Incidence and control of black spot syndrome of tiger nut

Tiger nut (Cyperus esculentum) is a very profitable crop in Valencia, Spain, but in the last years, part of the harvested tubers presents black spots in the skin making them unmarketable. Surveys performed in two consecutive years showed that about 10% of the tubers were severely affected by the black spot syndrome whose aetiology is unknown. Disease control procedures based on selection of tubers used as seed (seed tubers) or treatment with hot-water and/or chemicals were assayed in greenhouse. These assays showed that that this syndrome had a negative impact on the germination rate, tuber size and yield. Selection of asymptomatic seed tubers reduced drastically the incidence of the black …

Bayesian joint models for longitudinal and survival data

This paper takes a quick look at Bayesian joint models (BJM) for longitudinal and survival data. A general formulation for BJM is examined in terms of the sampling distribution of the longitudinal and survival processes, the conditional distribution of the random effects and the prior distribution. Next a basic BJM defined in terms of a mixed linear model and a Cox survival regression models is discussed and some extensions and other Bayesian topics are briefly outlined.

Sequential Monte Carlo Methods in Random Intercept Models for Longitudinal Data

Longitudinal modelling is common in the field of Biostatistical research. In some studies, it becomes mandatory to update posterior distributions based on new data in order to perform inferential process on-line. In such situations, the use of posterior distribution as the prior distribution in the new application of the Bayes’ theorem is sensible. However, the analytic form of the posterior distribution is not always available and we only have an approximated sample of it, thus making the process “not-so-easy”. Equivalent inferences could be obtained through a Bayesian inferential process based on the set that integrates the old and new data. Nevertheless, this is not always a real alterna…

The Chronology of Archaeological Assemblages Based on Automatic Bayesian Procedure: Eastern Iberia as Study Case

The purpose of this work is to show an automatic Bayesian procedure to obtain accurate chronological information of archaeological assemblages characterized by palimpsest or neither radiocarbon dates and whose temporal information comes only from bifacial flint arrowheads.In this work, a classification based on the Dirichlet-multinomial inferential process and its posterior predictive probability distribution are applied. Its purpose is to predict the chronological period of archaeological assemblages (levels or sites) based on the predictive probability distribution of each bifacial flint arrowhead types defined in the Eastern Iberia during the 4th and 3rd millennium cal BC. The results of…

Bayesian survival analysis with BUGS

Survival analysis is one of the most important fields of statistics in medicine and biological sciences. In addition, the computational advances in the last decades have favored the use of Bayesian methods in this context, providing a flexible and powerful alternative to the traditional frequentist approach. The objective of this article is to summarize some of the most popular Bayesian survival models, such as accelerated failure time, proportional hazards, mixture cure, competing risks, multi-state, frailty, and joint models of longitudinal and survival data. Moreover, an implementation of each presented model is provided using a BUGS syntax that can be run with JAGS from the R programmin…

Bayesian joint modeling of bivariate longitudinal and competing risks data: An application to study patient-ventilator asynchronies in critical care patients

Mechanical ventilation is a common procedure of life support in intensive care. Patient-ventilator asynchronies (PVAs) occur when the timing of the ventilator cycle is not simultaneous with the timing of the patient respiratory cycle. The association between severity markers and the events death or alive discharge has been acknowledged before, however, little is known about the addition of PVAs data to the analyses. We used an index of asynchronies (AI) to measure PVAs and the SOFA (sequential organ failure assessment) score to assess overall severity. To investigate the added value of including the AI, we propose a Bayesian joint model of bivariate longitudinal and competing risks data. Th…

Data Analysis Using Hierarchical Generalized Linear Models with R

Bootstrapping profit change: An application to Spanish banks

The aim of this study is to provide a tool which enables us to conduct statistical analysis in the context of changes in productivity and profit. We build on previous initiatives to decompose profit change into mutually exclusive and exhaustive sources. To do this we use distance functions, which are calculated empirically using linear programming techniques. However, we may not learn a great deal by solving these linear programs unless methods of statistical analysis are used to examine the properties of the relevant estimators. Our purpose is to provide a methodology based on bootstrap that allows us to conduct statistical inference for the profit change decomposition. Thus, it will be po…

Sensitivity analysis of efficiency and Malmquist productivity indices: An application to Spanish savings banks

Hypothesis testing and statistical precision in the context of non-parametric efficiency and productivity measurement have been investigated since the early 1990s. Recent contributions focus on this matter through the use of resampling methods-i.e., bootstrapping techniques. However, empirical evidence is still practically non-existent. This gap is more noticeable in the case of banking efficiency studies, where the literature is immense. In this work, we explore productivity growth and productive efficiency for Spanish savings banks over the (initial) post-deregulation period 1992-1998 using Data Envelopment Analysis (DEA) and bootstrapping techniques. Results show that productivity growth…

Modeling the isothermal inactivation curves of Listeria innocua CECT 910 in a vegetable beverage under low-temperature treatments and different pH levels

Thermal inactivation kinetics of Listeria innocua CECT 910 inoculated in a vegetable beverage at three pH conditions (4.25, 4.75, and 5.20), four levels of temperature (50, 55, 60, 65℃), and different treatment times (0–75 min) were obtained. Survival curves did not follow a log-linear relationship and consequently were fitted to various mathematical models: Weibull, Geeraerd, Cerf with shoulder, and the modified Gompertz equation. Results indicated that the best model for the treatment conditions was the modified Gompertz equation, which provides the best goodness-of-fit and the lowest Akaike information criterion value. Sensitivity analysis indicated that the most influential factors affe…

Bayesian inference in Markovian queues

This paper is concerned with the Bayesian analysis of general queues with Poisson input and exponential service times. Joint posterior distribution of the arrival rate and the individual service rate is obtained from a sample consisting inn observations of the interarrival process andm complete service times. Posterior distribution of traffic intensity inM/M/c is also obtained and the statistical analysis of the ergodic condition from a decision point of view is discussed.

S. Typhimurium virulence changes caused by exposure to different non-thermal preservation treatments using C. elegans

The aims of this research study were: (i) to postulate Caenorhabditis elegans (C. elegans) as a useful organism to describe infection by Salmonella enterica serovar Typhimurium (S. Typhimurium), and (ii) to evaluate changes in virulence of S. Typhimurium when subjected repetitively to different antimicrobial treatments. Specifically, cauliflower by-product infusion, High Hydrostatic Pressure (HHP), and Pulsed Electric Fields (PEF). This study was carried out by feeding C. elegans with different microbial populations: E. coli OP50 (optimal conditions), untreated S. Typhimurium, S. Typhimurium treated once and three times with cauliflower by-product infusion, S. Typhimurium treated once and f…

Bayesian classification for dating archaeological sites via projectile points

Dating is a key element for archaeologists. We propose a Bayesian approach to provide chronology to sites that have neither radiocarbon dating nor clear stratigraphy and whose only information comes from lithic arrowheads. This classifier is based on the Dirichlet-multinomial inferential process and posterior predictive distributions. The procedure is applied to predict the period of a set of undated sites located in the east of the Iberian Peninsula during the IVth and IIIrd millennium cal. BC.

Two-Stage Bayesian Approach for GWAS With Known Genealogy

Genome-wide association studies (GWAS) aim to assess relationships between single nucleotide polymorphisms (SNPs) and diseases. They are one of the most popular problems in genetics, and have some peculiarities given the large number of SNPs compared to the number of subjects in the study. Individuals might not be independent, especially in animal breeding studies or genetic diseases in isolated populations with highly inbred individuals. We propose a family-based GWAS model in a two-stage approach comprising a dimension reduction and a subsequent model selection. The first stage, in which the genetic relatedness between the subjects is taken into account, selects the promising SNPs. The se…

An Ordinal Joint Model for Breast Cancer

We propose a Bayesian joint model to analyze the association between longitudinal measurements of an ordinal marker and time to a relevant event. The longitudinal process is defined in terms of a proportional-odds cumulative logit model and the time-to-event process through a left-truncated Cox proportional hazards model with information of the longitudinal marker and baseline covariates. Both longitudinal and survival processes are connected by a common vector of random effects.

Frequentist and Bayesian approaches for a joint model for prostate cancer risk and longitudinal prostate-specific antigen data

The paper describes the use of frequentist and Bayesian shared-parameter joint models of longitudinal measurements of prostate-specific antigen (PSA) and the risk of prostate cancer (PCa). The motivating dataset corresponds to the screening arm of the Spanish branch of the European Randomized Screening for Prostate Cancer study. The results show that PSA is highly associated with the risk of being diagnosed with PCa and that there is an age-varying effect of PSA on PCa risk. Both the frequentist and Bayesian paradigms produced very close parameter estimates and subsequent 95% confidence and credibility intervals. Dynamic estimations of disease-free probabilities obtained using Bayesian infe…

Inference and prediction in bulk arrival queues and queues with service in stages

This paper deals with the statistical analysis from a Bayesian point of view, of bulk arrival queues where the batch size is considered as a fixed constant. The focus is on prediction of the usual measures of performance of the system in the steady state. The probability generating function of the posterior predictive distribution of the number of customers in the system and the Laplace transform of the posterior predictive distribution of the waiting time in the system are obtained. Numerical inversion of these transforms is considered. Inference and prediction of its equivalent single queue with service in stages is also discussed.

Understanding disease mechanisms with models of signaling pathway activities

Background Understanding the aspects of the cell functionality that account for disease or drug action mechanisms is one of the main challenges in the analysis of genomic data and is on the basis of the future implementation of precision medicine. Results Here we propose a simple probabilistic model in which signaling pathways are separated into elementary sub-pathways or signal transmission circuits (which ultimately trigger cell functions) and then transforms gene expression measurements into probabilities of activation of such signal transmission circuits. Using this model, differential activation of such circuits between biological conditions can be estimated. Thus, circuit activation s…

Bayesian Immature Survival Analysis of the Largest Colony of Common Murre (Uria aalge) in the Baltic Sea

In long-lived species, such as seabirds, immature survival is the most important life history parameter after adult survival. The assessment of immature survival has often been difficult due to extended periods in which young birds remain unobservable at sea. This study presents results on survival of immature Common Murre (Uria aalge) obtained from an extensive mark-recapture study of a large colony at Stora Karlso in the Baltic Sea, Sweden. This colony, in contrast with other colonies, has the unique feature that many 1-year-old birds return to the colony (12%). Between 2006 and 2016, 28,930 chicks were marked at fledging, of which 5,493 individuals were later resighted in the colony. Ann…

Sequential Monte Carlo methods in Bayesian joint models for longitudinal and time-to-event data

The statistical analysis of the information generated by medical follow-up is a very important challenge in the field of personalized medicine. As the evolutionary course of a patient's disease progresses, his/her medical follow-up generates more and more information that should be processed immediately in order to review and update his/her prognosis and treatment. Hence, we focus on this update process through sequential inference methods for joint models of longitudinal and time-to-event data from a Bayesian perspective. More specifically, we propose the use of sequential Monte Carlo (SMC) methods for static parameter joint models with the intention of reducing computational time in each…

Bayesian design in queues: An application to aeronautic maintenance

We exploit Bayesian criteria for designing M/M/c//r queueing systems with spares. For illustration of our approach we use a real problem from aeronautic maintenance, where the numbers of repair crews and spare planes must be sufficiently large to meet the necessary operational capacity. Bayesian guarantees for this to happen can be given using predictive or posterior distributions.

A Bayesian analysis of a queueing system with unlimited service

Abstract A queueing system occurs when “customers” arrive at some facility requiring a certain type of “service” provided by the “servers”. Both the arrival pattern and the service requirements are usually taken to be random. If all the servers are busy when customers arrive, they usually wait in line to get served. Queues possess a number of mathematical challenges and have been mainly approached from a probability point of view, and statistical analysis are very scarce. In this paper we present a Bayesian analysis of a Markovian queue in which customers are immediately served upon arrival, and hence no waiting lines form. Emergency and self-service facilities provide many examples. Techni…

Bayesian approach to urinary ESBL-producing Escherichia coli

This is a retrospective study about the prevalence of ESBL-producing Escherichia coli (EEC) in urinary specimens from patients from the Comunitat Valenciana from January 2007 to December 2008. Data were retrieved from RedMIVA, and Bayesian generalized linear mixed models were considered to study the prevalence of EEC with regard to demographical and microbiological factors. The total number of infections considered was 164,502, the amount of urinary isolates was 70,827 belonging to 49,304 different patients, and 5,161 (7.3%) of the urinary isolates were EEC. Three out of four E. coli were isolated in women (76.8%), men showed higher rates of EEC (9.7% in men vs. 6.5% in women). EEC patients…

Bayesian prediction inM/M/1 queues

Simple queues with Poisson input and exponential service times are considered to illustrate how well-suited Bayesian methods are used to handle the common inferential aims that appear when dealing with queue problems. The emphasis will mainly be placed on prediction; in particular, we study the predictive distribution of usual measures of effectiveness in anM/M/1 queue system, such as the number of customers in the queue and in the system, the waiting time in the queue and in the system, the length of an idle period and the length of a busy period.

Simulation in the Simple Linear Regression Model

Summary This article presents an activity which simulates the linear regression model in order to verify the probabilistic behaviour of the resulting least-squares statistics in practice.

Bayesian longitudinal models for exploring European sardine fishing in the Mediterranean Sea

In the Mediterranean Sea, catches are dominated by small pelagic fish, representing nearly the 49\% of the total harvest. Among them, the European sardine (Sardina pilchardus) is one of the most commercially important species showing high over-exploitation rates in recent last years. In this study we analysed the European sardine landings in the Mediterranean Sea from 1970 to 2014. We made use of Bayesian longitudinal linear mixed models in order to assess differences in the temporal evolution of fishing between and within countries. Furthermore, we modelled the subsequent joint evolution of artisanal and industrial fisheries. Overall results confirmed that Mediterranean fishery time series…

Bayesian analysis of a disability model for lung cancer survival

Bayesian reasoning, survival analysis and multi-state models are used to assess survival times for Stage IV non-small-cell lung cancer patients and the evolution of the disease over time. Bayesian estimation is done using minimum informative priors for the Weibull regression survival model, leading to an automatic inferential procedure. Markov chain Monte Carlo methods have been used for approximating posterior distributions and the Bayesian information criterion has been considered for covariate selection. In particular, the posterior distribution of the transition probabilities, resulting from the multi-state model, constitutes a very interesting tool which could be useful to help oncolog…

Bayesian methods in cost-effectiveness studies: objectivity, computation and other relevant aspects.

In a probabilistic sensitivity analysis (PSA) of a cost-effectiveness (CE) study, the unknown parameters are considered as random variables. A crucial question is what probabilistic distribution is suitable for synthesizing the available information (mainly data from clinical trials) about these parameters. In this context, the important role of Bayesian methodology has been recognized, where the parameters are of a random nature. We explore, in the context of CE analyses, how formal objective Bayesian methods can be implemented. We fully illustrate the methodology using two CE problems that frequently appear in the CE literature. The results are compared with those obtained with other popu…

A Bayesian hidden Markov model for assessing the hot hand phenomenon in basketball shooting performance

Sports data analytics is a relevant topic in applied statistics that has been growing in importance in recent years. In basketball, a player or team has a hot hand when their performance during a match is better than expected or they are on a streak of making consecutive shots. This phenomenon has generated a great deal of controversy with detractors claiming its non-existence while other authors indicate its evidence. In this work, we present a Bayesian longitudinal hidden Markov model that analyses the hot hand phenomenon in consecutive basketball shots, each of which can be either missed or made. Two possible states (cold or hot) are assumed in the hidden Markov chains of events, and the…

Bayesian joint modeling for assessing the progression of chronic kidney disease in children.

Joint models are rich and flexible models for analyzing longitudinal data with nonignorable missing data mechanisms. This article proposes a Bayesian random-effects joint model to assess the evolution of a longitudinal process in terms of a linear mixed-effects model that accounts for heterogeneity between the subjects, serial correlation, and measurement error. Dropout is modeled in terms of a survival model with competing risks and left truncation. The model is applied to data coming from ReVaPIR, a project involving children with chronic kidney disease whose evolution is mainly assessed through longitudinal measurements of glomerular filtration rate.

Bayesian joint ordinal and survival modeling for breast cancer risk assessment

We propose a joint model to analyze the structure and intensity of the association between longitudinal measurements of an ordinal marker and time to a relevant event. The longitudinal process is defined in terms of a proportional-odds cumulative logit model. Time-to-event is modeled through a left-truncated proportionalhazards model, which incorporates information of the longitudinal marker as well as baseline covariates. Both longitudinal and survival processes are connected by means of a common vector of random effects. General inferences are discussed under the Bayesian approach and include the posterior distribution of the probabilities associated to each longitudinal category and the …

Bayesian assessment of times to diagnosis in breast cancer screening

Breast cancer is one of the diseases with the most profound impact on health in developed countries and mammography is the most popular method for detecting breast cancer at a very early stage. This paper focuses on the waiting period from a positive mammogram until a confirmatory diagnosis is carried out in hospital. Generalized linear mixed models are used to perform the statistical analysis, always within the Bayesian reasoning. Markov chain Monte Carlo algorithms are applied for estimation by simulating the posterior distribution of the parameters and hyperparameters of the model through the free software WinBUGS.

Analysis of the renal transplant waiting list in the País Valencià (Spain).

In this paper we analyse the renal transplant waiting list of the Pais Valencia in Spain, using Queueing theory. The customers of this queue are patients with end-stage renal failure waiting for a kidney transplant. We set up a simplified model to represent the flow of the customers through the system, and perform Bayesian inference to estimate parameters in the model. Finally, we consider several scenarios by tuning the estimations achieved and computationally simulate the behaviour of the queue under each one. The results indicate that the system could reach equilibrium at some point in the future and the model forecasts a slow decrease in the size of the waiting list in the short and mid…

Bayesian correlated models for assessing the prevalence of viruses in organic and non-organic agroecosystems

Cultivation of horticultural species under organic management has increased in importance in recent years. However, the sustainability of this new production method needs to be supported by scientific research, especially in the field of virology. We studied the prevalence of three important virus diseases in agroecosystems with regard to its management system: organic versus non-organic, with and without greenhouse. Prevalence was assessed by means of a Bayesian correlated binary model which connects the risk of infection of each virus within the same plot and was defined in terms of a logit generalized linear mixed model (GLMM). Model robustness was checked through a sensitivity analysis …

Re: Antimicrobial Resistance in More Than 100,000 Escherichia coli Isolates According to Culture Site and Patient Age, Gender, and Location

ABSTRACT Escherichia coli and the antimicrobial pressure exerted on this microorganism can be modulated by factors dependent on the host. In this paper, we describe the distribution of antimicrobial resistance to amikacin, tobramycin, ampicillin, amoxicillin clavulanate, cefuroxime, cefoxitin, cefotaxime, imipenem, ciprofloxacin, fosfomycin, nitrofurantoin, and trimetoprim-sulfametoxazole in more than 100,000 E. coli isolates according to culture site and patient age, gender, and location. Bayesian inference was planned in all statistical analysis, and Markov chain Monte Carlo simulation was employed to estimate the model parameters. Our findings show the existence of a marked difference in…

Síntomas, signos y estadística: Aplicaciones de la estadística en ciencias de la salud y de la vida

La determinación o constatación experimental de los mecanismos fisiológicos de las enfermedades suele ser una tarea muy compleja. Esto ha convertido a la epidemiología en la principal herramienta de generación de conocimiento en el ámbito médico. La epidemiología aprende sobre las enfermedades a partir de la observación de la salud en colectivos de personas, en lugar de la observación individual de éstas. Si la principal herramienta de generación de conocimiento médico se basa en la observación de colectivos de personas (muestras de una población) de las que querremos aprender (hacer inferencia), resulta claro el nexo entre la estadística y la medicina. A lo largo de este artículo ilustramo…

Bayesian regularization for flexible baseline hazard functions in Cox survival models.

Fully Bayesian methods for Cox models specify a model for the baseline hazard function. Parametric approaches generally provide monotone estimations. Semi-parametric choices allow for more flexible patterns but they can suffer from overfitting and instability. Regularization methods through prior distributions with correlated structures usually give reasonable answers to these types of situations. We discuss Bayesian regularization for Cox survival models defined via flexible baseline hazards specified by a mixture of piecewise constant functions and by a cubic B-spline function. For those "semi-parametric" proposals, different prior scenarios ranging from prior independence to particular c…

Geographical variation in pharmacological prescription

Promoting rational drug administration in treatments is one of the most important issues in Public Health. Bayesian hierarchical models are a very useful tool for incorporating geographical information into the analysis of pharmacological prescription data. They allow the mapping of spatial components which express the trend of geographical variation. In addition, these models are able to deal with uncertainty in a sequential way through prior distributions on parameters and hyperparameters. Bayes' theorem combines all types of information and provides the posterior distribution which is computed through Markov Chain Monte Carlo (MCMC) simulation methods. Simulated data for pharmacological …

Bayesian hierarchical nonlinear modelling of intra-abdominal volume during pneumoperitoneum for laparoscopic surgery

Laparoscopy is an operation carried out in the abdomen or pelvis through small incisions with external visual control by a camera. This technique needs the abdomen to be insufflated with carbon dioxide to obtain a working space for surgical instruments' manipulation. Identifying the critical point at which insufflation should be limited is crucial to maximizing surgical working space and minimizing injurious effects. Bayesian nonlinear growth mixed-effects models are applied to data coming from a repeated measures design. This study allows to assess the relationship between the insufflation pressure and the intra--abdominal volume.

A probabilistic expert system for predicting the risk of Legionella in evaporative installations

Research highlights? The bacterium Legionella usually lives in water sources such as cooling towers. ? We discuss a probabilistic expert system for predicting the risk of Legionella. ? The expert system has a master-slave architecture. ? The inference engine is implemented through Bayesian reasoning. ? Bayesian networks model and connect relationships for chemical and physical variables. Early detection in water evaporative installations is one of the keys to fighting against the bacterium Legionella, the main cause of Legionnaire's disease. This paper discusses the general structure, elements and operation of a probabilistic expert system capable of predicting the risk of Legionella in rea…

Bayesian hierarchical models in manufacturing bulk service queues

In this paper, Queueing Theory and Bayesian statistical tools are used to analyze the congestion of various manufacturing bulk service queues with the same characteristics that are working independently of one another and in equilibrium. Hierarchical models are discussed in order to develop the whole inferential process for the parameters governing the system. Markov Chain Monte Carlo methods and numerical inversion of transforms are addressed to compute the posterior predictive distributions of the usual measures of performance in practice.

An Approach for the Evaluation of Risk Impact of Changes Addressing Uncertainties in a Surveillance Requirement Optimization Context

This paper presents an approach for the evaluation of risk impact of Surveillance Requirement changes addressing identification, treatment and analysis of uncertainties in an integrated manner, which is intended to be used in an optimization context. It is also presented an example of application of the methodology to study a SF change of the Reactor Protection System of a Nuclear Power Plant.

M.J. (Susie) Bayarri

What Does Objective Mean in a Dirichlet-multinomial Process?

Summary The Dirichlet-multinomial process can be seen as the generalisation of the binomial model with beta prior distribution when the number of categories is larger than two. In such a scenario, setting informative prior distributions when the number of categories is great becomes difficult, so the need for an objective approach arises. However, what does objective mean in the Dirichlet-multinomial process? To deal with this question, we study the sensitivity of the posterior distribution to the choice of an objective Dirichlet prior from those presented in the available literature. We illustrate the impact of the selection of the prior distribution in several scenarios and discuss the mo…

Spatial and temporal variations of water repellency and probability of its occurrence in calcareous Mediterranean rangeland soils affected by fires

Abstract Water repellency (WR) is a common soil property in many fire-affected ecosystems, but it also occurs in long-unburned terrain. It can vary in space at different scales (between point and pedon or slope and catchment) and time (during the same day, between seasons or years, or with a post-fire recovery period). This paper: i) reports on the occurrence and persistence of WR in fire-affected calcareous forest soils under Mediterranean climatic conditions, examining its spatial variability at macro-, meso- and micro-scales, and monthly changes with soil moisture content; and ii) develops exploratory models to estimate the probability of the natural background (not fire-induced) WR to o…

Bayesian Survival Analysis to Model Plant Resistance and Tolerance to Virus Diseases

Viruses constitute a major threat to large-scale production of crops worldwide producing important economical losses and undermining sustainability. We evaluated a new plant variety for resistance and tolerance to a specific virus through a comparison with other well-known varieties. The study is based on two independent Bayesian accelerated failure time models which assess resistance and tolerance survival times. Information concerning plant genotype and virus biotype were considered as baseline covariates and error terms were assumed to follow a modified standard Gumbel distribution. Frequentist approach to these models was also considered in order to compare the results of the study from…

Statistical performance of a multiclass bulk production queueing system

Abstract In this paper, we discuss how to statistically analyze a make-to-stock production system the behaviour of which depends on a multiclass bulk queueing system. The performance of the system is evaluated in terms of the different demands of products, processing times and, mainly, through the finished product inventory and other related measures that quantify the queueing effects in the system. A numerical example which illustrates the applicability of the results in an inventory scenario is also discussed.

Bayesian Analysis of Population Health Data

The analysis of population-wide datasets can provide insight on the health status of large populations so that public health officials can make data-driven decisions. The analysis of such datasets often requires highly parameterized models with different types of fixed and random effects to account for risk factors, spatial and temporal variations, multilevel effects and other sources on uncertainty. To illustrate the potential of Bayesian hierarchical models, a dataset of about 500,000 inhabitants released by the Polish National Health Fund containing information about ischemic stroke incidence for a 2-year period is analyzed using different types of models. Spatial logistic regression and…

Bayesian longitudinal models for paediatric kidney transplant recipients

Chronic kidney disease is a progressive loss of renal function which results in the inability of the kidneys to properly filter waste from the blood. Renal function is usually estimated by the glomerular filtration rate (eGFR), which decreases with the worsening of the disease. Bayesian longitudinal models with covariates, random effects, serial correlation and measurement error are discussed to analyse the progression of eGFR in first transplanted children taken from a study in Valencia, Spain.