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
Lugar: Auditorio de Estudios Generales Letras
11.15-12.30 PLENARIA 1
Tıtulo: A BAYESIAN FEATURE ALLOCATION MODEL FOR TUMOR HETERO-
GENEITY
Ponente: Peter Muller, University of Texas - USA
Lugar: Auditorio de Estudios Generales Letras
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
Lugar: Auditorio de Estudios Generales Letras
1.30-3.00 PAUSA
3.00-4.00 CONFERENCIA 2
Tıtulo: 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
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
4.00-5.00 CONFERENCIA 4
Tıtulo: DIAGNOSTICS FOR CENSORED MIXED-EFFECTS MODELS USING THE
MULTIVARIATE T-DISTRIBUTION
Ponente: Mauricio Castro, Universidad de Concepcion - 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
Tıtulo: AN INTRODUCTION TO STATISTICAL MODELING FOR FINANCIAL DA-
TA
Ponente: Francisco Louzada, Universidad de Sao Paulo - Brasil
Lugar: Auditorio de Estudios Generales Letras
5.15-7.15 MINICURSO 2
Tıtulo: LA INTEGRAL DE ITO
Ponente: Jonathan Farfan, Pontificia Universidad Catolica del Peru
Lugar: Sala de Conferencias de Estudios Generales Letras
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
Lugar: Auditorio de Estudios Generales Letras
Jueves, 14 de agosto de 2014:
9.00-11.00 MINICURSO 3
Tıtulo: STOCHASTIC VIABILITY AND APPLICATIONS
Ponente: Michel De Lara, Ecole des Ponts ParisTech, Universite Paris-Est, Paris - Fran-
cia
Lugar: Sala de Conferencias de Estudios Generales Letras
9.00-11.00 MINICURSO 4
Tıtulo: 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
3
CAPITULO 2. PROGRAMA
11.15-12.30 PLENARIA 3
Tıtulo: GOODNESS OF FIT TESTS AND CONFIDENCE BANDS FOR DISTRIBU-
TION 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
Tıtulo: TIME-CONSISTENCY: FROM OPTIMIZATION TO RISK MEASURES
Ponente: Michel De Lara, Ecole des Ponts ParisTech, Universite Paris-Est, Paris - Fran-
cia
Lugar: Auditorio de Estudios Generales Letras
4.00-5.00 SESION DE POSTER
Lugar: Pasadizo EEGGLL primer piso
5.00-5.15 COFFEE BREAK
Lugar: Auditorio de Estudios Generales Letras
5.15-7.15 MINICURSO 1
Tıtulo: AN INTRODUCTION TO STATISTICAL MODELING FOR FINANCIAL DA-
TA
Ponente: Francisco Louzada, Universidad de Sao Paulo - Brasil
Lugar: Auditorio de Estudios Generales Letras
5.15-7.15 MINICURSO 2
Tıtulo: LA INTEGRAL DE ITO
Ponente: Jonathan Farfan, Pontificia Universidad Catolica del Peru
Lugar: Sala de Conferencias de Estudios Generales Letras
7.15-8.30 PLENARIA 4
Tıtulo: 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
Tıtulo: STOCHASTIC VIABILITY AND APPLICATIONS
Ponente: Michel De Lara, Ecole des Ponts ParisTech, Universite Paris-Est, Paris - Fran-
cia
4
CAPITULO 2. PROGRAMA
Lugar: Sala de Conferencias de Estudios Generales Letras
9.00-11.00 MINICURSO 4
Tıtulo: 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
11.15-12.30 SESION DE COMUNICACIONES
Lugar: Auditorio y sala de conferencias de Estudios Generales Letras
12.30-3.00 PAUSA
3.00-4.00 CONFERENCIA 6
Tıtulo: 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
Tıtulo: MODELING DISTRIBUTION UNCERTAINTY IN ACTIVE PORTFOLIO MA-
NAGEMENT
Ponente: Luis Chavez Bedoya, Universidad Esan
Lugar: Sala de Conferencias de Estudios Generales Letras
4.00-5.00 CONFERENCIA 8
Tıtulo: A NEW DISTRIBUTION TO THE MODELING OF DISPERSION IN BINO-
MIAL DATA WITH APLICATIONS
Ponente: Jorge Bazan, Universidad de Sao 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
Tıtulo: BAYESIAN MODELING OF SPARSE HIGH DIMENSIONAL DATA USING
DIVERGENCE MEASURES
Ponente: Dipak Dey, University of Connecticut - USA
Lugar: Auditorio de Estudios Generales Letras
5
CAPITULO 2. PROGRAMA
6.15-6.30 CLAUSURA
Lugar: Auditorio de Estudios Generales Letras
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
CAPITULO 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 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
CAPITULO 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.
10
CAPITULO 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.
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
CAPITULO 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.
16
CAPITULO 5. CONFERENCIAS
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
CAPITULO 5. CONFERENCIAS
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
CAPITULO 5. CONFERENCIAS
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
CAPITULO 6. COMUNICACIONES ORALES
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
CAPITULO 6. COMUNICACIONES ORALES
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
CAPITULO 6. COMUNICACIONES ORALES
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
CAPITULO 6. COMUNICACIONES ORALES
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 predic- tion 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 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
CAPITULO 6. COMUNICACIONES ORALES
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
CAPITULO 6. COMUNICACIONES ORALES
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
CAPITULO 6. COMUNICACIONES ORALES
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 me- dida 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
CAPITULO 7. SESION DE POSTER
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 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
CAPITULO 7. SESION DE POSTER
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
CAPITULO 7. SESION DE POSTER
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
CAPITULO 7. SESION DE POSTER
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
CAPITULO 7. SESION DE POSTER
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
CAPITULO 7. SESION DE POSTER
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
1 Pontificia Universidad Catolica del Peru.
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
CAPITULO 7. SESION DE POSTER
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
CAPITULO 7. SESION DE POSTER
POSTER 10
ALGUNAS EXTENSIONES DE LA DISTRIBUCION
BIRNBAUM-SAUNDERS CON MIXTURA DE ESCALA
NORMAL: UN ABORDAJE BAYESIANO
Edwin Chaina,1
1 Pontificia Universidad Catolica del Peru.
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 ana- lisis de influencia caso a caso, basado
en la divergencia de Kullback-Leibler.
38
CAPITULO 7. SESION DE POSTER
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
Sala de Conferencias de EGGLL
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
Sala de Conferencias de EGGLL
Minicurso 4
Wellner
Auditorio de EGGLL
Minicurso 3
de Lara
Sala de Conferencias de EGGLL
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
Sala de Conferencias de EGGLL
Minicurso 1
Louzada
Auditorio de EGGLL
Minicurso 2
Farfán
Sala de Conferencias de EGGLL