Ana Justel

A multivariate Kolmogorov-Smirnov test of goodness of fit

This paper presents a distribution-free multivariate Kolmogorov-Smirnov goodness-of-fit test. The test uses a statistic which is built using Rosenblatts transformation and an algorithm is developed to compute it in the bivariate case. An approximate test, that can be easily computed in any dimension, is also presented. The power of these multivariate tests is studied in a simulation study.

Estimating Mixtures of Regressions

This article shows how Bayesian inference for switching regression models and their generalizations can be achieved by the specification of loss functions which overcome the label switching problem common to all mixture models. We also derive an extension to models where the number of components in the mixture is unknown, based on the birthand-death technique developed in recent literature. The methods are illustrated on various real datasets.

Time series clustering based on forecast densities

A new clustering method for time series is proposed, based on the full probability density of the forecasts. First, a resampling method combined with a nonparametric kernel estimator provides estimates of the forecast densities. A measure of discrepancy is then defined between these estimates and the resulting dissimilarity matrix is used to carry out the required cluster analysis. Applications of this method to both simulated and real life data sets are discussed.

Principal components for multivariate functional data

A principal component method for multivariate functional data is proposed. Data can be arranged in a matrix whose elements are functions so that for each individual a vector of p functions is observed. This set of p curves is reduced to a small number of transformed functions, retaining as much information as possible. The criterion to measure the information loss is the integrated variance. Under mild regular conditions, it is proved that if the original functions are smooth this property is inherited by the principal components. A numerical procedure to obtain the smooth principal components is proposed and the goodness of the dimension reduction is assessed by two new measures of the proportion of explained variability. The method performs as expected in various controlled simulated data sets and provides interesting conclusions when it is applied to real data sets.

Regional weather survey on Byers Peninsula, Livingston Island, South Shetland Islands, Antarctica

Abstract In 2001 the LIMNOPOLAR Project was launched with the aim of addressing the suitability of freshwater ecosystems as useful sentinels of climate change. In this project, an automatic weather station was deployed on Byers Peninsula (Livingston Island, South Shetland Islands) near several freshwater ecosystems under research. Here the multi-year data recorded are presented and compared with meteorological time series from the observatories at the Spanish Juan Carlos I Station, Deception Island and Bellingshausen Station. Lake freezing and thawing periods and snow cover are also investigated. The main results indicate that Byers Peninsula is affected by the very cloudy and wet Antarctic maritime climate. Mean annual temperature is -2.8°C and summer mean temperatures are above freezing. The region shows moderate winds over the year and with moderate, mostly liquid precipitation during the summer. There is a significant linear relationship with meteorological records obtained from Juan Carlos I Station located on the east of Livingston Island. Correlations between meteorological data from both sites are high but with colder and much windier conditions on Byers Peninsula. Therefore, the usefulness and accuracy of meteorological records in the interpretation of ecosystem dynamics are presented.

Soil trampling in an Antarctic Specially Protected Area: tools to assess levels of human impact.

Abstract Research in extremely delicate environments must be sensitive to the need to minimize impacts caused simply through the presence of research personnel. This study investigates the effectiveness of current advice relating to travel on foot over Antarctic vegetation-free soils. These are based on the concentration of impacts through the creation of properly signed and identified paths. In order to address these impacts, we quantified three factors - resistance to compression, bulk density and free-living terrestrial arthropod abundance - in areas of human activity over five summer field seasons at the Byers Peninsula (Livingston Island, South Shetland Islands). Studies included instances of both experimentally controlled use and natural non-controlled situations. The data demonstrate that a minimum human presence is sufficient to alter both physical and biological characteristics of Byers Peninsula soils, although at the lowest levels of human activity this difference was not significant in comparison with adjacent undisturbed control areas. On the other hand, a limited resilience of physical properties was observed in Antarctic soils, thus it is crucial not to exceed the soils natural recovery capability.

Selection of Variables for Cluster Analysis and Classification Rules

In this article we introduce two procedures for variable selection in cluster analysis and classification rules. One is mainly aimed at detecting the “noisy” noninformative variables, while the other also deals with multicolinearity and general dependence. Both methods are designed to be used after a “satisfactory” grouping procedure has been carried out. A forward–backward algorithm is proposed to make such procedures feasible in large datasets. A small simulation is performed and some real data examples are analyzed.

Gibbs Sampling Will Fail in Outlier Problems with Strong Masking

Abstract This article discusses the convergence of the Gibbs sampling algorithm when it is applied to the problem of outlier detection in regression models. Given any vector of initial conditions, theoretically, the algorithm converges to the true posterior distribution. However, the speed of convergence may slow down in a high-dimensional parameter space where the parameters are highly correlated. We show that the effect of the leverage in regression models makes very difficult the convergence of the Gibbs sampling algorithm in sets of data with strong masking. The problem is illustrated with examples.

Pollution and physiological variability in gentoo penguins at two rookeries with different levels of human visitation.

Abstract Human activity and specifically tourism has been increasing in Antarctica over the last few years. Few studies have examined the indirect effects of human visits on Antarctic penguin rookeries. This work aims to study the differences between a highly visited (Hannah Point) and a rarely visited (Devils Point, Byers Peninsula) gentoo penguin rookery on Livingston Island. Our results suggest that potential indirect effects of human impact are observed in gentoo penguins at Hannah Point, a colony heavily visited by tourists. Penguins at Hannah Point showed a higher presence of heavy metals such as Pb and Ni and a higher number of erythrocytic nuclear abnormalities than penguins at Devils Point. Immunological parameters showed different results depending on whether we consider the cellular response - the number of lymphocytes being higher in penguins from Hannah Point - or the humoral response - the level of immunoglobulins being higher in penguins from Devils Point. Measurements of corticosterone levels in feathers and heterophil/lymphocyte (H/L) ratio in blood showed lower levels in the heavily visited rookery than in the rarely visited rookery. Finally, we did not detect Campylobacter jejuni, a bacteria potentially transmitted by humans in either of the populations and we did not find any difference in the prevalence of Campylobacter lari between the populations.

Pattern recognition via projection-based kNN rules

A new procedure for pattern recognition is introduced based on the concepts of random projections and nearest neighbors. It can be considered as an improvement of the classical nearest neighbor classification rules. Besides the concept of neighbors, the notion of district, a larger set into which the data will be projected, is introduced. Then a one-dimensional kNN method is applied to the projected data on randomly selected directions. This method, which is more accurate to handle high-dimensional data, has some robustness properties. The procedure is also universally consistent. Moreover, the method is challenged with the Isolet data set where a very high classification score is obtained.