A hybrid method for the probabilistic maximal covering location-allocation problem

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Estimação espaço-temporal das perdas não técnicas no sistema de distribuição de energia elétrica

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A graphical tool for an analytical approach of scattering photons by the Compton effect

The photons scattered by the Compton effect can be used to characterize the physical properties of a given sample due to the influence that the electron density exerts on the number of scattered photons. However, scattering measurements involve experimental and physical factors that must be carefully analyzed to predict uncertainty in the detection of Compton photons. This paper presents a method for the optimization of the geometrical parameters of an experimental arrangement for Compton scattering analysis, based on its relations with the energy and incident flux of the X-ray photons. In addition, the tool enables the statistical analysis of the information displayed and includes the coefficient of variation (CV) measurement for a comparative evaluation of the physical parameters of the model established for the simulation. (C) 2012 Elsevier B.V. All rights reserved.

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.

On Equilibrium Distribution of a Reversible Growth Model

We study a probabilistic model of interacting spins indexed by elements of a finite subset of the d-dimensional integer lattice, da parts per thousand yen1. Conditions of time reversibility are examined. It is shown that the model equilibrium distribution converges to a limit distribution as the indexing set expands to the whole lattice. The occupied site percolation problem is solved for the limit distribution. Two models with similar dynamics are also discussed.

Bagging k-dependence probabilistic networks: An alternative powerful fraud detection tool

Fraud is a global problem that has required more attention due to an accentuated expansion of modern technology and communication. When statistical techniques are used to detect fraud, whether a fraud detection model is accurate enough in order to provide correct classification of the case as a fraudulent or legitimate is a critical factor. In this context, the concept of bootstrap aggregating (bagging) arises. The basic idea is to generate multiple classifiers by obtaining the predicted values from the adjusted models to several replicated datasets and then combining them into a single predictive classification in order to improve the classification accuracy. In this paper, for the first time, we aim to present a pioneer study of the performance of the discrete and continuous k-dependence probabilistic networks within the context of bagging predictors classification. Via a large simulation study and various real datasets, we discovered that the probabilistic networks are a strong modeling option with high predictive capacity and with a high increment using the bagging procedure when compared to traditional techniques. (C) 2012 Elsevier Ltd. All rights reserved.

A Robust Structural PGN Model for Control of Cell-Cycle Progression Stabilized by Negative Feedbacks

The cell division cycle comprises a sequence of phenomena controlled by a stable and robust genetic network. We applied a probabilistic genetic network (PGN) to construct a hypothetical model with a dynamical behavior displaying the degree of robustness typical of the biological cell cycle. The structure of our PGN model was inspired in well-established biological facts such as the existence of integrator subsystems, negative and positive feedback loops, and redundant signaling pathways. Our model represents genes interactions as stochastic processes and presents strong robustness in the presence of moderate noise and parameters fluctuations. A recently published deterministic yeast cell-cycle model does not perform as well as our PGN model, even upon moderate noise conditions. In addition, self stimulatory mechanisms can give our PGN model the possibility of having a pacemaker activity similar to the observed in the oscillatory embryonic cell cycle.

Probabilistic Envelope Curves for Extreme Rainfall Events - Curve Inviluppo Probabilistiche per Precipitazioni Estreme

A regional envelope curve (REC) of flood flows summarises the current bound on our experience of extreme floods in a region. RECs are available for most regions of the world. Recent scientific papers introduced a probabilistic interpretation of these curves and formulated an empirical estimator of the recurrence interval T associated with a REC, which, in principle, enables us to use RECs for design purposes in ungauged basins. The main aim of this work is twofold. First, it extends the REC concept to extreme rainstorm events by introducing the Depth-Duration Envelope Curves (DDEC), which are defined as the regional upper bound on all the record rainfall depths at present for various rainfall duration. Second, it adapts the probabilistic interpretation proposed for RECs to DDECs and it assesses the suitability of these curves for estimating the T-year rainfall event associated with a given duration and large T values. Probabilistic DDECs are complementary to regional frequency analysis of rainstorms and their utilization in combination with a suitable rainfall-runoff model can provide useful indications on the magnitude of extreme floods for gauged and ungauged basins. The study focuses on two different national datasets, the peak over threshold (POT) series of rainfall depths with duration 30 min., 1, 3, 9 and 24 hrs. obtained for 700 Austrian raingauges and the Annual Maximum Series (AMS) of rainfall depths with duration spanning from 5 min. to 24 hrs. collected at 220 raingauges located in northern-central Italy. The estimation of the recurrence interval of DDEC requires the quantification of the equivalent number of independent data which, in turn, is a function of the cross-correlation among sequences. While the quantification and modelling of intersite dependence is a straightforward task for AMS series, it may be cumbersome for POT series. This paper proposes a possible approach to address this problem.

Structure learning of graphical models for task-oriented robot grasping

In the collective imaginaries a robot is a human like machine as any androids in science fiction. However the type of robots that you will encounter most frequently are machinery that do work that is too dangerous, boring or onerous. Most of the robots in the world are of this type. They can be found in auto, medical, manufacturing and space industries. Therefore a robot is a system that contains sensors, control systems, manipulators, power supplies and software all working together to perform a task. The development and use of such a system is an active area of research and one of the main problems is the development of interaction skills with the surrounding environment, which include the ability to grasp objects. To perform this task the robot needs to sense the environment and acquire the object informations, physical attributes that may influence a grasp. Humans can solve this grasping problem easily due to their past experiences, that is why many researchers are approaching it from a machine learning perspective finding grasp of an object using information of already known objects. But humans can select the best grasp amongst a vast repertoire not only considering the physical attributes of the object to grasp but even to obtain a certain effect. This is why in our case the study in the area of robot manipulation is focused on grasping and integrating symbolic tasks with data gained through sensors. The learning model is based on Bayesian Network to encode the statistical dependencies between the data collected by the sensors and the symbolic task. This data representation has several advantages. It allows to take into account the uncertainty of the real world, allowing to deal with sensor noise, encodes notion of causality and provides an unified network for learning. Since the network is actually implemented and based on the human expert knowledge, it is very interesting to implement an automated method to learn the structure as in the future more tasks and object features can be introduced and a complex network design based only on human expert knowledge can become unreliable. Since structure learning algorithms presents some weaknesses, the goal of this thesis is to analyze real data used in the network modeled by the human expert, implement a feasible structure learning approach and compare the results with the network designed by the expert in order to possibly enhance it.

A probabilistic approach to classify the levee reliability

This work aims to evaluate the reliability of these levee systems, calculating the probability of “failure” of determined levee stretches under different loads, using probabilistic methods that take into account the fragility curves obtained through the Monte Carlo Method. For this study overtopping and piping are considered as failure mechanisms (since these are the most frequent) and the major levee system of the Po River with a primary focus on the section between Piacenza and Cremona, in the lower-middle area of the Padana Plain, is analysed. The novelty of this approach is to check the reliability of individual embankment stretches, not just a single section, while taking into account the variability of the levee system geometry from one stretch to another. This work takes also into consideration, for each levee stretch analysed, a probability distribution of the load variables involved in the definition of the fragility curves, where it is influenced by the differences in the topography and morphology of the riverbed along the sectional depth analysed as it pertains to the levee system in its entirety. A type of classification is proposed, for both failure mechanisms, to give an indication of the reliability of the levee system based of the information obtained by the fragility curve analysis. To accomplish this work, an hydraulic model has been developed where a 500-year flood is modelled to determinate the residual hazard value of failure for each stretch of levee near the corresponding water depth, then comparing the results with the obtained classifications. This work has the additional the aim of acting as an interface between the world of Applied Geology and Environmental Hydraulic Engineering where a strong collaboration is needed between the two professions to resolve and improve the estimation of hydraulic risk.

Numerical model of the human cornea based on stromal microstructure: identification of mechanical properties for two age groups

The optical quality of the human eye mainly depends on the refractive performance of the cornea. The shape of the cornea is a mechanical balance between intraocular pressure and tissue intrinsic stiffness. Several surgical procedures in ophthalmology alter the biomechanics of the cornea to provoke local or global curvature changes for vision correction. Legitimated by the large number of surgical interventions performed every day, the demand for a deeper understanding of corneal biomechanics is rising to improve the safety of procedures and medical devices. The aim of our work is to propose a numerical model of corneal biomechanics, based on the stromal microstructure. Our novel anisotropic constitutive material law features a probabilistic weighting approach to model collagen fiber distribution as observed on human cornea by Xray scattering analysis (Aghamohammadzadeh et. al., Structure, February 2004). Furthermore, collagen cross-linking was explicitly included in the strain energy function. Results showed that the proposed model is able to successfully reproduce both inflation and extensiometry experimental data (Elsheikh et. al., Curr Eye Res, 2007; Elsheikh et. al., Exp Eye Res, May 2008). In addition, the mechanical properties calculated for patients of different age groups (Group A: 65-79 years; Group B: 80-95 years) demonstrate an increased collagen cross-linking, and a decrease in collagen fiber elasticity from younger to older specimen. These findings correspond to what is known about maturing fibrous biological tissue. Since the presented model can handle different loading situations and includes the anisotropic distribution of collagen fibers, it has the potential to simulate clinical procedures involving nonsymmetrical tissue interventions. In the future, such mechanical model can be used to improve surgical planning and the design of next generation ophthalmic devices.

An Urn Model for Cascading Failures on a Lattice

A cascading failure is a failure in a system of interconnected parts, in which the breakdown of one element can lead to the subsequent collapse of the others. The aim of this paper is to introduce a simple combinatorial model for the study of cascading failures. In particular, having in mind particle systems and Markov random fields, we take into consideration a network of interacting urns displaced over a lattice. Every urn is Pólya-like and its reinforcement matrix is not only a function of time (time contagion) but also of the behavior of the neighboring urns (spatial contagion), and of a random component, which can represent either simple fate or the impact of exogenous factors. In this way a non-trivial dependence structure among the urns is built, and it is used to study default avalanches over the lattice. Thanks to its flexibility and its interesting probabilistic properties, the given construction may be used to model different phenomena characterized by cascading failures such as power grids and financial networks.

A Functional-Based Distribution Diagnostic for a Linear Model with Correlated Outcomes: Technical Report

Despite the widespread popularity of linear models for correlated outcomes (e.g. linear mixed modesl and time series models), distribution diagnostic methodology remains relatively underdeveloped in this context. In this paper we present an easy-to-implement approach that lends itself to graphical displays of model fit. Our approach involves multiplying the estimated marginal residual vector by the Cholesky decomposition of the inverse of the estimated marginal variance matrix. Linear functions or the resulting "rotated" residuals are used to construct an empirical cumulative distribution function (ECDF), whose stochastic limit is characterized. We describe a resampling technique that serves as a computationally efficient parametric bootstrap for generating representatives of the stochastic limit of the ECDF. Through functionals, such representatives are used to construct global tests for the hypothesis of normal margional errors. In addition, we demonstrate that the ECDF of the predicted random effects, as described by Lange and Ryan (1989), can be formulated as a special case of our approach. Thus, our method supports both omnibus and directed tests. Our method works well in a variety of circumstances, including models having independent units of sampling (clustered data) and models for which all observations are correlated (e.g., a single time series).

Cholesky Residuals for Assessing Normal Errors in a Linear Model with Correlated Outcomes: Technical Report

Despite the widespread popularity of linear models for correlated outcomes (e.g. linear mixed models and time series models), distribution diagnostic methodology remains relatively underdeveloped in this context. In this paper we present an easy-to-implement approach that lends itself to graphical displays of model fit. Our approach involves multiplying the estimated margional residual vector by the Cholesky decomposition of the inverse of the estimated margional variance matrix. The resulting "rotated" residuals are used to construct an empirical cumulative distribution function and pointwise standard errors. The theoretical framework, including conditions and asymptotic properties, involves technical details that are motivated by Lange and Ryan (1989), Pierce (1982), and Randles (1982). Our method appears to work well in a variety of circumstances, including models having independent units of sampling (clustered data) and models for which all observations are correlated (e.g., a single time series). Our methods can produce satisfactory results even for models that do not satisfy all of the technical conditions stated in our theory.

A HIDDEN MARKOV MODEL FOR JOINT ESTIMATION OF GENOTYPE AND COPY NUMBER IN HIGH-THROUGHPUT SNP CHIPS

Amplifications and deletions of chromosomal DNA, as well as copy-neutral loss of heterozygosity have been associated with diseases processes. High-throughput single nucleotide polymorphism (SNP) arrays are useful for making genome-wide estimates of copy number and genotype calls. Because neighboring SNPs in high throughput SNP arrays are likely to have dependent copy number and genotype due to the underlying haplotype structure and linkage disequilibrium, hidden Markov models (HMM) may be useful for improving genotype calls and copy number estimates that do not incorporate information from nearby SNPs. We improve previous approaches that utilize a HMM framework for inference in high throughput SNP arrays by integrating copy number, genotype calls, and the corresponding confidence scores when available. Using simulated data, we demonstrate how confidence scores control smoothing in a probabilistic framework. Software for fitting HMMs to SNP array data is available in the R package ICE.