III JIPE 2014 III JORNADA INTERNACIONAL DE PROBABILIDAD Y ESTAD´ISTICA Pontificia Universidad Cat´ olica del Per´ u Lima, 13 al 15 de agosto 2014

Organiza: Secci´on Matem´aticas - PUCP

Auspicio: Maestr´ıa en Estad´ıstica - PUCP Maestr´ıa en Matem´aticas Aplicadas - PUCP Maestr´ıa en Matem´aticas - PUCP Escuela de Posgrado - PUCP Facultad de Estudios Generales Letras- PUCP

Comit´ e Cient´ıfico James P. Hughes, University of Washington - USA Alejandro Jara, Pontificia Universidad Cat´olica de Chile Giancarlo Sal y Rosas, Pontificia Universidad Cat´olica del Per´ u Jonathan Farf´ an, Pontificia Universidad Cat´olica del Per´ u Eladio Oca˜ na, Pontificia Universidad Cat´olica del Per´ u ´ Michel de Lara, Ecole des Ponts Paris Tech - Francia

Comit´ e Organizador Cristian Bayes Arturo Calder´on Richard Ch´avez Abelardo Jord´an Luis Valdivieso

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´Indice general

´ 1. PRESENTACION

1

2. PROGRAMA

2

3. PLENARIAS

7

4. MINICURSOS

11

5. CONFERENCIAS

13

6. COMUNICACIONES ORALES

19

´ DE POSTER 7. SESION

28

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´ 1. PRESENTACION La Pontificia Universidad Cat´ olica del Per´ u, a trav´es de la Secci´on de Matem´aticas y el apoyo de las maestr´ıas de Estad´ıstica, Matem´aticas y Matem´aticas Aplicadas, est´a organizando la III Jornada Internacional de Probabilidad y Estad´ıstica (III JIPE). Este evento internacional, que se viene realiz´ andose en la Universidad desde el a˜ no 2010, se ha convertido en el principal evento de su ´ area a nivel nacional y uno de los eventos m´as importantes de su g´enero a nivel de Sudam´erica. El evento se llevar´ a a cabo los d´ıas mi´ercoles 13, jueves 14 y viernes 15 de Agosto del 2014. El evento reunir´ a a varios investigadores de renombre mundial en el ´area, quienes expondr´an y compartir´ an los resultados de sus trabajos a trav´es de 5 sesiones plenarias, 8 conferencias, 4 mini-cursos, una sesi´on de comunicaciones y una sesi´on de p´osters. El Comit´e Organizador Lima, 13 de agosto de 2014

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2. PROGRAMA Mi´ ercoles, 13 de agosto de 2014 ´ 9.00-11.00 INSCRIPCION Lugar: Auditorio de Estudios Generales Letras ´ 11.00-11.15 INAUGURACION Lugar: Auditorio de Estudios Generales Letras 11.15-12.30 PLENARIA 1 T´ıtulo: A BAYESIAN FEATURE ALLOCATION MODEL FOR TUMOR HETEROGENEITY Ponente: Peter M¨ uller, University of Texas - USA Lugar: Auditorio de Estudios Generales Letras 12.30-1.30 CONFERENCIA 1 T´ıtulo: PREDICTING FOOTBALL MATCH OUTCOMES: THE 2014 FIFA WORLD CUP TOURNAMENT CASE Ponente: Francisco Louzada, Universidad de S˜ao Paulo - Brasil Lugar: Auditorio de Estudios Generales Letras 1.30-3.00 PAUSA 3.00-4.00 CONFERENCIA 2 T´ıtulo: PRACTICAL BAYESIAN DESIGN AND ANALYSIS OF NON-INFERIORITY TRIAL WITH SURVIVAL RESPONSE Ponente: Debajyoti Sinha, Florida State University - USA Lugar: Auditorio de Estudios Generales Letras 4.00-5.00 CONFERENCIA 3 T´ıtulo: MINIMUM DISTANCE ESTIMATION OF HIGH FREQUENCY TRANSACTION DATA Ponente: Mauricio Zevallos, Universidade Estadual de Campinas - Brasil Lugar: Sala de Conferencias de Estudios Generales Letras

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CAP´ITULO 2. PROGRAMA 4.00-5.00 CONFERENCIA 4 T´ıtulo: DIAGNOSTICS FOR CENSORED MIXED-EFFECTS MODELS USING THE MULTIVARIATE T-DISTRIBUTION Ponente: Mauricio Castro, Universidad de Concepci´on - Chile Lugar: Auditorio de Estudios Generales Letras 5.00-5.15 COFFEE BREAK Lugar: Auditorio de Estudios Generales Letras 5.15-7.15 MINICURSO 1 T´ıtulo: AN INTRODUCTION TO STATISTICAL MODELING FOR FINANCIAL DATA Ponente: Francisco Louzada, Universidad de S˜ao Paulo - Brasil Lugar: Auditorio de Estudios Generales Letras 5.15-7.15 MINICURSO 2 T´ıtulo: LA INTEGRAL DE ITO Ponente: Jonathan Farf´ an, Pontificia Universidad Cat´olica del Per´ u Lugar: Sala de Conferencias de Estudios Generales Letras 7.15-8.30 PLENARIA 2 T´ıtulo: MULTI-STAGE STOCHASTIC OPTIMIZATION: SOLUTION AND SCENARIO GENERATION METHODS Ponente: David L. Woodruff, University of California, Davis - USA Lugar: Auditorio de Estudios Generales Letras Jueves, 14 de agosto de 2014: 9.00-11.00 MINICURSO 3 T´ıtulo: STOCHASTIC VIABILITY AND APPLICATIONS ´ Ponente: Michel De Lara, Ecole des Ponts ParisTech, Universit´e Paris-Est, Paris - Francia Lugar: Sala de Conferencias de Estudios Generales Letras 9.00-11.00 MINICURSO 4 T´ıtulo: EMPIRICAL PROCESS THEORY FOR STATISTICS Ponente: Jon Wellner, University of Washington - USA Lugar: Auditorio de Estudios Generales Letras 11.00-11.15 COFFEE BREAK Lugar: Auditorio de Estudios Generales Letras

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CAP´ITULO 2. PROGRAMA 11.15-12.30 PLENARIA 3 T´ıtulo: GOODNESS OF FIT TESTS AND CONFIDENCE BANDS FOR DISTRIBUTION FUNCTIONS: SOME NEW APPROACHES Ponente: Jon Wellner, University of Washington - USA Lugar: Auditorio de Estudios Generales Letras 12.30-3.00 PAUSA 3.00-4.00 CONFERENCIA 5 T´ıtulo: TIME-CONSISTENCY: FROM OPTIMIZATION TO RISK MEASURES ´ Ponente: Michel De Lara, Ecole des Ponts ParisTech, Universit´e Paris-Est, Paris - Francia Lugar: Auditorio de Estudios Generales Letras ´ DE POSTER 4.00-5.00 SESION Lugar: Pasadizo EEGGLL primer piso 5.00-5.15 COFFEE BREAK Lugar: Auditorio de Estudios Generales Letras 5.15-7.15 MINICURSO 1 T´ıtulo: AN INTRODUCTION TO STATISTICAL MODELING FOR FINANCIAL DATA Ponente: Francisco Louzada, Universidad de S˜ao Paulo - Brasil Lugar: Auditorio de Estudios Generales Letras 5.15-7.15 MINICURSO 2 T´ıtulo: LA INTEGRAL DE ITO Ponente: Jonathan Farf´ an, Pontificia Universidad Cat´olica del Per´ u Lugar: Sala de Conferencias de Estudios Generales Letras 7.15-8.30 PLENARIA 4 T´ıtulo: PHASE TRANSITION FOR A SYSTEM OF ACTIVATED RANDOM WALKS Ponente: Augusto Texeira, Instituto Nacional de Matematica Pura y Aplicada, Brasil Lugar: Auditorio de Estudios Generales Letras Viernes, 15 de agosto de 2014: 9.00-11.00 MINICURSO 3 T´ıtulo: STOCHASTIC VIABILITY AND APPLICATIONS ´ Ponente: Michel De Lara, Ecole des Ponts ParisTech, Universit´e Paris-Est, Paris - Francia

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CAP´ITULO 2. PROGRAMA Lugar: Sala de Conferencias de Estudios Generales Letras 9.00-11.00 MINICURSO 4 T´ıtulo: EMPIRICAL PROCESS THEORY FOR STATISTICS Ponente: Jon Wellner, University of Washington - USA Lugar: Auditorio de Estudios Generales Letras 11.00-11.15 COFFEE BREAK Lugar: Auditorio de Estudios Generales Letras ´ DE COMUNICACIONES 11.15-12.30 SESION Lugar: Auditorio y sala de conferencias de Estudios Generales Letras 12.30-3.00 PAUSA 3.00-4.00 CONFERENCIA 6 T´ıtulo: Por confirmar Ponente: Andrea Rotnitzky, Universidad de Harvard - USA y Universidad di Tella Argentina Lugar: Auditorio de Estudios Generales Letras 4.00-5.00 CONFERENCIA 7 T´ıtulo: MODELING DISTRIBUTION UNCERTAINTY IN ACTIVE PORTFOLIO MANAGEMENT Ponente: Luis Ch´ avez Bedoya, Universidad Esan Lugar: Sala de Conferencias de Estudios Generales Letras 4.00-5.00 CONFERENCIA 8 T´ıtulo: A NEW DISTRIBUTION TO THE MODELING OF DISPERSION IN BINOMIAL DATA WITH APLICATIONS Ponente: Jorge Baz´ an, Universidad de S˜ao Paulo - Brasil Lugar: Auditorio de Estudios Generales Letras 5.00-5.15 COFFEE BREAK Lugar: Auditorio de Estudios Generales Letras 5.15-6.15 PLENARIA 5 T´ıtulo: BAYESIAN MODELING OF SPARSE HIGH DIMENSIONAL DATA USING DIVERGENCE MEASURES Ponente: Dipak Dey, University of Connecticut - USA Lugar: Auditorio de Estudios Generales Letras

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CAP´ITULO 2. PROGRAMA 6.15-6.30 CLAUSURA Lugar: Auditorio de Estudios Generales Letras

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3. PLENARIAS PLENARIA 1 A BAYESIAN FEATURE ALLOCATION MODEL FOR TUMOR HETEROGENEITY Peter M¨ uller UT Austin.

Resumen We characterize tumor variability by hypothetical latent cell types that are defined by the presence of some subset of recorded SNV’s. (single nucleotide variants, that is, point mutations). Assuming that each sample is composed of some sample-specific proportions of these cell types we can then fit the observed proportions of SNV’s for each sample. In other words, by fitting the observed proportions of SNV’s in each sample we impute latent underlying cell types, essentially by a deconvolution of the observed proportions as a weighted average of binary indicators that define cell types by the presence or absence of different SNV’s. Taking a Bayesian perspective, we proceed with a prior probability model for all relevant unknown quantities, including in particular a prior probability model on the binary indicators that characterize the latent cell types by selecting (or not) the recorded SNV’s. Such prior models are known as feature allocation models. We define a simplified version of the Indian buffet process, one of the most traditional feature allocation models.

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CAP´ITULO 3. PLENARIAS

PLENARIA 2 MULTI-STAGE STOCHASTIC OPTIMIZATION: SOLUTION AND SCENARIO GENERATION METHODS David L. Woodruff Graduate School of Management, UC Davis, Davis CA USA.

Resumen In this talk we will review the formulation of multi-stage stochastic optimization problems and a solution method known as progressive hedging. As a practical matter, in order to solve these problems, one needs probabilistic forecasts in the form of scenarios and software for the optimization algorithms. On the software side, we will review Pyomo that is a modeling language that supports a full range of linear and non-linear modeling constructs in a Python environment so scripting is natural and powerful. An extension for stochastic programming called PySP provides automated formation of deterministic equivalents and also provides an extensible implementation of PH. Scenario generation is an also an area of active research. We will describe some methods in the literature as well as work by a research team looking the unit commitment problem for electricity generation.

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CAP´ITULO 3. PLENARIAS

PLENARIA 3 GOODNESS OF FIT TESTS AND CONFIDENCE BANDS FOR DISTRIBUTION FUNCTIONS: SOME NEW APPROACHES Jon A. Wellner Department of Statistics, University of Washington, Seattle, WA.

Resumen Goodness-of-fit testing has enjoyed a resurgence of interest due to applications involving repeated significance testing (or combination of tests) in a variety of applied fields including genomics and astronomy. In this talk I will describe new and old families of goodness-offit tests based on phi-divergences and modifications thereof. I will describe the asymptotic null distribution theory of the test statistics and their modifications: the modifications result in new procedures which refine those of Berk and Jones (1979) and Owen (1995). Roughly speaking, the high power and accuracy of the procedures of Berk and Jones / Owen in the tail regions of distributions are essentially preserved while gaining considerably in the central region. This talk is based on joint work with Lutz Duembgen and Leah Jager.

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CAP´ITULO 3. PLENARIAS

PLENARIA 4 PHASE TRANSITION FOR A SYSTEM OF ACTIVATED RANDOM WALKS Augusto Teixeira Instituto Nacional de Matematica Pura e Aplicada, Brasil.

Resumen On the d-dimensional lattice, we consider a system with two types of particles (A and B), which is governed by the following rules. Particles of type A perform independent, continuous time simple random walks until they turn into B-particles, which happen at rate r. While at state B particles do not move at all, simply waiting to be ’awakened’ by some walker of type A. More precisely, whenever two or more particles share a site they all turn into A-type immediately. In this talk we will comment on a recent work, proving that for any dimensions, this system gets adsorbed if the initial configuration has low enough density. We will give a brief overview of the proof, which shows that for such low densities the particles organize themselves into hierarchical cities of B-particles, reaching a stable configuration. This settles the conjectured phase transition for this model. This talk is based in a joint work with Vladas Sidoravicius.

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CAP´ITULO 3. PLENARIAS

PLENARIA 5 BAYESIAN MODELING OF SPARSE HIGH DIMENSIONAL DATA USING DIVERGENCE MEASURES Dipak K. Dey Department of Statistics, University of Connecticut, CT, USA.

Resumen We introduce a novel divergence based approach, called Bregman divergence, to model sparse high dimensional problems. We also introduce a new prior which induces a new version of the (approximate) adaptive lasso in a Bayesian framework. Unlike the original adaptive lasso in which the weights should be pre-specified prior to the estimation, in our approach the coefficient estimates are directly used as the weights. In addition, due to the generality of the Bregman divergence, the proposed model is easily extended to generalized linear models as well as the group lasso.

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4. MINICURSOS MINICURSO 1 ˜ A ` MODELAGEM ESTAT´ISTICA PARA INTRODUC ¸ AO ´ DADOS DE CREDITO Francisco Louzada Universidade de S˜ ao Paulo, Brasil.

Resumen Os modelos de credit scoring tˆem sido utilizados como uma das principais ferramentas de suporte `a concess˜ ao de cr´edito. O desenvolvimento de tais modelos tem como base a constru¸c˜ao de um procedimento formal para descrever quais caracter´ısticas dos clientes est˜ao, efetivamente, relacionadas com o seu risco de cr´edito e qual a intensidade e dire¸c˜ao desse relacionamento. O objetivo b´ asico os modelos de credit scoring ´e gera¸c˜ao de um escore ou de um grupo de escores atrav´es dos quais clientes potenciais possam ser ordenados segundo a sua chance de inadimplˆencia. Neste Minicurso os procedimentos estat´ısticos comumente utilizados na modelagem de credit scoring s˜ao apresentados.

MINICURSO 2 LA INTEGRAL DE ITO Jonathan Farf´an Pontificia Universidad Cat´ olica del Per´ u.

Resumen El objetivo principal de este minicurso es exhibir de manera explicita los pasos de la construcci´on de la integral de Ito en el caso en que el integrador es un Movimiento Browniano y luego ver los pasos de la construcci´on con integradores m´as generales. Para tal fin, ser´an necesarios introducir algunos conceptos previos tales como: tipos de convergencia de variables aleatorias, tiempos de parada, Movimiento Browniano y martingalas.

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CAP´ITULO 4. MINICURSOS

MINICURSO 3 STOCHASTIC VIABILITY AND APPLICATIONS Michel De Lara ´ Ecole des Ponts ParisTech, Universit´e Paris-Est, Paris, France.

Resumen Mathematical viability theory strives to identify proper initial states and to display strategies that channel the trajectories of a control dynamical system within constraints, over a given time span. We show how to extend the viability framework in the presence of uncertainties. In the robust and stochastic cases, we outline dynamic programming equations. We showcase two examples of robust and stochastic viability: the management of anchovy-hake fisheries in the Peruvian upwelling ecosystem, and hydropower dam management under a “tourism” constraint.

MINICURSO 4 EMPIRICAL PROCESS THEORY FOR STATISTICS Jon Wellner Department of Statistics, University of Washington, Seattle, WA.

Resumen This course will cover some of the basics of empirical process theory and the application of the theory to problems in statistics. The focus will be on some of the basic convergence theory and methods together with inequalities for dealing with minimum contrast and maximum likelihood estimators in nonparametric and semiparametric models.

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5. CONFERENCIAS CONFERENCIA 1 PREDICTING FOOTBALL MATCH OUTCOMES: THE 2014 FIFA WORLD CUP TOURNAMENT CASE Francisco Louzada Universidade de S˜ ao Paulo, Brasil.

Resumen In this talk we discuss a simulation-based method for predicting football match outcomes. We model the number of goals of two opposing teams as a Poisson distribution whose mean is proportional to the relative technical level of opponents. FIFA ratings were taken as the measure of technical level of teams as well as experts? opinions on the scores of the matches were taken in account to construct the prior distributions of the parameters on a full Bayesian approach. Tournament simulations were performed in order to estimate probabilities of winning the tournament assuming different values for the weight attached to the experts information and different choices for the sequence of weights attached to the previous observed matches. The methodology is illustrated on the 2014 Football Word Cup. This is a joint work with Adriano K. Suzuki, Luis E. B. Salasar, Anderson Ara and Jose G. Leite.

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CAP´ITULO 5. CONFERENCIAS

CONFERENCIA 2 PRACTICAL BAYESIAN DESIGN AND ANALYSIS OF NON-INFERIORITY TRIAL WITH SURVIVAL RESPONSE Debajyoti Sinha Department of Statistics, Florida State University, FL, USA.

Resumen In bio-pharmaceutical industry, the clinical trials for determining the non-inferiority of a new treatment compared to an existing treatment of proven efficacy are becoming important tools for approving alternative treatment that may have other crucial advantages such as easier administration, lower cost, better tolerance (e.g., less toxicity than the cytotoxic drugs for solid tumors), better local resistance to cancer, and protection against drug resistance (for combination therapy). Such trials will also play prominent roles for evaluating immunotherapy agents including cancer vaccines and for assessing most modern-day antibiotics (e.g., quinolones, macrolides, linezolid, tigecycline, daptomycin). However, we show that the popular non-inferiority testing procedure for survival response suffers from higher than nominal type I error rate when survival responses from two treatment arms do not satisfy the underlying strict modeling assumption. We present a formulation of the hypothesis of non-inferiority of two treatments as a statistical hypothesis involving only the survival odds-ratio parameter. We further show that our new Bayesian non-inferiority test has the correct type I and type-II error rates under a wide class of models. These results show that use of our Bayesian test based on utility function is a safer and more statistical practice for non-inferiority trials of survival responses than the commonly used log-rank based tests.

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CAP´ITULO 5. CONFERENCIAS

CONFERENCIA 3 MINIMUM DISTANCE ESTIMATION OF HIGH FREQUENCY TRANSACTION DATA Mauricio Zevallos Universidade Estadual de Campinas, Brasil.

Resumen The modeling of durations, defined as the time between consecutive financial transactions, has been received much attention in statistics and financial econometrics. In the literature, several duration models have been proposed. In the Stochastic Conditional Duration (SCD) model the evolution of the durations is assumed to be driven by a latent factor. The purpose for the use of the latent variable is that it captures the unobservable information flow on the market. However, the SCD model has no closed form for its likelihood and hence the maximum likelihood estimation method is difficult to implement. In this paper a Minimum Distance Estimation (MDE) method for SCD models is presented. The MDE method is based on the minimization of the distance between sample and population autocorrelations. The main advantage of this method is that it allows for a computationally efficient estimation in which the precision of the estimates can be easily calculated. Monte Carlo experiments indicate that the proposed estimator performs very well even for time series with million observations. In addition, the methodology is illustrated with the analysis of high frequency transaction data.

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CAP´ITULO 5. CONFERENCIAS

CONFERENCIA 4 DIAGNOSTICS FOR CENSORED MIXED-EFFECTS MODELS USING THE MULTIVARIATE t-DISTRIBUTION Luis M. Castro Cepero Universidad de Concepci´ on, Chile.

Resumen In biomedical studies on HIV RNA dynamics, the viral loads generate repeated measures that are often subjected to (upper and lower) detection limits, and hence these responses are either left- or right-censored. Linear and non-linear mixed-effects censored (LMEC/NLMEC) models are routinely used to analyze these longitudinal data, with normality assumptions for the random effects and residual errors. However, the derived inference may not be robust when these underlying normality assumptions are questionable, specially presence of outliers and thick-tails. Motivated by this, Matos et al. (2013b) recently proposed an exact EMtype algorithm for LMEC/NLMEC models using a multivariate Student-t distribution, with closed-form expressions at the E-step. In this paper, we develop influence diagnostics for LMEC/NLMEC models using multivariate Student-t density, based on the conditional expectation of the complete data log-likelihood which eliminates the complexity associated with the approach of Cook (1977, 1986) for censored mixed-effects models. The new methodology is illustrated through an application to a longitudinal HIV dataset using the NLMEC framework. In addition, a simulation study is presented, which explores the accuracy of the proposed measures in detecting influential observations in heavy-tailed censored data under different perturbation schemes.

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CAP´ITULO 5. CONFERENCIAS

CONFERENCIA 5 TIME-CONSISTENCY: FROM OPTIMIZATION TO RISK MEASURES Michel De Lara ´ Ecole des Ponts ParisTech, Universit´e Paris-Est, Paris, France.

Resumen Stochastic optimal control is concerned with sequential decision-making under uncertainty. The theory of dynamic risk measures gives values to stochastic processes (costs) as time goes on and information accumulates. Both theories coin, under the same vocable of time-consistency (or dynamic-consistency), two different notions: the latter is consistency between successive evaluations of a stochastic processes by a dynamic risk measure as information accumulates (a form of monotonicity); the former is consistency between solutions to inter-temporal stochastic optimization problems as information accumulates. Interestingly, time-consistency in stochastic optimal control and time-consistency for dynamic risk measures meet in their use of dynamic programming, or nested, equations. We provide a theoretical framework that offers i) basic ingredients to jointly define dynamic risk measures and corresponding inter-temporal stochastic optimization problems ii) common sets of assumptions that lead to time-consistency for both. Our theoretical framework highlights the role of time and risk preferences, materialized in one-step aggregators, in time-consistency. Depending on how you move from one-step time and risk preferences to inter-temporal time and risk preferences, and depending on their compatibility (commutation), you will or will not observe time-consistency. We also shed light on the relevance of information structure by giving an explicit role to a state control dynamical system, with a state that parameterizes risk measures and is the input to optimal policies.

CONFERENCIA 6 Por confirmar Andrea Rotnitzky Universidad de Harvard - USA y Universidad di Tella - Argentina.

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CAP´ITULO 5. CONFERENCIAS

CONFERENCIA 7 MODELING DISTRIBUTION UNCERTAINTY IN ACTIVE PORTFOLIO MANAGEMENT Luis Chavez-Bedoya Universidad Esan, Per´ u.

Resumen In the framework of active portfolio management, we propose a novel methodology to incorporate the relative confidence given to the distribution of consensus excess returns with respect to the forecasted one. This methodology uses a particular case of the generalized hyperbolic distribution, and provides an intuitive and simple form to incorporate distribution uncertainty since closed-form expressions for the optimal portfolio weights are available for the unconstrained optimization problem.

CONFERENCIA 8 A NEW DISTRIBUTION TO THE MODELING OF DISPERSION IN BINOMIAL DATA WITH APLICATIONS Jorge Luis Baz´an Instituto de Ciˆencias Matem´ aticas e de Computa¸c˜ ao, Universidade de S˜ ao Paulo- Brasil.

Resumen The Bernoulli process is one of the most important random processes in Statistics. In the common case, given the probability of success, the outcome of one trial has no influence over the outcome of another trial. Unfortunately, many real-world applications with over- or under-dispersed data this assumption of independence is violated and the Bernoulli process or the Binomial variable derived of this process will be not useful, which limit their applications in Data analysis. In contrast, Dispersion count data are common in many applications which had lead to the developing of new statistical models. In this talk introduce the novel model named CMP Binomial which is an particular correlated binomial model. Data analysis to several applications are presented.

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6. COMUNICACIONES ORALES ´ ORAL 1 COMUNICACION NUMERICAL APPROXIMATION TO MELLIN CONVOLUTION BY MIXTURES OF EXPONENTIALS Jorge Luis Torrej´on Matos,1 1

Julio Michael Stern,1

Deparment of Applied Mathematics, Institute of Mathematics and Statistics - University of S˜ ao Paulo.

Resumen The purpose of this work is to calculate the compositional models of FBST (the Full Bayesian Significance Test) studied by Stern (The rules of logic composition for the Bayesian epistemic e-Values - 2007). The objective of this work is to find an approximation method numericaly efficient that can replace the condensation methods described by Kaplan. Two techniques are compared: First, the approximation of Mellin convolution using discretization and condensation described by Kaplan (An Improved Condensation Procedure in Discrete Probability Distribution Calculation - 1987), second, the approximation of Mellin convolution using mixtures of exponentials described by Dufresne (Fitting combinations of exponentials to probability distributions - 2007) to calculate the Fourier convolution and then to apply the operator described by Collins (The relationship between Fourier and Mellin transforms, with applications to probability and stochastic processes - 2011) to transform the usual convolution to Mellin convolution.

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CAP´ITULO 6. COMUNICACIONES ORALES

´ ORAL 2 COMUNICACION BARE BONES PARTICLE SWARM OPTIMIZATION WITH SCALE MATRIX ADAPTATION Mauro Campos,1 1 2

Renato A. Krohling,2 ,

Ivan Enriquez

1

Department of Statistics, Federal University of Esp´ırito Santo, Vit´ oria ES, Brazil.

Department of Production Engineering and with the Graduate Program in Computer Science, Federal University of Esp´ırito Santo, Vit´ oria ES, Brazil.

Resumen Bare bones particle swarm optimization (BBPSO) is a swarm algorithm which has shown potential for solving single-objective unconstrained optimization problems over continuous search spaces. However, it suffers of the premature convergence problem which means it may get trapped into a local optimum when solving multimodal problems. In order to address this drawback and improve the performance of the BBPSO, we propose a variant of this algorithm, named by us as BBPSO with scale matrix adaptation (SMA), SMA-BBPSO for short reference. In the SMA-BBPSO, the position of a particle is selected from a multivariate t-distribution with a rule for adaptation of its scale matrix. We use the multivariate tdistribution in its hierarchical form, as a scale mixtures of normal distributions. The tdistribution has heavier tails than those of the normal distribution, which increases the ability of the particles to escape from a local optimum. In addition, our approach includes the normal distribution as a particular case. As a consequence, the t-distribution can be applied during the optimization process by maintaining the proper balance between exploration and exploitation. We also propose a simple update rule to adapt the scale matrix associated with a particle. Our strategy consists in adapting the scale matrix of a particle such that the best position found by any particle in its neighborhood is sampled with maximum likelihood in the next iteration. A theoretical analysis was developed to explain how the SMA-BBPSO works and an empirical study was carried out to evaluate the performance of the proposed algorithm. The experimental results show the suitability of the proposed approach in terms of effectiveness to find good solutions for all benchmark problems investigated. Nonparametric statistical tests indicate that SMA-BBPSO shows a statistically significant improvement compared with other swarm algorithms.

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CAP´ITULO 6. COMUNICACIONES ORALES

´ ORAL 3 COMUNICACION INFERENCE FOR THE BIVARIATE BIRNBAUM-SAUNDERS DISTRIBUTION Luis Benites,1 1

Filidor Vilca,1

V´ıctor Leiva2

Departamento de Estat´ıstica, Universidade Estadual de Campinas, Brazil. 2

Instituto de Estad´ıstica, Universidad de Valpara´ıso, Chile.

Resumen Multivariate distributions are a topic largely studied and, particularly, because of its applicability, the bivariate case is often taken into account. Birnbaum-Saunders distributions have been widely considered due to their good properties and highly useful for modeling different types of phenomena. We investigate estimation and hypothesis testing in the bivariate Birnbaum- Saunders distribution. About estimation, modified moment and maximum likelihood methods are employed. We prove that the modified moment estimators are consistent and asymptotically normal distributed. Regarding hypothesis testing, likelihood ratio, score and Wald statistics are analyzed. We obtain the Fisher information in a matrix form, which facilitates the implementation of the score and Wald statistics. We validate our approach with simulated and real-world data. Our study provides new findings and improves the results proposed until now on this topic.

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CAP´ITULO 6. COMUNICACIONES ORALES

´ ORAL 4 COMUNICACION THE EXPONENTIATED UNIFORM DISTRIBUTION: THEORY AND APPLICATION Luiz Ricardo Nakamura,1 1

Thiago Gentil Ramires,1

Edwin Moises Marcos Ortega1

Departamento de Ciˆencias Exatas, Escola Superior de Agricultura Luiz de Queiroz, Universidade de S˜ ao Paulo,Piracicaba, S˜ ao Paulo, Brazil .

Resumen Recently, a wide range of distributions are being created in order to model several distinct problems. In some of these problems, the response variable has a limited support, and the most common approaches in these cases are to truncate some distribution or perform some kind of transformation in the variable. In this work we propose an alternative distribution to model data sets with limited support, so-called exponentiated uniform (EU) distribution, which generalizes the uniform model. Let X be an uniform random variable with cumulative density function (cdf) G(x) = (x−a)/(b−a), where −∞ < a < b < ∞. Therefore, considering the class of distribution in Gupta and Kundu (2001) given by F (x) = [G(x)]α , where α > 0 is a scale parameter, we obtain the cdf of EU distribution. We notice that, when a = 0 and b = 1, the Beta(α, 1) is obtained as a special case. We also provide some properties of this new distribution, such as moments, mean deviations and Bonferroni and Lorenz curves. As an application, we use the maximum likelihood method to fit the distribution to a real data set obtained from Feigl and Zelen (1965), which represents patients who died of acute myelogenous leukemia, comparing its results with the Gamma-Uniform, Beta GeneralizedExponential, Beta-Exponential, Beta-Pareto, Exponential Poisson, Beta Generalized HalfNormal and Generalized Half- Normal distributions. The results show that the proposed distribution obtained a similar or better fit to the data set.

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CAP´ITULO 6. COMUNICACIONES ORALES

´ ORAL 5 COMUNICACION CENSORED LINEAR REGRESSION MODELS FOR IRREGULARLY OBSERVED LONGITUDINAL DATA USING THE MULTIVARIATE-t DISTRIBUTION Aldo M. Garay,1 1

Luis M. Castro,2

Jacek Leskow,3

Victor H. Lachos1

Departamento de Estat´ıstica, Universidade Estadual de Campinas, Brazil. 2

Department of Statistics, Universidad de Concepci´ on, Chile. 3

Technical University of Cracow, Poland.

Resumen In AIDS studies it is quite common to observe viral load measurements collected irregularly over time. Moreover, these measurements can be subjected to some upper and/or lower detection limits depending on the quantification assays. A complication arises when these continuous repeated measures have a heavy-tailed behavior. Motivated by these issues in longitudinal studies, we propose a robust structure for a censored linear model based on the multivariate Student-t distribution. To address the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is employed. An efficient EM-type algorithm is developed for computing the maximum likelihood estimates, obtaining as a by product the standard errors of the fixed effects and the log-likelihood function. The proposed algorithm uses closed-form expressions at the E-step, that rely on formulas for the mean and variance of a truncated multivariate Student-t distribution. The methodology is illustrated through an application to an HIV-AIDS study and several simulation studies.

24

CAP´ITULO 6. COMUNICACIONES ORALES

´ ORAL 6 COMUNICACION ROBUST BOOTSTRAP PREDICTION INTERVALS FOR RETURNS AND VOLATILITIES IN GARCH MODELS. Carlos Truc´ıos Maza,1 1 2

Luiz K. Hotta,1

Esther Ruiz2

Department of Statistics, University of Campinas, Brazil.

Department of Statistics, University Carlos III of Madrid, Spain.

Resumen The GARCH models are widely used to modeling volatility, and an important part of modeling volatility is the construction of predic- tion intervals. Traditional methods of constructing prediction intervals for time series normally assume that the model parameters are known, and the innovations are normally distributed. When these assumptions are not true, the prediction interval obtained usually has the wrong cov- erage. These assumptions are not satisfied in financial time series and we cannot use the usual approach. An alternative to this approach is to ob- tain prediction intervals using bootstrap procedures. Pascual, Romo and Ruiz (Computational Statistics & Data Analysis, v50, 2293-2312, 2006) (PRR) propose an algorithm to obtain prediction intervals for returns and volatilities in GARCH models using bootstrap procedures and has shown good performance. A lot of works has been done to obtain prediction intervals using the PRR algorithm, although, the effects of outliers in this algorithm has not been verified. We show that when the series are contaminated with outliers the PRR algorithm do not work very well. In this work we analyze by mean of Monte Carlo experiments the effect of outliers in the construction of return and volatility prediction intervals and propose methods robust to the presence of outliers.

25

CAP´ITULO 6. COMUNICACIONES ORALES

´ ORAL 7 COMUNICACION ´ ESTOCASTICA ´ SIMULACION DE ESQUEMAS PIRAMIDALES TIPO PONZI. Lilia Quituisaca-Samaniego ,1 1

Juan Mayorga-Zambrano,2

Pa´ ul Medina3

Direcci´ on de Estudios Anal´ıticos Estad´ısticos, Instituto Nacional de Estad´ıstica y Censos, Quito, Ecuador. 2

Pontificia Universidad Cat´ olica del Ecuador - Sede Ambato, Ambato, Ecuador.

3 3

Instituto Gregorio Mill´ an, Universidad Carlos III de Madrid, Madrid, Espa˜ na.

Departamento de Ciencias Exactas, Universidad de la Fuerzas Armadas ESPE, Quito, Ecuador.

Resumen Mediante simulaci´ on, se estudian varios casos de fraude provocados por pir´amides financieras tipo Ponzi (incluyendo los casos Madoff, DRFE y Cabrera); la t´ecnica empleada corresponde a la implementaci´ on computacional de un modelo estoc´astico dise˜ nado por J. Mayorga-Zambrano.Se comparan datos reales con aquellos generados por el software implementado; en particular, se estudia la evoluci´on del n´ umero de clientes, del monto de estafa y del tiempo estimado de duraci´ on de la pir´amide.

26

CAP´ITULO 6. COMUNICACIONES ORALES

´ ORAL 8 COMUNICACION ´ EL DESARROLLO DE LOS MERCADOS DOMESTICOS DE RENTA FIJA Y VARIABLE Y EL ROL DE LOS FONDOS DE PENSIONES Mar´ıa Nela Seijas Gim´enez1 1

Universidad ORT Uruguay.

Resumen Los sistemas personales de capitalizaci´on individual han experimentado un importante crecimiento en las u ´ltimas d´ecadas, siguiendo la tendencia de envejecimiento de las poblaciones y las crisis de los sistemas de pensiones de beneficios definidos. El objetivo del presente trabajo es determinar si la implantaci´on de estos esquemas de pensiones ha impulsado el desarrollo de los mercados de capitales dom´esticos a nivel global, en el per´ıodo 1990-2011. La estrategia metodol´ ogica comprende regresiones de paneles incluyendo indicadores de profundidad y liquidez de los mercados de acciones y bonos as´ı como herramientas estad´ısticas ´ ´ de Arbol de expansi´ on m´ınima y Arbol jer´arquico y t´ecnicas de clasificaci´on aplicadas sobre informaci´ on estad´ıstica representativa de la performance de los sistemas. El an´alisis realizado permite comprobar que los fondos de pensiones de capitalizaci´on individual han significado un est´ımulo a la profundidad accionaria en los mercados de capitales. Se evidencia asimismo una causalidad negativa con la liquidez accionaria, lo que est´a vinculado con el perfil a largo plazo de su gesti´ on de portafolios previsionales. Ambos indicadores reciben los impactos positivos de mayor magnitud desde los sistemas incluidos en el cl´ uster de maduraci´on avanzada. La profundidad de la deuda p´ ublica es estimulada fundamentalmente por los sistemas voluntarios, tambi´en asociados a mejoras en el desarrollo accionario. Los cl´ usteres de maduraci´on gradual baja e incipiente ejercen impactos significativos sobre la deuda p´ ublica, lo que est´a en l´ınea con la literatura y resulta razonable con el portafolio de inversiones que suele caracterizar a los fondos de pensiones en sus primeras etapas de vida.

27

CAP´ITULO 6. COMUNICACIONES ORALES

´ ORAL 9 COMUNICACION THE CODISPERSION MAP: A GRAPHICAL TOOL TO VISUALIZE THE ASSOCIATION BETWEEN TWO SPATIAL PROCESSES Ronny Vallejos,1 1

Felipe Osorio,1

Diego Mancilla1

Departamento de Matem´ atica, Universidad T´ecnica Federico Santa Mar´ıa, Valpara´ıso, Chile.

Resumen The codispersion coefficient quantifies the association between two spatial processes for a particular direction (spatial lag) on the two-dimensional space. When this coefficient is computed for many directions it is useful to display those values on a single graph. In this talk, we suggest a graphical tool called the codispersion map to visualize the spatial correlation between two sequences on the plane. We describe how to construct the codispersion map for regular and non-regular lattices providing algorithms in both cases. Three examples with real data are given to illustrate how useful this map can be to detect those directions for which the codispersion coefficient attains its maximum and minimum values. The first example deals with the Murray smelter site dataset in an industrially contaminated area in Utah, USA. The second example is concerned with a forest dataset collected in the south of Chile. The third example illustrates the capability of the codispersion coefficient to assess the similarity between digital images. Finally, some remarks and an outline of topics to be addressed in future research will be given.

28

´ DE POSTER 7. SESION POSTER 1 MODELOS DE RESPUESTA ALEATORIZADA ´ A ESTUDIANTES ESTRATIFICADA: UNA APLICACION ´ DE LA FACULTAD DE CIENCIAS MATEMATICAS DE LA UNMSM Doris G´ omez Ticer´ an, Bartolo Gotarate

Ana C´ardenas Rojas,

Olga Solano D´avila Portuguez, 1

Ysabel Adriazola Cruz

Olga Solano

D´avila1 ,

F´elix

Blanca Martinez

Orlando Giraldo Laguna

Facultad de Ciencias Matem´ aticas, UNMSM.

Resumen En el presente trabajo estudiamos tres Modelos de Respuestas Aleatorizada (MRA) Estratificada, utilizadas en encuestas donde se utilizan preguntas delicadas. Realizamos una aplicaci´on en el comportamiento de j´ovenes de la Facultad de Ciencias Matem´aticas de la UNMSM, para investigar la proporci´on de personas que han consumido pasta b´asica de coca´ına (PBC) por lo menos una vez en su vida; la proporci´on de consumidores actuales del PBC; la proporci´ on de personas que han tenido relaciones sexuales con m´as de dos personas durante toda su vida; la proporci´ on de personas que consumen alcohol todos los fines de semana y la proporci´ on de persona que han llevado o han consumido sin pagar alg´ un producto de alg´ un supermercado. La poblaci´ on en estudio comprende los alumnos matriculados en la FCM el semestre 2009-II

29

´ DE POSTER CAP´ITULO 7. SESION

POSTER 2 ´ ACADEMICO ´ ESTUDIO DEL ESTRES EN ESTUDIANTES UNIVERSITARIOS DE LA FACULTAD DE CIENCIAS ´ ´ MATEMATICAS UTILIZANDO METODOS MULTIVARIANTES Olga Solano,1 Martinez1 ,

Doris G´ omez1 , Orlando 1

Giraldo1 ,

Ana C´ardenas1 , Mendoza

F´elix Bartolo1 ,

Jacinto1 ,

, Blanca

Olga Bola˜ nos2

Facultad de Ciencias Matem´ aticas, UNMSM. 2

Facultad de Psicolog´ıa. URP.

Resumen En el presente trabajo realizamos una comparaci´on del estr´es acad´emico en los estudiantes matriculados en la Facultad de Ciencias Matem´aticas (FCM) de la UNMSM seg´ un g´enero, utilizando el instrumento de me- dida de la Subescala de Estresores Acad´emicos (E-CEA) y m´etodos multivariantes, en particular la estad´ıstica T 2 de Hotelling (Johnson y Wichern, 1992), para analizar los datos recolectados. En el dise˜ no muestral, se utiliz´o el muestreo aleatorio estratificado con afijaci´ on proporcional al tama˜ no de cada estrato (Scheffer y Mendenhall, 2007) considerando como estratos a las Escuelas Acad´emicas Profesionales (E.A.P.) de la FCM. Para el c´ alculo del tama˜ no de muestra se consider´o un l´ımite para el error de estimaci´on del 5,07 %, con un nivel de cofianza del 95 % y la informaci´on proporcionada por la Direcci´ on Acad´emica de la FCM, de los alumnos matriculados el primer semestre del a˜ no acad´emico 2013, el tama˜ no de muestra fue de 314 alumnos, repartidos en forma proporcional a las cuatro E.A.P. de la FCM. En el mes de julio se aplic´o el instrumento de medida de la E-CEA.

30

´ DE POSTER CAP´ITULO 7. SESION

POSTER 3 MULTIVARIATE ANALYSIS APPLIED IN AGRONOMIC CHARACTERIZATION OF A COLLECTION ZAPOTE PLANTS (POUTERIA SAPOTA (JACQ.) H. MOORE & ST) Renan Mercuri Pinto,1

Thiago Gentil Ramires1 ,

Ezequiel Abraham L´ opez Bautista1 ,

, L´ ucio Borges de Ara´ ujo1 , Santos

1

Luiz Ricardo Nakamura1 , Carlos Tadeu dos

Dias1

Departamento de Ciˆencias Exatas, Escola Superior de Agricultura Luiz de Queiroz, Universidade de S˜ ao Paulo - Piracicaba, S˜ o Paulo, Brazil..

Resumen Zapote (Pouteria sapota) is a fruit tree of sapotaceas family originally from the tropical region of Central America and its importance is due to the almost complete utilization of the tree (fruit, seeds and wood) by industries. Thus, the study of its features becomes indispensable for selecting the most promising genotypes to increase the profitability of its production. In this study, it was used a dataset of 63 zapote trees placed in the botanical garden of Centro Agron´ omico Tropical de Investigaci´on y Ense˜ nanza (CATIE), located in Turrialba, Costa Rica. 17 quantitative characteristics were measured from the trees, in order to evaluate the yield potential through the application of two multivariate statistical techniques: factor analysis (FA) and cluster analysis (CA). Firstly, the FA was performed and the 17 initial characteristics were reduced to four common factors: i) Factor 1: “fruit”; ii) Factor 2: “tree structure”; iii) Factor 3: “seed”; and iv) Factor 4: “sowing time and leaf”. These four factors, which represent 69.7 % of the original varia- bility, were selected by the scree plot method. Thereafter, using these four factors, a CA was performed allowing the formation of five groups of trees with different characteristics. This methodology revealed the most promising trees in the economic point of view.

31

´ DE POSTER CAP´ITULO 7. SESION

POSTER 4 SOIL CHEMICAL PROPERTIES IN PRECISION AGRICULTURE: DIMENSIONALITY REDUCTION BY PRINCIPAL COMPONENT ANALYSIS Nat´alia da Silva Martins,1

Renan Mercuri Pinto,1

Erik Augusto Barreto Junior,1 1

Luiz Ricardo Nakamura,1

Carlos Tadeu dos Santos Dias1

Departamento de Ciˆencias Exatas, Escola Superior de Agricultura Luiz de Queiroz, Universidade de S˜ ao Paulo - Piracicaba, S˜ o Paulo, Brazil..

Resumen Precision agriculture (PA) is a form of management that seeks to conform application of inputs and agronomic practices to the needs of the soil and crop. This technique has been widespread over the last two decades due to the perception that fields are not homogeneous, and conventional management is not the most efficient way to conduct an agricultural production. One of the basic assumptions of the PA is the knowledge of the variability of soil properties and, due to this fact, the measurement of a large set of variables is required. The purpose of this study is to evaluate, by principal component analysis (PCA), the reduction of data dimensionality intending to understand how chemical attributes contribute to the variability in soil. 14 variables were measured through 60 georeferenced soil samples located in Botucatu, S˜ ao Paulo, Brazil. PCA was performed and the original dataset was reducted to three components, selected by the scree plot, which retained 73,57 % of the initial variability. The first component revealed that potential hydrogen (pH), calcium, magnesium and sum of bases, were the largest contributors to soil variability. The results obtained on this research can be used as a base for the development of more accurate intervention strategies, through the PA.

32

´ DE POSTER CAP´ITULO 7. SESION

POSTER 5 ´ MOVILIDAD ENDOGENA Y VARIACIONES ´ ´ PARA ECUADOR DEMOGRAFICAS: UNA APLICACION Luis Antamba ,1 1

Pa´ ul Medina,2

Direcci´ on de Estudios Anal´ıticos Estad´ısticos, Instituto Nacional de Estad´ıstica y Censos, Quito, Ecuador. 2 2

Instituto Gregorio Mill´ an, Universidad Carlos III de Madrid, Madrid, Espa˜ na.

Departamento de Ciencias Exactas, Universidad de las Fuerzas Armadas, Sangolqu´ı, Ecuador.

Resumen Se establece un modelo que describe la movilidad interna y externa a nivel provincial de la poblaci´ on ecuatoriana, considerando su autoidentificaci´on ´etnica(ind´ıgena y no ind´ıgena). El estudio se basa en un modelo estoc´astico basado en las cadenas de Markov. Para la investigaci´ on se han tomado como base los datos del Censo de Poblaci´on y Vivienda 2010, elaborado por el Instituto Nacional de Estad´ıstica y Censos (INEC).

33

´ DE POSTER CAP´ITULO 7. SESION

POSTER 6 ´ ANALISIS DE INFLUENCIA DEL MODELO DE ´ BETA POR INFERENCIA BAYESIANA REGRESION Jim Silvestre,1 1

Maestr´ıa en Estad´ıstica - Pontificia Universidad Cat´ olica del Per´ u.

Resumen El objetivo de esta presentaci´ on es mostrar como se realiza un an´alisis de influencia desde el punto de vista de la inferencia Bayesiana al modelo de regresi´on Beta. Se utilizar´a especificamente dos medidas de influencia: La ordenada predictiva condicional (CPO) y la divergencia Kullback Leibler. Se simular´an datos de la regresi´on Beta considerando para esto computaci´ on intensiva sobre diferentes escenarios as´ı como tambi´en se estimar´a las medidas en menci´on utilizando MCMC. Finalmente se presenta una aplicaci´on desarrollada con datos del Instituto Australiano del Deporte (AIS)

34

´ DE POSTER CAP´ITULO 7. SESION

POSTER 7 ´ PORTAFOLIOS OPTIMOS BAJO ESTIMADORES ROBUS´ TOS CLASICOS Y BAYESIANOS CON APLICACIONES AL MERCADO PERUANO DE ACCIONES Alberto Vera ,1 1 2

Cristian Bayes,2

Banco de Cr´edito del Per´ u.

Pontificia Universidad Cat´ olica del Per´ u.

Resumen La teor´ıa del Portafolio, propuesta por Markowitz, es una de las m´as importantes en el ´ambito financiero. En ella, un agente busca lograr un nivel ´optimo de sus inversiones considerando el nivel de riesgo y rentabilidad de un portafolio, conformado por un conjunto de acciones burs´ atiles. En este trabajo se propone una extensi´on a la estimaci´on cl´asica del riesgo en la teor´ıa del Portafolio usando Estimadores Robustos tales como los obtenidos por los m´etodos del Elipsoide de Volumen m´ınimo, el Determinante de Covarianza M´ınima, el Estimador Ortogonalizado de Gnanadesikan y Kettenring, el Estimador con base en la matriz de Covarianzas de la distribuci´on t- Student Multivariada y la Inferencia Bayesiana. En este u ´ltimo caso, se hace uso de los modelos Normal Multivariado y t-student multivariado. En todos los modelos descritos se eval´ ua el impacto econ´omico que se logra si se usaran estas t´ecnicas en el Portafolio del inversionista en lugar de la estimaci´on cl´asica. Para esto se utilizar´ an activos de la Bolsa de Valores de Lima.

35

´ DE POSTER CAP´ITULO 7. SESION

POSTER 8 ´ DE LOS INTERVALOS DE UNA APLICACION CONFIANZA PARA LA MEDIANA DE SUPERVIVENCIA ´ DE COX EN EL MODELO DE REGRESION Jorge A. Mondrag´on,1 1

Elizabeth Doig Camino,2

Pontificia Universidad Cat´ olica del Per´ u.

Resumen El presente trabajo estudi´ o el m´etodo propuesto por Tze y Zheng (2006) aplic´andolo a la obtenci´ on de intervalos de con?anza para la mediana de supervivencia de l´ıneas m´oviles de una empresa de telecomunicaciones. Esta metodolog´ıa se aplic´o con el objeto de conocer el riesgo de vida promedio de la l´ınea m´ovil as´ı como de qu´e manera inciden las covariables sobre el tiempo hasta el incumplimiento del pago de los clientes de la empresa. Para ello se hizo uso de una extensi´ on del modelo de Cox empleando la estimaci´on m´axi- mo veros´ımil para obtener nuevas estimaciones del vector de par´ametros mediante el m´etodo bootstrap lo que permiti´ o la construcci´ on de los intervalos de con?anza para la mediana de supervivencia.

36

´ DE POSTER CAP´ITULO 7. SESION

POSTER 9 ESTUDIO SOBRE LOS FACTORES DE RIESGO MATERNOS ASOCIADOS A LA MORTALIDAD PERINATAL EN EL HOSPITAL UNIVERSITARIO DEL VALLE “EVARISTO GARCIA” DE LA CIUDAD DE SANTIAGO DE CALI PARA EL PERIODO 2001-2006 Javier Olaya,1

Clara Isabel Orozco,1 1

Katherin Holguin,1

Jorge Mej´ıa,2

Universidad del Valle, Cali - Colombia. 2

Grupo Cemiya.

Resumen Este estudio tiene como prop´ osito principal identificar los factores maternos asociados a las muertes perinatales ocurridas en el Hospital Universitario del Valle “Evaristo Garc´ıa” de la ciudad Cali- Colombia, adem´ as de cuantificar el riesgo y determinar el valor predictivo de los factores identificados; para tal fin se uso informaci´on recolectada en el Departamento de Ginecolog´ıa y Obstetricia sobre algunas madres y reci´en nacidos registrados en ese periodo. Este an´alisis se realiza a trav´es de la aplicaci´on de dos m´etodos de clasificaci´on, tales como ´ Modelo de Regresi´ on Log´ıstico y Arboles de Clasificaci´on, que permiten agrupar y discriminar los ni˜ nos que viven y mueren descritos mediante las caracter´ısticas de las madres. Adem´as se valora la capacidad predictiva de estos m´etodos usando la tasa de correcta clasificaci´on y el ´area bajo la curva ROC. Se encontr´ o que el riesgo de que el ni˜ no muera en la etapa perinatal se eleva cuando la madre presenta antecedente de muerte perinatal, fue anestesiada durante el parto, tiene embarazo m´ ultiple y present´o patolog´ıas como preeclampsia, hemorragias, anemia cr´ onica y ruptura de membranas, otros factores responsables de estas muertes son la edad, estado civil y el per´ıodo Interg´enesico. Los factores identificados presentaron un poder de predicci´ on moderado de aproximadamente el 70 %.

37

´ DE POSTER CAP´ITULO 7. SESION

POSTER 10 ´ ALGUNAS EXTENSIONES DE LA DISTRIBUCION BIRNBAUM-SAUNDERS CON MIXTURA DE ESCALA NORMAL: UN ABORDAJE BAYESIANO Edwin Chai˜ na,1 1

Pontificia Universidad Cat´ olica del Per´ u.

Resumen El tiempo de fatiga de los materiales ha sido un problema, de gran importancia en el ´area de ingenier´ıa, el modelo Birnbaum Saunder(BS) que ha sido originado a partir de un problema f´ısico, que es un da˜ no estructural que ocurre cuando un material es expuesto a estr´es y tensi´ on, este da˜ no acumulativo que produce la fatiga de materiales fue identificada como una importante causa de fallas en estructuras de ingenieria. Durante las u ´ltimas d´ecadas se fue desenvolviendo extensiones para este modelo y su apli- cabilidad en otras ´areas, como medicina, biolog´ıa, etc. Uno de los principales problemas para escoger una distribuci´on estad´ıstica, es que frecuentemente varios modelos ajustan los datos bien en la parte central, m´as, no en tanto, en los extremos de la distribuci´on, colocando en duda la decisi´on para seleccionar algunos de los modelos propuestos. En este trabajo, presentamos un estudio del modelo “log-escala de mixtura Birnbaum Saun- der (log-SMBS)”, basado en la distribuci´on de escala de mixtura normal(SMN), que es una extensi´on del modelo log-BS. Abordaremos el problema desde una perspectiva Bayesiana ba- sada en M´etodos de Monte Carlo via Cadenas de Markov (MCMC). Para detectar posibles observaciones influyentes en los modelos considerados, fue usado el m´etodo Bayesiano de an´a- lisis de influencia caso a caso, basado en la divergencia de Kullback-Leibler.

38

´ DE POSTER CAP´ITULO 7. SESION

POSTER 11 CLUSTERING REPEATED ORDINAL DATA A BAYESIAN HIERARCHICAL APPROACH TO ESTIMATE FINITE MIXTURES Roy Costilla,1 1

Ivy Liu,1

Richard Arnold,1

School of Mathematics, Statistics and Operations Research. Victoria University of Wellington .

Resumen Analyses of ordinal data are very common but often do not fully exploit its ordinal nature. They are often treated as continuous by assigning numerical scores to ordinal categories and thus assuming that they are equally spaced. Also, traditional cluster approaches such as kmeans, hierarchical clustering, and association analysis are not based on likelihoods and thus statistical inference tools are not available. Further, approaches that treat ordinal data as nominal reduce their statistical power for inference because they ignore the ranked nature of the categories.

39

III Jornada Internacional de Probabilidad y Estadística Hora

Miércoles 13

9.00-11.00

Inscripción Auditorio de EGGLL

11.00-11.15 11.15-12.30

12.30-1.30

Inauguración Plenaria 1 Müller Auditorio de EGGLL Conferencia 1 Louzada Auditorio de EGGLL

4.00-5.00

Minicurso 3 de Lara Sala de Conferencias de EGGLL

6-15-7.15

7.15-8.30

Minicurso 4 Wellner Auditorio de EGGLL

Minicurso 3 de Lara Sala de Conferencias de EGGLL

Minicurso 4 Wellner Auditorio de EGGLL

Coffee break Plenaria 3 Wellner Auditorio de EGGLL

Sesión de Comunicaciones

Pausa

Conferencia 2 Sinha Auditorio de EGGLL Conferencia 3 Conferencia 4 Zevallos Castro Sala de Conferencias de EGGLL Auditorio de EGGLL

Conferencia 5 de Lara Auditorio de EGGLL Sesión de Poster

Conferencia 6 Rotnitzky Auditorio de EGGLL Conferencia 7 Conferencia 8 Chávez-Bedoya Bazán Sala de Conferencias de EGGLL Auditorio de EGGLL

Coffee break

5.00-5.15 5.15-6.15

Viernes 15

Pausa

1.30-3.00

3.00-4.00

Jueves 14

Minicurso 1 Louzada Auditorio de EGGLL

Minicurso 2 Farfán Sala de Conferencias de EGGLL

Plenaria 2 Woodruff Auditorio de EGGLL

Minicurso 1 Louzada Auditorio de EGGLL

Minicurso 2 Farfán Sala de Conferencias de EGGLL

Plenaria 4 Texeira Auditorio de EGGLL

Plenaria 5 Dey Auditorio de EGGLL Clausura