Parameter recovery for a skew-normal IRT model under a Bayesian approach: hierarchical framework, prior and kernel sensitivity and sample size

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is an interest in studying latent variables (or latent traits). Usually such latent traits are assumed to be random variables and a convenient distribution is assigned to them. A very common choice for such a distribution has been the standard normal. Recently, Azevedo et al. [Bayesian inference for a skew-normal IRT model under the centred parameterization, Comput. Stat. Data Anal. 55 (2011), pp. 353-365] proposed a skew-normal distribution under the centred parameterization (SNCP) as had been studied in [R. B. Arellano-Valle and A. Azzalini, The centred parametrization for the multivariate skew-normal distribution, J. Multivariate Anal. 99(7) (2008), pp. 1362-1382], to model the latent trait distribution. This approach allows one to represent any asymmetric behaviour concerning the latent trait distribution. Also, they developed a Metropolis-Hastings within the Gibbs sampling (MHWGS) algorithm based on the density of the SNCP. They showed that the algorithm recovers all parameters properly. Their results indicated that, in the presence of asymmetry, the proposed model and the estimation algorithm perform better than the usual model and estimation methods. Our main goal in this paper is to propose another type of MHWGS algorithm based on a stochastic representation (hierarchical structure) of the SNCP studied in [N. Henze, A probabilistic representation of the skew-normal distribution, Scand. J. Statist. 13 (1986), pp. 271-275]. Our algorithm has only one Metropolis-Hastings step, in opposition to the algorithm developed by Azevedo et al., which has two such steps. This not only makes the implementation easier but also reduces the number of proposal densities to be used, which can be a problem in the implementation of MHWGS algorithms, as can be seen in [R.J. Patz and B.W. Junker, A straightforward approach to Markov Chain Monte Carlo methods for item response models, J. Educ. Behav. Stat. 24(2) (1999), pp. 146-178; R. J. Patz and B. W. Junker, The applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses, J. Educ. Behav. Stat. 24(4) (1999), pp. 342-366; A. Gelman, G.O. Roberts, and W.R. Gilks, Efficient Metropolis jumping rules, Bayesian Stat. 5 (1996), pp. 599-607]. Moreover, we consider a modified beta prior (which generalizes the one considered in [3]) and a Jeffreys prior for the asymmetry parameter. Furthermore, we study the sensitivity of such priors as well as the use of different kernel densities for this parameter. Finally, we assess the impact of the number of examinees, number of items and the asymmetry level on the parameter recovery. Results of the simulation study indicated that our approach performed equally as well as that in [3], in terms of parameter recovery, mainly using the Jeffreys prior. Also, they indicated that the asymmetry level has the highest impact on parameter recovery, even though it is relatively small. A real data analysis is considered jointly with the development of model fitting assessment tools. The results are compared with the ones obtained by Azevedo et al. The results indicate that using the hierarchical approach allows us to implement MCMC algorithms more easily, it facilitates diagnosis of the convergence and also it can be very useful to fit more complex skew IRT models.

Probing the cosmic distance-duality relation with the Sunyaev-Zel'dovich effect, X-ray observations and supernovae Ia

Context. The angular diameter distances toward galaxy clusters can be determined with measurements of Sunyaev-Zel'dovich effect and X-ray surface brightness combined with the validity of the distance-duality relation, D-L(z)(1 + z)(2)/D-A(z) = 1, where D-L(z) and D-A(z) are, respectively, the luminosity and angular diameter distances. This combination enables us to probe galaxy cluster physics or even to test the validity of the distance-duality relation itself. Aims. We explore these possibilities based on two different, but complementary approaches. Firstly, in order to constrain the possible galaxy cluster morphologies, the validity of the distance-duality relation (DD relation) is assumed in the Lambda CDM framework (WMAP7). Secondly, by adopting a cosmological-model-independent test, we directly confront the angular diameters from galaxy clusters with two supernovae Ia (SNe Ia) subsamples (carefully chosen to coincide with the cluster positions). The influence of the different SNe Ia light-curve fitters in the previous analysis are also discussed. Methods. We assumed that eta is a function of the redshift parametrized by two different relations: eta(z) = 1 +eta(0)z, and eta(z) = 1 + eta(0)z/(1 + z), where eta(0) is a constant parameter quantifying the possible departure from the strict validity of the DD relation. In order to determine the probability density function (PDF) of eta(0), we considered the angular diameter distances from galaxy clusters recently studied by two different groups by assuming elliptical and spherical isothermal beta models and spherical non-isothermal beta model. The strict validity of the DD relation will occur only if the maximum value of eta(0) PDF is centered on eta(0) = 0. Results. For both approaches we find that the elliptical beta model agrees with the distance-duality relation, whereas the non-isothermal spherical description is, in the best scenario, only marginally compatible. We find that the two-light curve fitters (SALT2 and MLCS2K2) present a statistically significant conflict, and a joint analysis involving the different approaches suggests that clusters are endowed with an elliptical geometry as previously assumed. Conclusions. The statistical analysis presented here provides new evidence that the true geometry of clusters is elliptical. In principle, it is remarkable that a local property such as the geometry of galaxy clusters might be constrained by a global argument like the one provided by the cosmological distance-duality relation.

Feature-oriented regional modeling and simulations (FORMS) for the western South Atlantic: Southeastern Brazil region

The multi-scale synoptic circulation system in the southeastern Brazil (SEBRA) region is presented using a feature-oriented approach. Prevalent synoptic circulation structures, or ""features,"" are identified from previous observational studies. These features include the southward-flowing Brazil Current (BC), the eddies off Cabo Sao Tome (CST - 22 degrees S) and off Cabo Frio (CF - 23 degrees S), and the upwelling region off CF and CST. Their synoptic water-mass (T-S) structures are characterized and parameterized to develop temperature-salinity (T-S) feature models. Following [Gangopadhyay, A., Robinson, A.R., Haley, PJ., Leslie, W.J., Lozano, C.j., Bisagni, J., Yu, Z., 2003. Feature-oriented regional modeling and simulation (forms) in the gulf of maine and georges bank. Cont. Shelf Res. 23 (3-4), 317-353] methodology, a synoptic initialization scheme for feature-oriented regional modeling and simulation (FORMS) of the circulation in this region is then developed. First, the temperature and salinity feature-model profiles are placed on a regional circulation template and objectively analyzed with available background climatology in the deep region. These initialization fields are then used for dynamical simulations via the Princeton Ocean Model (POM). A few first applications of this methodology are presented in this paper. These include the BC meandering, the BC-eddy interaction and the meander-eddy-upwelling system (MEUS) simulations. Preliminary validation results include realistic wave-growth and eddy formation and sustained upwelling. Our future plan includes the application of these feature models with satellite, in-situ data and advanced data-assimilation schemes for nowcasting and forecasting the SEBRA region. (c) 2008 Elsevier Ltd. All rights reserved.

Shape analysis using fractal dimension: A curvature based approach

The present work shows a novel fractal dimension method for shape analysis. The proposed technique extracts descriptors from a shape by applying a multi-scale approach to the calculus of the fractal dimension. The fractal dimension is estimated by applying the curvature scale-space technique to the original shape. By applying a multi-scale transform to the calculus, we obtain a set of descriptors which is capable of describing the shape under investigation with high precision. We validate the computed descriptors in a classification process. The results demonstrate that the novel technique provides highly reliable descriptors, confirming the efficiency of the proposed method. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4757226]

A general framework for multi-compartmental analysis of drug chemotherapy dynamics in human immunodeficiency virus type-1 infected individuals

An optimal control strategy for the highly active antiretroviral therapy associated to the acquired immunodeficiency syndrome should be designed regarding a comprehensive analysis of the drug chemotherapy behavior in the host tissues, from major viral replication sites to viral sanctuary compartments. Such approach is critical in order to efficiently explore synergistic, competitive and prohibitive relationships among drugs and, hence, therapy costs and side-effect minimization. In this paper, a novel mathematical model for HIV-1 drug chemotherapy dynamics in distinct host anatomic compartments is proposed and theoretically evaluated on fifteen conventional anti-retroviral drugs. Rather than interdependence between drug type and its concentration profile in a host tissue, simulated results suggest that such profile is importantly correlated with the host tissue under consideration. Furthermore, the drug accumulative dynamics are drastically affected by low patient compliance with pharmacotherapy, even when a single dose lacks. (C) 2012 Elsevier Inc. All rights reserved.

Multi-planet extrasolar systems - detection and dynamics

20 years after the discovery of the first planets outside our solar system, the current exoplanetary population includes more than 700 confirmed planets around main sequence stars. Approximately 50% belong to multiple-planet systems in very diverse dynamical configurations, from two-planet hierarchical systems to multiple resonances that could only have been attained as the consequence of a smooth large-scale orbital migration. The first part of this paper reviews the main detection techniques employed for the detection and orbital characterization of multiple-planet systems, from the (now) classical radial velocity (RV) method to the use of transit time variations (TTV) for the identification of additional planetary bodies orbiting the same star. In the second part we discuss the dynamical evolution of multi-planet systems due to their mutual gravitational interactions. We analyze possible modes of motion for hierarchical, secular or resonant configurations, and what stability criteria can be defined in each case. In some cases, the dynamics can be well approximated by simple analytical expressions for the Hamiltonian function, while other configurations can only be studied with semi-analytical or numerical tools. In particular, we show how mean-motion resonances can generate complex structures in the phase space where different libration islands and circulation domains are separated by chaotic layers. In all cases we use real exoplanetary systems as working examples.

Incorporating label dependency into the binary relevance framework for multi-label classification

In multi-label classification, examples can be associated with multiple labels simultaneously. The task of learning from multi-label data can be addressed by methods that transform the multi-label classification problem into several single-label classification problems. The binary relevance approach is one of these methods, where the multi-label learning task is decomposed into several independent binary classification problems, one for each label in the set of labels, and the final labels for each example are determined by aggregating the predictions from all binary classifiers. However, this approach fails to consider any dependency among the labels. Aiming to accurately predict label combinations, in this paper we propose a simple approach that enables the binary classifiers to discover existing label dependency by themselves. An experimental study using decision trees, a kernel method as well as Naive Bayes as base-learning techniques shows the potential of the proposed approach to improve the multi-label classification performance.

Hierarchical multi-label classification using local neural networks

Hierarchical multi-label classification is a complex classification task where the classes involved in the problem are hierarchically structured and each example may simultaneously belong to more than one class in each hierarchical level. In this paper, we extend our previous works, where we investigated a new local-based classification method that incrementally trains a multi-layer perceptron for each level of the classification hierarchy. Predictions made by a neural network in a given level are used as inputs to the neural network responsible for the prediction in the next level. We compare the proposed method with one state-of-the-art decision-tree induction method and two decision-tree induction methods, using several hierarchical multi-label classification datasets. We perform a thorough experimental analysis, showing that our method obtains competitive results to a robust global method regarding both precision and recall evaluation measures.

Multi-objective evolutionary algorithm for single and multiple fault service restoration in large-scale distribution systems

Network reconfiguration for service restoration (SR) in distribution systems is a complex optimization problem. For large-scale distribution systems, it is computationally hard to find adequate SR plans in real time since the problem is combinatorial and non-linear, involving several constraints and objectives. Two Multi-Objective Evolutionary Algorithms that use Node-Depth Encoding (NDE) have proved able to efficiently generate adequate SR plans for large distribution systems: (i) one of them is the hybridization of the Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) with NDE, named NSGA-N; (ii) the other is a Multi-Objective Evolutionary Algorithm based on subpopulation tables that uses NDE, named MEAN. Further challenges are faced now, i.e. the design of SR plans for larger systems as good as those for relatively smaller ones and for multiple faults as good as those for one fault (single fault). In order to tackle both challenges, this paper proposes a method that results from the combination of NSGA-N, MEAN and a new heuristic. Such a heuristic focuses on the application of NDE operators to alarming network zones according to technical constraints. The method generates similar quality SR plans in distribution systems of significantly different sizes (from 3860 to 30,880 buses). Moreover, the number of switching operations required to implement the SR plans generated by the proposed method increases in a moderate way with the number of faults.

Structure of the N=50 As, Ge, Ga nuclei

The level structures of the N = 50 As-83, Ge-82, and Ga-81 isotones have been investigated by means of multi-nucleon transfer reactions. A first experiment was performed with the CLARA PRISMA setup to identify these nuclei. A second experiment was carried out with the GASP array in order to deduce the gamma-ray coincidence information. The results obtained on the high-spin states of such nuclei are used to test the stability of the N = 50 shell closure in the region of Ni-78 (Z = 28). The comparison of the experimental level schemes with the shell-model calculations yields an N = 50 energy gap value of 4.7(3) MeV at Z = 28. This value, in a good agreement with the prediction of the finite-range liquid-drop model as well as with the recent large-scale shell model calculations, does not support a weakening of the N = 50 shell gap down to Z = 28. (c) 2012 Elsevier B.V. All rights reserved.

Aerial Rivers and Lakes: Looking at Large-Scale Moisture Transport and Its Relation to Amazonia and to Subtropical Rainfall in South America

This is an observational study of the large-scale moisture transport over South America, with some analyses on its relation to subtropical rainfall. The concept of aerial rivers is proposed as a framework: it is an analogy between the main pathways of moisture flow in the atmosphere and surface rivers. Opposite to surface rivers, aerial rivers gain (lose) water through evaporation (precipitation). The magnitude of the vertically integrated moisture transport is discharge, and precipitable water is like the mass of the liquid column-multiplied by an equivalent speed it gives discharge. Trade wind flow into Amazonia, and the north/northwesterly flow to the subtropics, east of the Andes, are aerial rivers. Aerial lakes are the sections of a moisture pathway where the flow slows down and broadens, because of diffluence, and becomes deeper, with higher precipitable water. This is the case over Amazonia, downstream of the trade wind confluence. In the dry season, moisture from the aerial lake is transported northeastward, but weaker flow over southern Amazonia heads southward toward the subtropics. Southern Amazonia appears as a source of moisture to this flow. Aerial river discharge to the subtropics is comparable to that of the Amazon River. The variations of the amount of moisture coming from Amazonia have an important effect over the variability of discharge. Correlations between the flow from Amazonia and subtropical rainfall are not strong. However, some months within the set of dry seasons observed showed a strong increase (decrease) occurring together with an important increase (decrease) in subtropical rainfall.

A three-pronged approach to social business: a Brazilian multi-case analysis

Social businesses present a new paradigm to capitalism, in which private companies, non-profit organizations and civil society create a new type of business with the main objective of solving social problems with financial sustainability and efficiency through market mechanisms. As any new phenomenon, different authors conceptualize social businesses with distinct views. This article aims to present and characterize three different perspectives of social business definitions: the European, the American and that of the emerging countries. Each one of these views was illustrated by a different Brazilian case. We conclude with the idea that all the cases have similar characteristics, but also relevant differences that are more than merely geographical. The perspectives analyzed in this paper provide an analytical framework for understanding the field of social businesses. Moreover, the cases demonstrate that in the Brazilian context the field of social business is under construction and that as such it draws on different conceptual influences to deal with a complex and challenging reality.

A new method for decision making in multi-objective optimization problems

Many engineering sectors are challenged by multi-objective optimization problems. Even if the idea behind these problems is simple and well established, the implementation of any procedure to solve them is not a trivial task. The use of evolutionary algorithms to find candidate solutions is widespread. Usually they supply a discrete picture of the non-dominated solutions, a Pareto set. Although it is very interesting to know the non-dominated solutions, an additional criterion is needed to select one solution to be deployed. To better support the design process, this paper presents a new method of solving non-linear multi-objective optimization problems by adding a control function that will guide the optimization process over the Pareto set that does not need to be found explicitly. The proposed methodology differs from the classical methods that combine the objective functions in a single scale, and is based on a unique run of non-linear single-objective optimizers.