-subject variance-covariance matrix were available. Analysis of the enoxaparin dataset supported a two compartment model as superior to the one-compartment model, based on the posterior predictive check. Again, the full between-subject variance-covariance matrix parameters were available. Fully Bayesian approaches using MCMC methods, via WinBUGS, can offer added value for analysis of population pharmacokinetic data.