What Comes After the Prestige Disaster? An Entropic Approach to Modeling the Recurrence of Major Oil Tanker Spills in Galicia

A methodology is presented to investigate the recurrence of extraordinary events. The approach is fully general and complies with a canon of inference establishing a set of basic rationality requirements scientific reasoning should satisfy. In particular, we apply it to model the interarrival time between disastrous oil spills in the Galician coast in the northwest of Spain, one of the greatest risk areas in the world, as confirmed by the Prestige accident of November 2002. We formulate the problem within the logical probability framework, using plausible logic languages with observations to allow the appropriate expression of evidences. Therein, inference is regarded as the joint selection of a pair of reference and inferred probability distributions, which better encode the knowledge about potential times between incidents provided by the available evidences and other higher-order information at hand. To solve it, we employ the REF relative entropy method with fractile constraints. Next, we analyze the variability of the joint entropic solution, as knowledge that a time has elapsed since the last recorded spill is added, by conditioning the evidences. Attention is paid to the variability of two representative parameters: the average reference recurrence time and an inferred characteristic probability fractile for the time to an event. In contrast with classical results, the salient consequence is their nonconstancy with the elapsed time and the appearance of a variability pattern indicating an observational memory, even under the assumption of one-parameter exponential models, traditionally regarded as memoryless. Tanker accidentality is therefore dynamic, changing as time goes on with no further accidents. Generality of the methodology entails that identical conclusions would apply to hazard modeling of any other kind of extraordinary phenomena. This should be considered in risk assessment and management.     

Landslide Risk Models for Decision Making

This contribution presents a quantitative procedure for landslide risk analysis and zoning considering hazard, exposure (or value of elements at risk), and vulnerability. The method provides the means to obtain landslide risk models (expressing expected damage due to landslides on material elements and economic activities in monetary terms, according to different scenarios and periods) useful to identify areas where mitigation efforts will be most cost effective. It allows identifying priority areas for the implementation of actions to reduce vulnerability (elements) or hazard (processes). The procedure proposed can also be used as a preventive tool, through its application to strategic environmental impact analysis (SEIA) of land-use plans. The underlying hypothesis is that reliable predictions about hazard and risk can be made using models based on a detailed analysis of past landslide occurrences in connection with conditioning factors and data on past damage. The results show that the approach proposed and the hypothesis formulated are essentially correct, providing estimates of the order of magnitude of expected losses for a given time period. Uncertainties, strengths, and shortcomings of the procedure and results obtained are discussed and potential lines of research to improve the models are indicated. Finally, comments and suggestions are provided to generalize this type of analysis.     

Recursive characterization of a large family of discrete probability distributions showing extra-Poisson variation

This article analyses the broad family of discrete probability distributions generated by relating Prob (y) to Prob (y?1), …, Prob (y?n), for some n≥1, through a recursive equation. This family contains the binomial, negative binomial and Poisson distributions as well as the Katz family of distributions. In addition, the suggested family contains some convolutions of Poisson distributions and other generalized distributions, which provide models for Poisson overdispersion or underdispersion.     

Bayesian analysis of categorical data informatively censored

This article presents a general Bayesian analysis of incomplete categorical data considered as generated by a statistical model involving the categorical sampling process and the observable censoring process. The novelty is that we allow dependence of the censoring process paramenters on the sampling categories; i.e., an informative censoring process. In this way, we relax the assumptions under which both classical and Bayesian solutions have been de-veloped. The proposed solution is outlined for the relevant case of the censoring pattern based on partitions. It is completely developed for a simple but typical examples. Several possible extensions of our procedure are discussed in the final remarks.     

Describing extra-binomial variation with partially correlated models

Data in the form of proportions are often analyzed under a binomial model. However, because genuine random sampling is often infeasible, the subjects in the sample may be collected in clumps and the variances of the observed proportions may be considerably larger than those corresponding to the binomial model. A set of data from a study of the proportion of subjects testing positive to the disease toxoplasmosis is used in this article to motivate partially correlated binomial models capable of describing data observed in practical situations where clumped sampling is likely to appear, According to these models, the extra-binomial variance of the observed frequencies may range from a linear to a quadratic function of the sample size. An efficient algorithm for the evaluation of the resulting probability mass function is given.     

A Nonparametric Test for Symmetry Based on Freeman and Halton's Ideas on Contingency Tables

In this article, we propose a nonparametric method to test for symmetry in bivariate data. By using the extension of Fisher's exact treatment for 2 × 2 contingency tables proposed by Freeman and Halton (1951 Freeman , G. H. , Halton , J. H. ( 1951 ). Note on an exact treatment of contingency tables, goodness of fit and other problems of significance . Biometrika 38 : 141 – 149 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), we can test the hypothesis of equal distribution for two samples of integer valued variables. Then, by counting the number of observations belonging to each cell of a symmetric, appropriately built grid, we can produce the two samples of integers required to use this test for equal distribution. The resulting test for symmetry is potentially extendible to higher dimensions. A simulation study is performed to compare with some known tests (Bowker, 1948 Bowker , A. H. ( 1948 ). A test for symmetry in contingency tables . Journal of the American Statistical Association 43 : 572 – 574 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]; Hollander, 1971 Hollander , M. ( 1971 ). A nonparametric test for bivariate symmetry . Biometrika 58-1 : 203 – 212 .[Crossref], [Web of Science ®] , [Google Scholar]; and its improvement given in Krampe and Kuhnt, 2007 Krampe , A. , Kuhnt , S. ( 2007 ). Bowker's test for symmetry and modifications within the algebraic framework . Computational Statistics and Data Analysis 51 : 4124 – 4142 .[Crossref], [Web of Science ®] , [Google Scholar]). Our proposal represents a competitive option as a test for symmetry.     

Heteroscedastic Nonlinear Regression Models

A very general class of models for discrete data is introduced that includes log-linear, linear, and product models as special cases. Maximum likelihood equations are developed to yield a Fisher scoring algorithm for fitting the models to both complete and incomplete data. Two examples serve to underscore the usefulness of these models.     

Study of the quality of several asymptotic and near-exact approximations based on moments for the distribution of the Wilks Lambda statistic

In this paper a measure of proximity of distributions, when moments are known, is proposed. Based on cases where the exact distribution is known, evidence is given that the proposed measure is accurate to evaluate the proximity of quantiles (exact vs. approximated). The measure may be applied to compare asymptotic and near-exact approximations to distributions, in situations where although being known the exact moments, the exact distribution is not known or the expression for its probability density function is not known or too complicated to handle. In this paper the measure is applied to compare newly proposed asymptotic and near-exact approximations to the distribution of the Wilks Lambda statistic when both groups of variables have an odd number of variables. This measure is also applied to the study of several cases of telescopic near-exact approximations to the exact distribution of the Wilks Lambda statistic based on mixtures of generalized near-integer gamma distributions.