Valentina Mameli

A Generalization of the Skew-Normal Distribution: The Beta Skew-Normal

We consider a new generalization of the skew-normal distribution introduced by Azzalini (1985). We denote this distribution Beta skew-normal (BSN) since it is a special case of the Beta generated distribution (Jones, 2004). Some properties of the BSN are studied. We pay attention to some generalizations of the skew-normal distribution (Bahrami et al., 2009; Sharafi and Behboodian, 2008; Yadegari et al., 2008) and to their relations with the BSN.

MCM-41 support for ultrasmall γ-Fe2O3 nanoparticles for H2S removal

MCM-41 is proposed to build mesostructured Fe2O3-based sorbents as an alternative to other silica or alumina supports for mid-temperature H2S removal. MCM-41 was synthesized as micrometric (MCM41_M) and nanometric (MCM41_N) particles and impregnated through an efficient two-solvent (hexane–water) procedure to obtain the corresponding γ-Fe2O3@MCM-41 composites. The active phase is homogeneously dispersed within the 2 nm channels in the form of ultrasmall maghemite nanoparticles assuring a high active phase reactivity. The final micrometric (Fe_MCM41_M) and nanometric (Fe_MCM41_N) composites were tested as sorbents for hydrogen sulphide removal at 300 °C and the results were compared with a reference sorbent (commercial unsupported ZnO) and an analogous silica-based sorbent (Fe_SBA15). MCM-41 based sorbents, having the highest surface areas, showed superior performances that were retained after the first sulphidation cycle. Specifically, the micrometric sorbent (Fe_MCM41_M) showed a higher SRC value than the nanometric one (Fe_MCM41_N), due to the low stability of the nanosized particles over time caused by their high reactivity. Furthermore, the low regeneration temperature (300–350 °C), besides the high removal capacity, renders MCM41-based systems an alternative class of regenerable sorbents for thermally efficient cleaning up processes in Integrated Gasification Combined Cycles (IGCC) systems.

Large sample confidence intervals for the skewness parameter of the skew-normal distribution based on Fisher's transformation

The skew-normal model is a class of distributions that extends the Gaussian family by including a skewness parameter. This model presents some inferential problems linked to the estimation of the skewness parameter. In particular its maximum likelihood estimator can be infinite especially for moderate sample sizes and is not clear how to calculate confidence intervals for this parameter. In this work, we show how these inferential problems can be solved if we are interested in the distribution of extreme statistics of two random variables with joint normal distribution. Such situations are not uncommon in applications, especially in medical and environmental contexts, where it can be relevant to estimate the distribution of extreme statistics. A theoretical result, found by Loperfido [7], proves that such extreme statistics have a skew-normal distribution with skewness parameter that can be expressed as a function of the correlation coefficient between the two initial variables. It is then possible, using some theoretical results involving the correlation coefficient, to find approximate confidence intervals for the parameter of skewness. These theoretical intervals are then compared with parametric bootstrap intervals by means of a simulation study. Two applications are given using real data.

Some New Results on the Beta Skew-Normal Distribution

In this paper we study the Beta skew-normal distribution introduced by Mameli and Musio (2013). Some new properties of this distribution are derived including formulae for moments in particular cases and bi-modality properties. Furthermore, we provide expansions for its distribution and density functions. Bounds for the moments and the variance of the Beta skew-normal are derived. Some of the results presented in this work can be extended to the entire family of the Beta-generated distribution introduced by Jones (Test 13(1):1–43, 2004).

Bootstrap adjustments of signed scoring rule root statistics

ABSTRACT Scoring rules give rise to methods for statistical inference and are useful tools to achieve robustness or reduce computations. Scoring rule inference is generally performed through first-order approximations to the distribution of the scoring rule estimator or of the ratio-type statistic. In order to improve the accuracy of first-order methods even in simple models, we propose bootstrap adjustments of signed scoring rule root statistics for a scalar parameter of interest in presence of nuisance parameters. The method relies on the parametric bootstrap approach that avoids onerous calculations specific of analytical adjustments. Numerical examples illustrate the accuracy of the proposed method.

Reducing Dimensionality in Molecular Systems: A Bayesian Non-parametric Approach

In this paper we present a methodology that can be used to design experiments of complex systems characterized by a huge number of variables. The strategy combines the evolutionary principles with the information provided by statistical models tailored to the problem under consideration. Here, we are concerned with the process of design molecules, which is a quite challenging problem due to the presence of a high number of variables with a binary structure. Recent works on clustering of binary data and variable selection in the high-dimensional setting allow to develop an approach capable of recovering useful information derived from the incorporation of a grouping structure into the model.

Objective Bayesian inference with proper scoring rules

Standard Bayesian analyses can be difficult to perform when the full likelihood, and consequently the full posterior distribution, is too complex or even impossible to specify or if robustness with respect to data or to model misspecifications is required. In these situations, we suggest to resort to a posterior distribution for the parameter of interest based on proper scoring rules. Scoring rules are loss functions designed to measure the quality of a probability distribution for a random variable, given its observed value. Important examples are the Tsallis score and the Hyvärinen score, which allow us to deal with model misspecifications or with complex models. Also the full and the composite likelihoods are both special instances of scoring rules. The aim of this paper is twofold. Firstly, we discuss the use of scoring rules in the Bayes formula in order to compute a posterior distribution, named SR-posterior distribution, and we derive its asymptotic normality. Secondly, we propose a procedure for building default priors for the unknown parameter of interest that can be used to update the information provided by the scoring rule in the SR-posterior distribution. In particular, a reference prior is obtained by maximizing the average

Multi-objective Optimization in High-Dimensional Molecular Systems

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