III JIPE -...

III JIPE2014

III JORNADA INTERNACIONAL

DE PROBABILIDAD Y ESTADISTICA

Pontificia Universidad Catolica del Peru

Lima, 13 al 15 de agosto 2014

Organiza:

Seccion Matematicas - PUCP

Auspicio:

Maestrıa en Estadıstica - PUCP

Maestrıa en Matematicas Aplicadas - PUCP

Maestrıa en Matematicas - PUCP

Escuela de Posgrado - PUCP

Facultad de Estudios Generales Letras- PUCP

Comite Cientıfico

James P. Hughes, University of Washington - USA

Alejandro Jara, Pontificia Universidad Catolica de Chile

Giancarlo Sal y Rosas, Pontificia Universidad Catolica del Peru

Jonathan Farfan, Pontificia Universidad Catolica del Peru

Eladio Ocana, Pontificia Universidad Catolica del Peru

Michel de Lara, Ecole des Ponts Paris Tech - Francia

Comite Organizador

Cristian Bayes

Arturo Calderon

Richard Chavez

Abelardo Jordan

Luis Valdivieso

ii

Indice general

1. PRESENTACION 1

2. PROGRAMA 2

3. PLENARIAS 7

4. MINICURSOS 11

5. CONFERENCIAS 13

6. COMUNICACIONES ORALES 19

7. SESION DE POSTER 28

iii

1. PRESENTACION

La Pontificia Universidad Catolica del Peru, a traves de la Seccion de Matematicas y el apoyo

de las maestrıas de Estadıstica, Matematicas y Matematicas Aplicadas, esta organizando la

III Jornada Internacional de Probabilidad y Estadıstica (III JIPE). Este evento internacional,

que se viene realizandose en la Universidad desde el ano 2010, se ha convertido en el principal

evento de su area a nivel nacional y uno de los eventos mas importantes de su genero a nivel

de Sudamerica. El evento se llevara a cabo los dıas miercoles 13, jueves 14 y viernes 15 de

Agosto del 2014.

El evento reunira a varios investigadores de renombre mundial en el area, quienes ex-

pondran y compartiran los resultados de sus trabajos a traves de 5 sesiones plenarias, 8

conferencias, 4 mini-cursos, una sesion de comunicaciones y una sesion de posters.

El Comite Organizador

Lima, 13 de agosto de 2014

1

2. PROGRAMA

Miercoles, 13 de agosto de 2014

9.00-11.00 INSCRIPCION

Lugar: Auditorio de Estudios Generales Letras

11.00-11.15 INAUGURACION


11.15-12.30 PLENARIA 1

Tıtulo: A BAYESIAN FEATURE ALLOCATION MODEL FOR TUMOR HETERO-

GENEITY

Ponente: Peter Muller, University of Texas - USA


12.30-1.30 CONFERENCIA 1

Tıtulo: PREDICTING FOOTBALL MATCH OUTCOMES: THE 2014 FIFA WORLD

CUP TOURNAMENT CASE

Ponente: Francisco Louzada, Universidad de Sao Paulo - Brasil


1.30-3.00 PAUSA


Tıtulo: PRACTICAL BAYESIAN DESIGN AND ANALYSIS OF NON-INFERIORITY

TRIAL WITH SURVIVAL RESPONSE

Ponente: Debajyoti Sinha, Florida State University - USA



Tıtulo: MINIMUM DISTANCE ESTIMATION OF HIGH FREQUENCY TRANSAC-

TION DATA

Ponente: Mauricio Zevallos, Universidade Estadual de Campinas - Brasil

Lugar: Sala de Conferencias de Estudios Generales Letras

2

CAPITULO 2. PROGRAMA


Tıtulo: DIAGNOSTICS FOR CENSORED MIXED-EFFECTS MODELS USING THE

MULTIVARIATE T-DISTRIBUTION

Ponente: Mauricio Castro, Universidad de Concepcion - Chile


5.00-5.15 COFFEE BREAK


5.15-7.15 MINICURSO 1

Tıtulo: AN INTRODUCTION TO STATISTICAL MODELING FOR FINANCIAL DA-

TA




Tıtulo: LA INTEGRAL DE ITO

Ponente: Jonathan Farfan, Pontificia Universidad Catolica del Peru


7.15-8.30 PLENARIA 2

Tıtulo: MULTI-STAGE STOCHASTIC OPTIMIZATION: SOLUTION AND SCENA-

RIO GENERATION METHODS

Ponente: David L. Woodruff, University of California, Davis - USA


Jueves, 14 de agosto de 2014:


Tıtulo: STOCHASTIC VIABILITY AND APPLICATIONS

Ponente: Michel De Lara, Ecole des Ponts ParisTech, Universite Paris-Est, Paris - Fran-

cia



Tıtulo: EMPIRICAL PROCESS THEORY FOR STATISTICS

Ponente: Jon Wellner, University of Washington - USA




3


11.15-12.30 PLENARIA 3

Tıtulo: GOODNESS OF FIT TESTS AND CONFIDENCE BANDS FOR DISTRIBU-

TION FUNCTIONS: SOME NEW APPROACHES



12.30-3.00 PAUSA


Tıtulo: TIME-CONSISTENCY: FROM OPTIMIZATION TO RISK MEASURES


cia


4.00-5.00 SESION DE POSTER

Lugar: Pasadizo EEGGLL primer piso




Tıtulo: AN INTRODUCTION TO STATISTICAL MODELING FOR FINANCIAL DA-

TA




Tıtulo: LA INTEGRAL DE ITO

Ponente: Jonathan Farfan, Pontificia Universidad Catolica del Peru



Tıtulo: PHASE TRANSITION FOR A SYSTEM OF ACTIVATED RANDOM WALKS

Ponente: Augusto Texeira, Instituto Nacional de Matematica Pura y Aplicada, Brasil


Viernes, 15 de agosto de 2014:


Tıtulo: STOCHASTIC VIABILITY AND APPLICATIONS


cia

4




Tıtulo: EMPIRICAL PROCESS THEORY FOR STATISTICS





11.15-12.30 SESION DE COMUNICACIONES

Lugar: Auditorio y sala de conferencias de Estudios Generales Letras

12.30-3.00 PAUSA


Tıtulo: Por confirmar

Ponente: Andrea Rotnitzky, Universidad de Harvard - USA y Universidad di Tella -

Argentina



Tıtulo: MODELING DISTRIBUTION UNCERTAINTY IN ACTIVE PORTFOLIO MA-

NAGEMENT

Ponente: Luis Chavez Bedoya, Universidad Esan



Tıtulo: A NEW DISTRIBUTION TO THE MODELING OF DISPERSION IN BINO-

MIAL DATA WITH APLICATIONS

Ponente: Jorge Bazan, Universidad de Sao Paulo - Brasil





Tıtulo: BAYESIAN MODELING OF SPARSE HIGH DIMENSIONAL DATA USING

DIVERGENCE MEASURES

Ponente: Dipak Dey, University of Connecticut - USA


5


6.15-6.30 CLAUSURA


6

3. PLENARIAS

PLENARIA 1

A BAYESIAN FEATURE ALLOCATION MODEL FOR

TUMOR HETEROGENEITY

Peter Muller

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 muta-

tions). 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.

7

CAPITULO 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 auto-

mated 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.

8


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 re-

peated 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-of-

fit 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.

9


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.

10


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.

11

4. MINICURSOS

MINICURSO 1

INTRODUCAO A MODELAGEM ESTATISTICA PARA

DADOS DE CREDITO

Francisco Louzada

Universidade de Sao Paulo, Brasil.

Resumen

Os modelos de credit scoring tem sido utilizados como uma das principais ferramentas de

suporte a concessao de credito. O desenvolvimento de tais modelos tem como base a cons-

trucao de um procedimento formal para descrever quais caracterısticas dos clientes estao,

efetivamente, relacionadas com o seu risco de credito e qual a intensidade e direcao desse

relacionamento. O objetivo basico os modelos de credit scoring e geracao de um escore ou

de um grupo de escores atraves dos quais clientes potenciais possam ser ordenados segundo

a sua chance de inadimplencia. Neste Minicurso os procedimentos estatısticos comumente

utilizados na modelagem de credit scoring sao apresentados.

MINICURSO 2

LA INTEGRAL DE ITO

Jonathan Farfan

Pontificia Universidad Catolica del Peru.

Resumen

El objetivo principal de este minicurso es exhibir de manera explicita los pasos de la cons-

truccion de la integral de Ito en el caso en que el integrador es un Movimiento Browniano

y luego ver los pasos de la construccion con integradores mas generales. Para tal fin, seran

necesarios introducir algunos conceptos previos tales como: tipos de convergencia de variables

aleatorias, tiempos de parada, Movimiento Browniano y martingalas.

12

CAPITULO 4. MINICURSOS

MINICURSO 3

STOCHASTIC VIABILITY AND APPLICATIONS

Michel De Lara

Ecole des Ponts ParisTech, Universite 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.

13

5. CONFERENCIAS

CONFERENCIA 1

PREDICTING FOOTBALL MATCH OUTCOMES: THE

2014 FIFA WORLD CUP TOURNAMENT CASE

Francisco Louzada

Universidade de Sao 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 Baye-

sian approach. Tournament simulations were performed in order to estimate probabilities of

winning the tournament assuming different values for the weight attached to the experts in-

formation 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.

14

CAPITULO 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 ad-

ministration, 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 com-

bination therapy). Such trials will also play prominent roles for evaluating immunotherapy

agents including cancer vaccines and for assessing most modern-day antibiotics (e.g., qui-

nolones, 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.

15


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.

16


CONFERENCIA 4

DIAGNOSTICS FOR CENSORED MIXED-EFFECTS

MODELS USING THE MULTIVARIATE t-DISTRIBUTION

Luis M. Castro Cepero

Universidad de Concepcion, 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 EM-

type 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 ex-

pectation 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 fra-

mework. 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.

17


CONFERENCIA 5

TIME-CONSISTENCY: FROM OPTIMIZATION TO RISK

MEASURES

Michel De Lara

Ecole des Ponts ParisTech, Universite Paris-Est, Paris, France.

Resumen

Stochastic optimal control is concerned with sequential decision-making under uncer-

tainty. 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 infor-

mation 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 measu-

res 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 corres-

ponding 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 obser-

ve 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.

18


CONFERENCIA 7

MODELING DISTRIBUTION UNCERTAINTY IN

ACTIVE PORTFOLIO MANAGEMENT

Luis Chavez-Bedoya

Universidad Esan, Peru.

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 Bazan

Instituto de Ciencias Matematicas e de Computacao, Universidade de Sao 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.

19

6. COMUNICACIONES ORALES

COMUNICACION ORAL 1

NUMERICAL APPROXIMATION TO MELLIN

CONVOLUTION BY MIXTURES OF EXPONENTIALS

Jorge Luis Torrejon Matos,1 Julio Michael Stern,1

1Deparment of Applied Mathematics, Institute of Mathematics and Statistics - University of Sao

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.

20

CAPITULO 6. COMUNICACIONES ORALES

COMUNICACION ORAL 2

BARE BONES PARTICLE SWARM OPTIMIZATION

WITH SCALE MATRIX ADAPTATION

Mauro Campos,1 Renato A. Krohling,2, Ivan Enriquez 1

1Department of Statistics, Federal University of Espırito Santo, Vitoria ES, Brazil.

2Department of Production Engineering and with the Graduate Program in Computer Science,

Federal University of Espırito Santo, Vitoria 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 t-

distribution in its hierarchical form, as a scale mixtures of normal distributions. The t-

distribution 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.

21


COMUNICACION ORAL 3

INFERENCE FOR THE BIVARIATE

BIRNBAUM-SAUNDERS DISTRIBUTION

Luis Benites,1 Filidor Vilca,1 Vıctor Leiva2

1Departamento de Estatıstica, Universidade Estadual de Campinas, Brazil.

2Instituto de Estadıstica, Universidad de Valparaıso, Chile.

Resumen

Multivariate distributions are a topic largely studied and, particularly, because of its ap-

plicability, 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 biva-

riate Birnbaum- Saunders distribution. About estimation, modified moment and maximum

likelihood methods are employed. We prove that the modified moment estimators are consis-

tent 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 ap-

proach with simulated and real-world data. Our study provides new findings and improves

the results proposed until now on this topic.

22


COMUNICACION ORAL 4

THE EXPONENTIATED UNIFORM DISTRIBUTION:

THEORY AND APPLICATION

Luiz Ricardo Nakamura,1 Thiago Gentil Ramires,1 Edwin Moises Marcos Ortega1

1Departamento de Ciencias Exatas, Escola Superior de Agricultura Luiz de Queiroz, Universidade

de Sao Paulo,Piracicaba, Sao 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 Generalized-

Exponential, Beta-Exponential, Beta-Pareto, Exponential Poisson, Beta Generalized Half-

Normal and Generalized Half- Normal distributions. The results show that the proposed

distribution obtained a similar or better fit to the data set.

23


COMUNICACION ORAL 5

CENSORED LINEAR REGRESSION MODELS FOR

IRREGULARLY OBSERVED LONGITUDINAL DATA

USING THE MULTIVARIATE-t DISTRIBUTION

Aldo M. Garay,1 Luis M. Castro,2 Jacek Leskow,3 Victor H. Lachos1

1Departamento de Estatıstica, Universidade Estadual de Campinas, Brazil.

2Department of Statistics, Universidad de Concepcion, Chile.

3Technical University of Cracow, Poland.

Resumen

In AIDS studies it is quite common to observe viral load measurements collected irre-

gularly 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 irregu-

larly 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


COMUNICACION ORAL 6

ROBUST BOOTSTRAP PREDICTION INTERVALS FOR

RETURNS AND VOLATILITIES IN GARCH MODELS.

Carlos Trucıos Maza,1 Luiz K. Hotta,1 Esther Ruiz2

1Department of Statistics, University of Campinas, Brazil.

2Department 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 prediction intervals. Traditional methods of cons-

tructing 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 obtain 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


COMUNICACION ORAL 7

SIMULACION ESTOCASTICA DE ESQUEMAS

PIRAMIDALES TIPO PONZI.

Lilia Quituisaca-Samaniego ,1 Juan Mayorga-Zambrano,2 Paul Medina3

1Direccion de Estudios Analıticos Estadısticos, Instituto Nacional de Estadıstica y Censos, Quito,

Ecuador.

2Pontificia Universidad Catolica del Ecuador - Sede Ambato, Ambato, Ecuador.

3Instituto Gregorio Millan, Universidad Carlos III de Madrid, Madrid, Espana.

3Departamento de Ciencias Exactas, Universidad de la Fuerzas Armadas ESPE, Quito, Ecuador.

Resumen

Mediante simulacion, se estudian varios casos de fraude provocados por piramides fi-

nancieras tipo Ponzi (incluyendo los casos Madoff, DRFE y Cabrera); la tecnica empleada

corresponde a la implementacion computacional de un modelo estocastico disenado por J.

Mayorga-Zambrano.Se comparan datos reales con aquellos generados por el software imple-

mentado; en particular, se estudia la evolucion del numero de clientes, del monto de estafa y

del tiempo estimado de duracion de la piramide.

26


COMUNICACION ORAL 8

EL DESARROLLO DE LOS MERCADOS DOMESTICOS

DE RENTA FIJA Y VARIABLE Y EL ROL DE LOS

FONDOS DE PENSIONES

Marıa Nela Seijas Gimenez1

1Universidad ORT Uruguay.

Resumen

Los sistemas personales de capitalizacion individual han experimentado un importante

crecimiento en las ultimas decadas, siguiendo la tendencia de envejecimiento de las poblacio-

nes y las crisis de los sistemas de pensiones de beneficios definidos. El objetivo del presente

trabajo es determinar si la implantacion de estos esquemas de pensiones ha impulsado el

desarrollo de los mercados de capitales domesticos a nivel global, en el perıodo 1990-2011.

La estrategia metodologica comprende regresiones de paneles incluyendo indicadores de pro-

fundidad y liquidez de los mercados de acciones y bonos ası como herramientas estadısticas

de Arbol de expansion mınima y Arbol jerarquico y tecnicas de clasificacion aplicadas sobre

informacion estadıstica representativa de la performance de los sistemas. El analisis realizado

permite comprobar que los fondos de pensiones de capitalizacion individual han significado

un estımulo a la profundidad accionaria en los mercados de capitales. Se evidencia asimismo

una causalidad negativa con la liquidez accionaria, lo que esta vinculado con el perfil a lar-

go plazo de su gestion de portafolios previsionales. Ambos indicadores reciben los impactos

positivos de mayor magnitud desde los sistemas incluidos en el cluster de maduracion avan-

zada. La profundidad de la deuda publica es estimulada fundamentalmente por los sistemas

voluntarios, tambien asociados a mejoras en el desarrollo accionario. Los clusteres de madu-

racion gradual baja e incipiente ejercen impactos significativos sobre la deuda publica, lo que

esta en lınea 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


COMUNICACION ORAL 9

THE CODISPERSION MAP: A GRAPHICAL TOOL TO

VISUALIZE THE ASSOCIATION BETWEEN TWO

SPATIAL PROCESSES

Ronny Vallejos,1 Felipe Osorio,1 Diego Mancilla1

1Departamento de Matematica, Universidad Tecnica Federico Santa Marıa, Valparaıso, 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

7. SESION DE POSTER

POSTER 1

MODELOS DE RESPUESTA ALEATORIZADA

ESTRATIFICADA: UNA APLICACION A ESTUDIANTES

DE LA FACULTAD DE CIENCIAS MATEMATICAS DE

LA UNMSM

Doris Gomez Ticeran, Ana Cardenas Rojas, Ysabel Adriazola Cruz Felix

Bartolo Gotarate Olga Solano Davila Olga Solano Davila1, Blanca Martinez

Portuguez, Orlando Giraldo Laguna

1Facultad de Ciencias Matematicas, UNMSM.

Resumen

En el presente trabajo estudiamos tres Modelos de Respuestas Aleatorizada (MRA) Es-

tratificada, utilizadas en encuestas donde se utilizan preguntas delicadas. Realizamos una

aplicacion en el comportamiento de jovenes de la Facultad de Ciencias Matematicas de la

UNMSM, para investigar la proporcion de personas que han consumido pasta basica de co-

caına (PBC) por lo menos una vez en su vida; la proporcion de consumidores actuales del

PBC; la proporcion de personas que han tenido relaciones sexuales con mas de dos personas

durante toda su vida; la proporcion de personas que consumen alcohol todos los fines de se-

mana y la proporcion de persona que han llevado o han consumido sin pagar algun producto

de algun supermercado. La poblacion en estudio comprende los alumnos matriculados en la

FCM el semestre 2009-II

29

CAPITULO 7. SESION DE POSTER

POSTER 2

ESTUDIO DEL ESTRES ACADEMICO EN ESTUDIANTES

UNIVERSITARIOS DE LA FACULTAD DE CIENCIAS

MATEMATICAS UTILIZANDO METODOS

MULTIVARIANTES

Olga Solano,1 Doris Gomez1, Ana Cardenas1, Felix Bartolo1, , Blanca

Martinez1, Orlando Giraldo1, Mendoza Jacinto1, Olga Bolanos2

1 Facultad de Ciencias Matematicas, UNMSM.

2Facultad de Psicologıa. URP.

Resumen

En el presente trabajo realizamos una comparacion del estres academico en los estudiantes

matriculados en la Facultad de Ciencias Matematicas (FCM) de la UNMSM segun genero,

utilizando el instrumento de medida de la Subescala de Estresores Academicos (E-CEA) y

metodos multivariantes, en particular la estadıstica T 2 de Hotelling (Johnson y Wichern,

1992), para analizar los datos recolectados. En el diseno muestral, se utilizo el muestreo

aleatorio estratificado con afijacion proporcional al tamano de cada estrato (Scheffer y Men-

denhall, 2007) considerando como estratos a las Escuelas Academicas Profesionales (E.A.P.)

de la FCM. Para el calculo del tamano de muestra se considero un lımite para el error de

estimacion del 5,07 %, con un nivel de cofianza del 95 % y la informacion proporcionada por

la Direccion Academica de la FCM, de los alumnos matriculados el primer semestre del ano

academico 2013, el tamano 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 aplico el instrumento de medida de la

E-CEA.

30


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, Luiz Ricardo Nakamura1,

Ezequiel Abraham Lopez Bautista1, , Lucio Borges de Araujo1, Carlos Tadeu dos

Santos Dias1

1 Departamento de Ciencias Exatas, Escola Superior de Agricultura Luiz de Queiroz, Universidade

de Sao Paulo - Piracicaba, So Paulo, Brazil..

Resumen

Zapote (Pouteria sapota) is a fruit tree of sapotaceas family originally from the tropi-

cal 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 Agronomico Tropical de Investigacion y Ensenanza (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 tech-

niques: 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 variability, 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


POSTER 4

SOIL CHEMICAL PROPERTIES IN PRECISION

AGRICULTURE: DIMENSIONALITY REDUCTION BY

PRINCIPAL COMPONENT ANALYSIS

Natalia da Silva Martins,1 Renan Mercuri Pinto,1 Luiz Ricardo Nakamura,1

Erik Augusto Barreto Junior,1 Carlos Tadeu dos Santos Dias1

1 Departamento de Ciencias Exatas, Escola Superior de Agricultura Luiz de Queiroz, Universidade

de Sao Paulo - Piracicaba, So 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 pro-

duction. 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, Sao 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


POSTER 5

MOVILIDAD ENDOGENA Y VARIACIONES

DEMOGRAFICAS: UNA APLICACION PARA ECUADOR

Luis Antamba ,1 Paul Medina,2

1 Direccion de Estudios Analıticos Estadısticos, Instituto Nacional de Estadıstica y Censos, Quito,

Ecuador.

2Instituto Gregorio Millan, Universidad Carlos III de Madrid, Madrid, Espana.

2 Departamento de Ciencias Exactas, Universidad de las Fuerzas Armadas, Sangolquı, Ecuador.

Resumen

Se establece un modelo que describe la movilidad interna y externa a nivel provincial de

la poblacion ecuatoriana, considerando su autoidentificacion etnica(indıgena y no indıgena).

El estudio se basa en un modelo estocastico basado en las cadenas de Markov. Para la

investigacion se han tomado como base los datos del Censo de Poblacion y Vivienda 2010,

elaborado por el Instituto Nacional de Estadıstica y Censos (INEC).

33


POSTER 6

ANALISIS DE INFLUENCIA DEL MODELO DE

REGRESION BETA POR INFERENCIA BAYESIANA

Jim Silvestre,1

1 Maestrıa en Estadıstica - Pontificia Universidad Catolica del Peru.

Resumen

El objetivo de esta presentacion es mostrar como se realiza un analisis de influencia desde

el punto de vista de la inferencia Bayesiana al modelo de regresion Beta. Se utilizara es-

pecificamente dos medidas de influencia: La ordenada predictiva condicional (CPO) y la

divergencia Kullback Leibler. Se simularan datos de la regresion Beta considerando para esto

computacion intensiva sobre diferentes escenarios ası como tambien se estimara las medidas

en mencion utilizando MCMC. Finalmente se presenta una aplicacion desarrollada con datos

del Instituto Australiano del Deporte (AIS)

34


POSTER 7

PORTAFOLIOS OPTIMOS BAJO ESTIMADORES ROBUS-

TOS CLASICOS Y BAYESIANOS CON

APLICACIONES AL MERCADO PERUANO DE ACCIO-

NES

Alberto Vera ,1 Cristian Bayes,2

1 Banco de Credito del Peru.

2 Pontificia Universidad Catolica del Peru.

Resumen

La teorıa del Portafolio, propuesta por Markowitz, es una de las mas importantes en el ambi-

to financiero. En ella, un agente busca lograr un nivel optimo de sus inversiones consi-

derando el nivel de riesgo y rentabilidad de un portafolio, conformado por un conjun-

to de acciones bursatiles. En este trabajo se propone una extension a la estimacion clasi-

ca del riesgo en la teorıa del Portafolio usando Estimadores Robustos tales como los ob-

tenidos por los metodos del Elipsoide de Volumen mınimo, el Determinante de Covarian-

za Mınima, el Estimador Ortogonalizado de Gnanadesikan y Kettenring, el Estimador con ba-

se en la matriz de Covarianzas de la distribucion t- Student Multivariada y la Inferencia Baye-

siana. En este ultimo caso, se hace uso de los modelos Normal Multivariado y t-student multi-

variado. En todos los modelos descritos se evalua el impacto economico que se logra si se usa-

ran estas tecnicas en el Portafolio del inversionista en lugar de la estimacion clasica. Para es-

to se utilizaran activos de la Bolsa de Valores de Lima.

35


POSTER 8

UNA APLICACION DE LOS INTERVALOS DE

CONFIANZA PARA LA MEDIANA DE SUPERVIVENCIA

EN EL MODELO DE REGRESION DE COX

Jorge A. Mondragon,1 Elizabeth Doig Camino,2


Resumen

El presente trabajo estudio el metodo propuesto por Tze y Zheng (2006) aplicandolo a

la obtencion de intervalos de con?anza para la mediana de supervivencia de lıneas moviles

de una empresa de telecomunicaciones. Esta metodologıa se aplico con el objeto de conocer

el riesgo de vida promedio de la lınea movil ası como de que 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 extension del modelo de Cox empleando la estimacion maxi- mo verosımil

para obtener nuevas estimaciones del vector de parametros mediante el metodo bootstrap lo

que permitio la construccion de los intervalos de con?anza para la mediana de supervivencia.

36


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 Katherin Holguin,1 Jorge Mejıa,2

1 Universidad del Valle, Cali - Colombia.

2 Grupo Cemiya.

Resumen

Este estudio tiene como proposito principal identificar los factores maternos asociados a

las muertes perinatales ocurridas en el Hospital Universitario del Valle “Evaristo Garcıa” de

la ciudad Cali- Colombia, ademas de cuantificar el riesgo y determinar el valor predictivo de

los factores identificados; para tal fin se uso informacion recolectada en el Departamento de

Ginecologıa y Obstetricia sobre algunas madres y recien nacidos registrados en ese periodo.

Este analisis se realiza a traves de la aplicacion de dos metodos de clasificacion, tales como

Modelo de Regresion Logıstico y Arboles de Clasificacion, que permiten agrupar y discriminar

los ninos que viven y mueren descritos mediante las caracterısticas de las madres. Ademas se

valora la capacidad predictiva de estos metodos usando la tasa de correcta clasificacion y el

area bajo la curva ROC. Se encontro que el riesgo de que el nino muera en la etapa perinatal

se eleva cuando la madre presenta antecedente de muerte perinatal, fue anestesiada durante

el parto, tiene embarazo multiple y presento patologıas como preeclampsia, hemorragias,

anemia cronica y ruptura de membranas, otros factores responsables de estas muertes son la

edad, estado civil y el perıodo Intergenesico. Los factores identificados presentaron un poder

de prediccion moderado de aproximadamente el 70 %.

37


POSTER 10

ALGUNAS EXTENSIONES DE LA DISTRIBUCION

BIRNBAUM-SAUNDERS CON MIXTURA DE ESCALA

NORMAL: UN ABORDAJE BAYESIANO

Edwin Chaina,1


Resumen

El tiempo de fatiga de los materiales ha sido un problema, de gran importancia en el

area de ingenierıa, el modelo Birnbaum Saunder(BS) que ha sido originado a partir de un

problema fısico, que es un dano estructural que ocurre cuando un material es expuesto a

estres y tension, este dano acumulativo que produce la fatiga de materiales fue identificada

como una importante causa de fallas en estructuras de ingenieria. Durante las ultimas deca-

das se fue desenvolviendo extensiones para este modelo y su apli- cabilidad en otras areas,

como medicina, biologıa, etc. Uno de los principales problemas para escoger una distribucion

estadıstica, es que frecuentemente varios modelos ajustan los datos bien en la parte central,

mas, no en tanto, en los extremos de la distribucion, colocando en duda la decision 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 distribucion

de escala de mixtura normal(SMN), que es una extension del modelo log-BS. Abordaremos

el problema desde una perspectiva Bayesiana ba- sada en Metodos de Monte Carlo via Ca-

denas de Markov (MCMC). Para detectar posibles observaciones influyentes en los modelos

considerados, fue usado el metodo Bayesiano de analisis de influencia caso a caso, basado

en la divergencia de Kullback-Leibler.

38


POSTER 11

CLUSTERING REPEATED ORDINAL DATA A

BAYESIAN HIERARCHICAL APPROACH TO ESTIMATE

FINITE MIXTURES

Roy Costilla,1 Ivy Liu,1 Richard Arnold,1

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 k-

means, 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

Hora

11.00-11.15

12.30-1.30

1.30-3.00

3.00-4.00

4.00-5.00

Conferencia 3

Zevallos

Sala de Conferencias de EGGLL

Conferencia 4

Castro

Auditorio de EGGLL

Conferencia 7

Chávez-Bedoya


Conferencia 8

Bazán

Auditorio de EGGLL

5.00-5.15

5.15-6.15

6-15-7.15

7.15-8.30

III Jornada Internacional de Probabilidad y Estadística

Miércoles 13 Jueves 14 Viernes 15

9.00-11.00

Minicurso 3

de Lara


Minicurso 4

Wellner

Auditorio de EGGLL

Minicurso 3

de Lara


Minicurso 4

Wellner

Auditorio de EGGLL

Inscripción

Auditorio de EGGLL

Plenaria 5

Dey

Auditorio de EGGLL

11.15-12.30

Plenaria 1

Müller

Auditorio de EGGLL

Plenaria 3

Wellner

Auditorio de EGGLL

Sesión de Comunicaciones

Conferencia 1

Louzada

Auditorio de EGGLLPausa

Pausa

Clausura

Plenaria 2

Woodruff

Auditorio de EGGLL

Plenaria 4

Texeira

Auditorio de EGGLL

Inauguración Coffee break

Conferencia 2

Sinha

Auditorio de EGGLL

Conferencia 5

de Lara

Auditorio de EGGLL

Conferencia 6

Rotnitzky

Auditorio de EGGLL

Sesión de Poster

Coffee break

Minicurso 1

Louzada

Auditorio de EGGLL

Minicurso 2

Farfán


Minicurso 1

Louzada

Auditorio de EGGLL

Minicurso 2

Farfán


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