George Iliopoulos

Quantitative Assessment of Geotopes as an Effective Tool for Geoheritage Management

A quantitative methodology for the assessment of geotopes that can be used for the sustainable management and conservation of the geological heritage of an area is here presented. As sustainable development, education and conservation are core issues for the successful management of any protected area, this study focuses on the development of specific indexes necessary for determining values concerning the tourism, educational and protection requirements of geotopes. The proposed methodology is based on a series of criteria that cover not only the geological and geographical importance of a geotope but also its scientific, ecological, cultural, aesthetic and economic significance. Based on these criteria, the resulting scientific, ecological, cultural, aesthetic, economic and potential for use scores of each geotope are used to estimate, respectively, the touristic, educational and protection-need value indexes for each geotope on a scale ranging from 1 to 10. This methodology was implemented and tested in two areas in the island of Crete, namely the Psiloritis Natural Park, a European and Global geopark, and the Lassithi Mountains, producing reliable results, which are in agreement with the geopark’s activities and values. The proposed quantitative assessment method is, therefore, a useful tool. It serves the requirements for the adequate management and protection of geoheritage within a territory as it can reveal priorities for sustainable tourism development, including geotourism and educational tourism activities and the conservation of geotopes.

An Artificial Allocations Based Solution to the Label Switching Problem in Bayesian Analysis of Mixtures of Distributions

Label switching is a well-known problem occurring in MCMC outputs in Bayesian mixture modeling. In this article we propose a formal solution to this problem by considering the space of the artificial allocation variables. We show that there exist certain subsets of the allocation space leading to a class of nonsymmetric distributions that have the same support with the symmetric posterior distribution and can reproduce it by simply permuting the labels. Moreover, we select one of these distributions as a solution to the label switching problem using the simple matching distance between the artificial allocation variables. The proposed algorithm can be used in any mixture model and its computational cost depends on the length of the simulated chain but not on the parameter space dimension. Real and simulated data examples are provided in both univariate and multivariate settings. Supplemental material for this article is available online.

Fourier methods for testing multivariate independence

Recently a power study of some popular tests for bivariate independence based on ranks has been conducted. An alternative class of tests appropriate for testing not only bivariate, but also multivariate independence is developed, and their small-sample performance is studied. The test statistics employ the familiar equation between the joint characteristic function and the product of component characteristic functions, and may be written in a closed form convenient for computer implementation. Simulations on a distribution-free version of the new test statistic show that the proposed method compares well to standard methods of testing independence via the empirical distribution function. The methods are applied to multivariate observations incorporating data from several major stock-market indices. Issues pertaining to the theoretical properties of the new test are also addressed.

Tests of fit for the Rayleigh distribution based on the empirical Laplace transform

In this paper a class of goodness-of-fit tests for the Rayleigh distribution is proposed. The tests are based on a weighted integral involving the empirical Laplace transform. The consistency of the tests as well as their asymptotic distribution under the null hypothesis are investigated. As the decay of the weight function tends to infinity the test statistics approach limit values. In a particular case the resulting limit statistic is related to the first nonzero component of Neyman’s smooth test for this distribution. The new tests are compared with other omnibus tests for the Rayleigh distribution.

On the method of pivoting the CDF for exact confidence intervals with illustration for exponential mean under life-test with time constraints

Abstract Two requirements for pivoting a cumulative distribution function (CDF) in order to construct exact confidence intervals or bounds for a real-valued parameter θ are the monotonicity of this CDF with respect to θ and the existence of solutions of some pertinent equations for θ . The second requirement is not fulfilled by the CDF of the maximum likelihood estimator of the exponential scale parameter when the data come from some life-testing scenarios such as type-I censoring, hybrid type-I censoring, and progressive type-I censoring that are subject to time constraints. However, the method has been used in these cases probably because the nonexistence of the solution usually happens only with small probability. Here, we illustrate the problem by giving formal details in the case of type-I censoring and by providing some further examples. We also present a suitable extension of the basic pivoting method which is applicable in situations wherein the considered equations have no solution.

Estimation of parametric functions in Downton's bivariate exponential distribution

This paper considers estimation of the ratio of means and the regression function in Downtons (J. Roy. Statist. Soc B 32 (1970) 408) bivariate exponential distribution. Unbiased estimators are given and, by presenting improved estimators, they are shown to be inadmissible in terms of mean squared error. The results are derived by conditioning on an unobserved random sample from a geometric distribution which provides conditional independence for the statistics involved.

On improved interval estimation for the generalized variance

Abstract A confidence interval for the generalized variance of a matrix normal distribution with unknown mean is constructed which improves on the usual minimum size (i.e., minimum length or minimum ratio of endpoints) interval based on the sample generalized variance alone in terms of both coverage probability and size. The method is similar to the univariate case treated by Goutis and Casella (Ann. Statist. 19 (1991) 2015–2031).

Order-Restricted Semiparametric Inference for the Power Bias Model

The power bias model, a generalization of length-biased sampling, is introduced and investigated in detail. In particular, attention is focused on order-restricted inference. We show that the power bias model is an example of the density ratio model, or in other words, it is a semiparametric model that is specified by assuming that the ratio of several unknown probability density functions has a parametric form. Estimation and testing procedures under constraints are developed in detail. It is shown that the power bias model can be used for testing for, or against, the likelihood ratio ordering among multiple populations without resorting to any parametric assumptions. Examples and real data analysis demonstrate the usefulness of this approach.

Immunohistochemical expression of TGF-β1, p21WAF1, p53, Ki67, and angiogenesis in gastric carcinomas

AbstractBackground: Transforming growth factors-beta (TGF-βs) are multifunctional polypeptides with crucial role as regulators of cellular growth and differentiation. It has been reported that TGF-β1 plays a biphasic action on tumorigenesis thus inducing or inhibiting malignant properties of the epithelial cells. Methods: TGF-β1 expression was analyzed in 56 patients with gastric carcinoma by immunohistochemical methods and compared with the expression of p21, p53, and Ki67, as well as with angiogenesis. The correlation of these markers with clinicopathological parameters was also evaluated. Results: TGF-β1 expression was detected in 71% of tumors and was more frequent in adenocarcinomas of the intestinal type (p<0.001). Positivity of p21WAF1, and p53 was observed in 32% and 51% of the tumors, respectively. A high Ki67 proliferating index was detected in 53.5% of the tumors. TGF-β1 expression was significantly correlated with p21 expression (p<0.001) and was inversely correlated with microvessel density. p21 expression was also higher in tumors with low proliferating index (p<0.01). There was no apparent correlation between the expression of these markers and tumor stage, depth of invasion, or lymphnode metastases. Conclusion: The findings show that TGF-β1 may be involved in the activation of the cdk inhibitor p21WAF1 in gastric adenocarcinomas, suggesting p53-independent induction of p21 in gastric cells. TGF-β1 does not seem to contribute to the alteration of the angiogenic status of these tumors.

Asymptotic properties of numbers of observations near sample quantiles

In this paper, we show that the proportions of observations falling in the left and right vicinity of the k n th order statistic converge in probability to some population quantities. We then prove that suitably normalized versions of these variables are jointly asymptotically normal under some conditions. A generalization of this result to the case of proportions of observations in the vicinity of two or more central order statistics is established next. Some concluding remarks and a potential statistical application of these results are finally made.