Wave-height hazard analysis in Eastern Coast of Spain : Bayesian approach using generalized Pareto distribution

Standard practice of wave-height hazard analysis often pays little attention to the uncertainty of assessed return periods and occurrence probabilities. This fact favors the opinion that, when large events happen, the hazard assessment should change accordingly. However, uncertainty of the hazard estimates is normally able to hide the effect of those large events. This is illustrated using data from the Mediterranean coast of Spain, where the last years have been extremely disastrous. Thus, it is possible to compare the hazard assessment based on data previous to those years with the analysis including them. With our approach, no significant change is detected when the statistical uncertainty is taken into account. The hazard analysis is carried out with a standard model. Time-occurrence of events is assumed Poisson distributed. The wave-height of each event is modelled as a random variable which upper tail follows a Generalized Pareto Distribution (GPD). Moreover, wave-heights are assumed independent from event to event and also independent of their occurrence in time. A threshold for excesses is assessed empirically. The other three parameters (Poisson rate, shape and scale parameters of GPD) are jointly estimated using Bayes' theorem. Prior distribution accounts for physical features of ocean waves in the Mediterranean sea and experience with these phenomena. Posterior distribution of the parameters allows to obtain posterior distributions of other derived parameters like occurrence probabilities and return periods. Predictives are also available. Computations are carried out using the program BGPE v2.0

Bayesian Networks and the Value of the Evidence for the Forensic Two-Trace Transfer Problem

Forensic scientists face increasingly complex inference problems for evaluating likelihood ratios (LRs) for an appropriate pair of propositions. Up to now, scientists and statisticians have derived LR formulae using an algebraic approach. However, this approach reaches its limits when addressing cases with an increasing number of variables and dependence relationships between these variables. In this study, we suggest using a graphical approach, based on the construction of Bayesian networks (BNs). We first construct a BN that captures the problem, and then deduce the expression for calculating the LR from this model to compare it with existing LR formulae. We illustrate this idea by applying it to the evaluation of an activity level LR in the context of the two-trace transfer problem. Our approach allows us to relax assumptions made in previous LR developments, produce a new LR formula for the two-trace transfer problem and generalize this scenario to n traces.

Bayesian genetic parameters for body weight and survival of Nile tilapia farmed in Brazil

The objective of this study was to estimate genetic parameters for survival and weight of Nile tilapia (Oreochromis niloticus), farmed in cages and ponds in Brazil, and to predict genetic gain under different scenarios. Survival was recorded as a binary response (dead or alive), during harvest time in the 2008 grow-out period. Genetic parameters were estimated using a Bayesian mixed linear-threshold animal model via Gibbs sampling. The breeding population consisted of 2,912 individual fish, which were analyzed together with the pedigree of 5,394 fish. The heritabilities estimates, with 95% posterior credible intervals, for tagging weight, harvest weight and survival were 0.17 (0.09-0.27), 0.21 (0.12-0.32) and 0.32 (0.22-0.44), respectively. Credible intervals show a 95% probability that the true genetic correlations were in a favourable direction. The selection for weight has a positive impact on survival. Estimated genetic gain was high when selecting for harvest weight (5.07%), and indirect gain for tagging weight (2.17%) and survival (2.03%) were also considerable.

Monitoring the decreasing trend of testicular cancer mortality in Spain during 2005-2019 through a Bayesian approach

Purpose : To assess time trends of testicular cancer (TC) mortality in Spain for period 1985-2019 for age groups 15-74 years old through a Bayesian age-period-cohort (APC) analysis. Methods: A Bayesian age-drift model has been fitted to describe trends. Projections for 2005-2019 have been calculated by means of an autoregressive APC model. Prior precision for these parameters has been selected through evaluation of an adaptive precision parameter and 95% credible intervals (95% CRI) have been obtained for each model parameter. Results: A decrease of -2.41% (95% CRI: -3.65%; -1.13%) per year has been found for TC mortality rates in age groups 15-74 during 1985-2004, whereas mortality showed a lower annual decrease when data was restricted to age groups 15-54 (-1.18%; 95% CRI: -2.60%; -0.31%). During 2005-2019 is expected a decrease of TC mortality of 2.30% per year for men younger than 35, whereas a leveling off for TC mortality rates is expected for men older than 35. Conclusions: A Bayesian approach should be recommended to describe and project time trends for those diseases with low number of cases. Through this model it has been assessed that management of TC and advances in therapy led to decreasing trend of TC mortality during the period 1985-2004, whereas a leveling off for these trends can be considered during 2005-2019 among men older than 35.

Monitoring the decreasing trend of testicular cancer mortality in Spain during 2005-2019 through a Bayesian approach

Purpose : To assess time trends of testicular cancer (TC) mortality in Spain for period 1985-2019 for age groups 15-74 years old through a Bayesian age-period-cohort (APC) analysis. Methods: A Bayesian age-drift model has been fitted to describe trends. Projections for 2005-2019 have been calculated by means of an autoregressive APC model. Prior precision for these parameters has been selected through evaluation of an adaptive precision parameter and 95% credible intervals (95% CRI) have been obtained for each model parameter. Results: A decrease of -2.41% (95% CRI: -3.65%; -1.13%) per year has been found for TC mortality rates in age groups 15-74 during 1985-2004, whereas mortality showed a lower annual decrease when data was restricted to age groups 15-54 (-1.18%; 95% CRI: -2.60%; -0.31%). During 2005-2019 is expected a decrease of TC mortality of 2.30% per year for men younger than 35, whereas a leveling off for TC mortality rates is expected for men older than 35. Conclusions: A Bayesian approach should be recommended to describe and project time trends for those diseases with low number of cases. Through this model it has been assessed that management of TC and advances in therapy led to decreasing trend of TC mortality during the period 1985-2004, whereas a leveling off for these trends can be considered during 2005-2019 among men older than 35.

Monitoring the decreasing trend of testicular cancer mortality in Spain during 2005-2019 through a Bayesian approach

Purpose : To assess time trends of testicular cancer (TC) mortality in Spain for period 1985-2019 for age groups 15-74 years old through a Bayesian age-period-cohort (APC) analysis. Methods: A Bayesian age-drift model has been fitted to describe trends. Projections for 2005-2019 have been calculated by means of an autoregressive APC model. Prior precision for these parameters has been selected through evaluation of an adaptive precision parameter and 95% credible intervals (95% CRI) have been obtained for each model parameter. Results: A decrease of -2.41% (95% CRI: -3.65%; -1.13%) per year has been found for TC mortality rates in age groups 15-74 during 1985-2004, whereas mortality showed a lower annual decrease when data was restricted to age groups 15-54 (-1.18%; 95% CRI: -2.60%; -0.31%). During 2005-2019 is expected a decrease of TC mortality of 2.30% per year for men younger than 35, whereas a leveling off for TC mortality rates is expected for men older than 35. Conclusions: A Bayesian approach should be recommended to describe and project time trends for those diseases with low number of cases. Through this model it has been assessed that management of TC and advances in therapy led to decreasing trend of TC mortality during the period 1985-2004, whereas a leveling off for these trends can be considered during 2005-2019 among men older than 35.

Monitoring the decreasing trend of testicular cancer mortality in Spain during 2005-2019 through a Bayesian approach

Purpose : To assess time trends of testicular cancer (TC) mortality in Spain for period 1985-2019 for age groups 15-74 years old through a Bayesian age-period-cohort (APC) analysis. Methods: A Bayesian age-drift model has been fitted to describe trends. Projections for 2005-2019 have been calculated by means of an autoregressive APC model. Prior precision for these parameters has been selected through evaluation of an adaptive precision parameter and 95% credible intervals (95% CRI) have been obtained for each model parameter. Results: A decrease of -2.41% (95% CRI: -3.65%; -1.13%) per year has been found for TC mortality rates in age groups 15-74 during 1985-2004, whereas mortality showed a lower annual decrease when data was restricted to age groups 15-54 (-1.18%; 95% CRI: -2.60%; -0.31%). During 2005-2019 is expected a decrease of TC mortality of 2.30% per year for men younger than 35, whereas a leveling off for TC mortality rates is expected for men older than 35. Conclusions: A Bayesian approach should be recommended to describe and project time trends for those diseases with low number of cases. Through this model it has been assessed that management of TC and advances in therapy led to decreasing trend of TC mortality during the period 1985-2004, whereas a leveling off for these trends can be considered during 2005-2019 among men older than 35.

A comparison of Bayesian and frequentist approaches to incorporating external information for the prediction of prostate cancer risk.

We present the most comprehensive comparison to date of the predictive benefit of genetics in addition to currently used clinical variables, using genotype data for 33 single-nucleotide polymorphisms (SNPs) in 1,547 Caucasian men from the placebo arm of the REduction by DUtasteride of prostate Cancer Events (REDUCE®) trial. Moreover, we conducted a detailed comparison of three techniques for incorporating genetics into clinical risk prediction. The first method was a standard logistic regression model, which included separate terms for the clinical covariates and for each of the genetic markers. This approach ignores a substantial amount of external information concerning effect sizes for these Genome Wide Association Study (GWAS)-replicated SNPs. The second and third methods investigated two possible approaches to incorporating meta-analysed external SNP effect estimates - one via a weighted PCa 'risk' score based solely on the meta analysis estimates, and the other incorporating both the current and prior data via informative priors in a Bayesian logistic regression model. All methods demonstrated a slight improvement in predictive performance upon incorporation of genetics. The two methods that incorporated external information showed the greatest receiver-operating-characteristic AUCs increase from 0.61 to 0.64. The value of our methods comparison is likely to lie in observations of performance similarities, rather than difference, between three approaches of very different resource requirements. The two methods that included external information performed best, but only marginally despite substantial differences in complexity.

Wheat alleles introgress into selfing wild relatives: empirical estimates from approximate Bayesian computation in Aegilops triuncialis.

Extensive gene flow between wheat (Triticum sp.) and several wild relatives of the genus Aegilops has recently been detected despite notoriously high levels of selfing in these species. Here, we assess and model the spread of wheat alleles into natural populations of the barbed goatgrass (Aegilops triuncialis), a wild wheat relative prevailing in the Mediterranean flora. Our sampling, based on an extensive survey of 31 Ae. triuncialis populations collected along a 60 km × 20 km area in southern Spain (Grazalema Mountain chain, Andalousia, totalling 458 specimens), is completed with 33 wheat cultivars representative of the European domesticated pool. All specimens were genotyped with amplified fragment length polymorphism with the aim of estimating wheat admixture levels in Ae. triuncialis populations. This survey first confirmed extensive hybridization and backcrossing of wheat into the wild species. We then used explicit modelling of populations and approximate Bayesian computation to estimate the selfing rate of Ae. triuncialis along with the magnitude, the tempo and the geographical distance over which wheat alleles introgress into Ae. triuncialis populations. These simulations confirmed that extensive introgression of wheat alleles (2.7 × 10(-4) wheat immigrants for each Ae. triuncialis resident, at each generation) into Ae. triuncialis occurs despite a high selfing rate (Fis ≈ 1 and selfing rate = 97%). These results are discussed in the light of risks associated with the release of genetically modified wheat cultivars in Mediterranean agrosystems.

Two-dimensional probabilistic inversion of plane-wave electromagnetic data: Methodology, model constraints and joint inversion with electrical resistivity data

Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC) simulation are well suited to quantify parameter and model uncertainty of nonlinear inverse problems. Yet, application of such methods to CPU-intensive forward models can be a daunting task, particularly if the parameter space is high dimensional. Here, we present a 2-D pixel-based MCMC inversion of plane-wave electromagnetic (EM) data. Using synthetic data, we investigate how model parameter uncertainty depends on model structure constraints using different norms of the likelihood function and the model constraints, and study the added benefits of joint inversion of EM and electrical resistivity tomography (ERT) data. Our results demonstrate that model structure constraints are necessary to stabilize the MCMC inversion results of a highly discretized model. These constraints decrease model parameter uncertainty and facilitate model interpretation. A drawback is that these constraints may lead to posterior distributions that do not fully include the true underlying model, because some of its features exhibit a low sensitivity to the EM data, and hence are difficult to resolve. This problem can be partly mitigated if the plane-wave EM data is augmented with ERT observations. The hierarchical Bayesian inverse formulation introduced and used herein is able to successfully recover the probabilistic properties of the measurement data errors and a model regularization weight. Application of the proposed inversion methodology to field data from an aquifer demonstrates that the posterior mean model realization is very similar to that derived from a deterministic inversion with similar model constraints.

Moths behaving like butterflies. Evolutionary loss of long range attractant pheromones in Castniid Moths: A Paysandisia archon model

Background: In the course of evolution butterflies and moths developed two different reproductive behaviors. Whereas butterflies rely on visual stimuli for mate location, moths use the"female calling plus male seduction" system, in which females release long-range sex pheromones to attract conspecific males. There are few exceptions from this pattern but in all cases known female moths possess sex pheromone glands which apparently have been lost in female butterflies. In the day-flying moth family Castniidae ("butterfly-moths"), which includes some important crop pests, no pheromones have been found so far. Methodology/Principal Findings: Using a multidisciplinary approach we described the steps involved in the courtship of P. archon, showing that visual cues are the only ones used for mate location; showed that the morphology and fine structure of the antennae of this moth are strikingly similar to those of butterflies, with male sensilla apparently not suited to detect female-released long range pheromones; showed that its females lack pheromone-producing glands, and identified three compounds as putative male sex pheromone (MSP) components of P. archon, released from the proximal halves of male forewings and hindwings. Conclusions/Significance: This study provides evidence for the first time in Lepidoptera that females of a moth do not produce any pheromone to attract males, and that mate location is achieved only visually by patrolling males, which may release a pheromone at short distance, putatively a mixture of Z,E-farnesal, E,E-farnesal, and (E,Z)-2,13-octadecadienol. The outlined behavior, long thought to be unique to butterflies, is likely to be widespread in Castniidae implying a novel, unparalleled butterfly-like reproductive behavior in moths. This will also have practical implications in applied entomology since it signifies that the monitoring/control of castniid pests should not be based on the use of female-produced pheromones, as it is usually done in many moths.

Bayesian Networks for the Age Classification of Living Individuals: a Study on Transition Analysis

Over the past few decades, age estimation of living persons has represented a challenging task for many forensic services worldwide. In general, the process for age estimation includes the observation of the degree of maturity reached by some physical attributes, such as dentition or several ossification centers. The estimated chronological age or the probability that an individual belongs to a meaningful class of ages is then obtained from the observed degree of maturity by means of various statistical methods. Among these methods, those developed in a Bayesian framework offer to users the possibility of coherently dealing with the uncertainty associated with age estimation and of assessing in a transparent and logical way the probability that an examined individual is younger or older than a given age threshold. Recently, a Bayesian network for age estimation has been presented in scientific literature; this kind of probabilistic graphical tool may facilitate the use of the probabilistic approach. Probabilities of interest in the network are assigned by means of transition analysis, a statistical parametric model, which links the chronological age and the degree of maturity by means of specific regression models, such as logit or probit models. Since different regression models can be employed in transition analysis, the aim of this paper is to study the influence of the model in the classification of individuals. The analysis was performed using a dataset related to the ossifications status of the medial clavicular epiphysis and results support that the classification of individuals is not dependent on the choice of the regression model.

Bayesian Estimation of Noise

In mathematical modeling the estimation of the model parameters is one of the most common problems. The goal is to seek parameters that fit to the measurements as well as possible. There is always error in the measurements which implies uncertainty to the model estimates. In Bayesian statistics all the unknown quantities are presented as probability distributions. If there is knowledge about parameters beforehand, it can be formulated as a prior distribution. The Bays’ rule combines the prior and the measurements to posterior distribution. Mathematical models are typically nonlinear, to produce statistics for them requires efficient sampling algorithms. In this thesis both Metropolis-Hastings (MH), Adaptive Metropolis (AM) algorithms and Gibbs sampling are introduced. In the thesis different ways to present prior distributions are introduced. The main issue is in the measurement error estimation and how to obtain prior knowledge for variance or covariance. Variance and covariance sampling is combined with the algorithms above. The examples of the hyperprior models are applied to estimation of model parameters and error in an outlier case.

Statistical Analysis of an SEIR Epidemic Model

This thesis was focussed on statistical analysis methods and proposes the use of Bayesian inference to extract information contained in experimental data by estimating Ebola model parameters. The model is a system of differential equations expressing the behavior and dynamics of Ebola. Two sets of data (onset and death data) were both used to estimate parameters, which has not been done by previous researchers in (Chowell, 2004). To be able to use both data, a new version of the model has been built. Model parameters have been estimated and then used to calculate the basic reproduction number and to study the disease-free equilibrium. Estimates of the parameters were useful to determine how well the model fits the data and how good estimates were, in terms of the information they provided about the possible relationship between variables. The solution showed that Ebola model fits the observed onset data at 98.95% and the observed death data at 93.6%. Since Bayesian inference can not be performed analytically, the Markov chain Monte Carlo approach has been used to generate samples from the posterior distribution over parameters. Samples have been used to check the accuracy of the model and other characteristics of the target posteriors.

Searching for consensus in ahp-group decision making. A bayesian perspective

This paper sets out to identify the initial positions of the different decisionmakers who intervene in a group decision making process with a reducednumber of actors, and to establish possible consensus paths between theseactors. As a methodological support, it employs one of the most widely-knownmulticriteria decision techniques, namely, the Analytic Hierarchy Process(AHP). Assuming that the judgements elicited by the decision makers follow theso-called multiplicative model (Crawford and Williams, 1985; Altuzarra et al.,1997; Laininen and Hämäläinen, 2003) with log-normal errors and unknownvariance, a Bayesian approach is used in the estimation of the relative prioritiesof the alternatives being compared. These priorities, estimated by way of themedian of the posterior distribution and normalised in a distributive manner(priorities add up to one), are a clear example of compositional data that will beused in the search for consensus between the actors involved in the resolution ofthe problem through the use of Multidimensional Scaling tools