A default Bayesian procedure for the Generalized Pareto Distribution

The generalized Pareto distribution is used to model the exceedances over a threshold in a number of fields, including the analysis of environmental extreme events and financial data analysis. We use this model in a default Bayesian framework where no prior information is available on unknown model parameters. Using a large simulation study, we compare the performance of our posterior estimations of parameters with other methods proposed in the literature. We show that our procedure also allows to make inferences in other quantities of interest in extreme value analysis without asymptotic arguments. We apply the proposed methodology to a real data set

A bayesian approach for estimating extreme quantiles under a semiparametric mixture model

In this paper we propose an additive mixture model, where one component is the Generalized Pareto distribution (GPD) that allows us to estimate extreme quantiles. GPD plays an important role in modeling extreme quantiles for the wide class of distributions belonging to the maximum domain of attraction of an extreme value model. One of the main difficulty with this modeling approach is the choice of the threshold u, such that all observations greater than u enter into the likelihood function of the GPD model. Difficulties are due to the fact that GPD parameter estimators are sensible to the choice of u. In this work we estimate u, and other parameters, using suitable priors in a Bayesian approach. In particular, we propose to model all data, extremes and non-extremes, using a semiparametric model for data below u, and the GPD for the exceedances over u. In contrast to the usual estimation techniques for u, in this setup we account for uncertainty on all GPD parameters, including u, via their posterior distributions. A Monte Carlo study shows that posterior cred- ible intervals also have frequentist coverages. We further illustrate the advantages of our approach on two applications from insurance

Contact-state classification of human- demonstrated robot compliant motion tasks using the boosting algorithm

Robot programming by demonstration is a robot programming paradigm in which a human operator directly demonstrates the task to be performed. In this paper, we focus on programming by demonstration of compliant motion tasks, which are tasks that involve contacts between an object manipulated by the robot and the environment in which it operates. Critical issues in this paradigm are to distinguish essential actions from those that are not relevant for the correct execution of the task and to transform this information into a robot-independent representa- tion. Essential actions in compliant motion tasks are the contacts that take place, and therefore, it is important to understand the sequence of contact states that occur during a demonstration, called contact classification or contact segmentation. We propose a contact classification algorithm based on a supervised learning algorithm, in particular on a stochastic gradient boosting algo- rithm. The approach described in this paper is accurate and does not depend on the geometric model of the objects involved in the demonstration. It neither relies on the kinestatic model of the contact interactions nor on the contact state graph, whose computation is usually of prohibitive complexity even for very simple geometric object models

A default Bayesian approach for regression on extremes

A default Bayesian approach to predict extreme events in the presence of explanatory variables is presented. In the prediction model, covariates are introduced, using a non-homogenous Poisson-Generalized Pareto Distribution (GPD) point process, which allows for variation in the tail behaviour. The prior distribution proposed is based on a Jeffreys’ rule for regression parameters, extending the results previously obtained for an independent and identically distributed random sample drawn from the GPD. Special attention is given to mean return levels as an important summarizer. Inference is performed approximately via Markov chain Monte Carlo methods and the posterior distribution turns out to be relatively easy to be computed. The model is applied to two real datasets from meteorological applications

Goodness-of-Fit of Conditional Regression Models for Multiple Imputation

We propose the calibrated posterior predictive p-value (cppp) as an interpretable goodness-of-fit (GOF) measure for regression models in sequential regression multiple imputation (SRMI). The cppp is uniformly distributed under the assumed model, while the posterior predictive p-value (ppp) is not in general and in particular when the percentage of missing data, pm, increases. Uniformity of cppp allows the analyst to evaluate properly the evidence against the assumed model. We show the advantages of cppp over ppp in terms of power in detecting common departures from the assumed model and, more importantly, in terms of robustness with respect to pm. In the imputation phase, which provides a complete database for general statistical analyses, default and improper priors are usually needed, whereas the cppp requires a proper prior on regression parameters. We avoid this problem by introducing the use of a minimum training sample that turns the improper prior into a proper distribution. The dependency on the training sample is naturally accounted for by changing the training sample at each step of the SRMI. Our results come from theoretical considerations together with simulation studies and an application to a real data set of anthropometric measures

A matching prior for the shape parameter of the skew-normal distribution

This paper deals with the issue of perform- ing a default Bayesian analysis on the shape parameter of the skew-normal distribution. Our approach is based on a suit- able pseudo-likelihood function and a matching prior distri- bution for this parameter, when location (or regression) and scale parameters are unknown. This approach is important for both theoretical and practical reasons. From a theoreti- cal perspective, it is shown that the proposed matching prior is proper thus inducing a proper posterior distribution for the shape parameter, also when the likelihood is monotone. From the practical perspective, the proposed approach has the advantages of avoiding the elicitation on the nuisance pa- rameters and the computation of multidimensional integrals

Helicobacter pylori and intestinal parasites are not detrimental to the nutritional status of Amerindians

Gastrointestinal parasites have evolved with humans and colonize many asymptomatic subjects. We in- vestigated the influence of microbial gastrointestinal colonization on the nutritional status of rural Amerindians (40 males and 61 females). Helicobacter pylori was detected by 13C-breath test, and intestinal parasites were detected in fecal specimens. Body morphometry and bioelectrical impedance measurements were measured. Although Amerindians showed low height and weight for age, they had an adequate body mass index, morphometric parameters, and cell mass. Intestinal parasites were detected in 99% of the subjects, with no detrimental effect on nutritional parameters. Helico- bacter pylori was present in 82% of adults and half the children, and was positively correlated with improved nutritional status. Despite the high prevalence of gastrointestinal microbes often associated with disease, the studied population of Amerindians had a body morphometry and composition indicative of good nutritional status, and improved in children positive for gastric H. pylori

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 oncologists and patients make efficient and effective decisions