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Short-course Room: CA 12 - 2.10, School of Sciences,
Azurém, Guimarães
Thursday, October 3rd 2019
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Short-Course
Abstract:
This short course consists of presenting the fundamental
ideas concerning formulation and statistical analysis of Bayesian
models, including reference to computational means that allow its
implementation. The course syllabus includes the following topics:
Bayesian methodology concepts, Prior information representation, Basic
applications, Bayesian model evaluation, inference via Markov chain
Monte Carlo methods, Applications to some statistical problems.
Giovani Silva e Carlos Daniel Paulino
Dep. Matemática, Instituto Superior Técnico e Centro de Estatística e
Aplicações, Universidade de Lisboa
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11:00-12:30
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Introduction to Bayesian Statistics -
Part I
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14:00-16:00
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Introduction to Bayesian Statistics -
Part II
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16:30-18:00
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Introduction to Bayesian Statistics -
Part III
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Conference Room: CA 12 - 0.26, School of Sciences,
Azurém, Guimarães
Friday, October 4th 2019
10:15-11:00
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Cristina Amado (University of Minho and
NIPE)
Abstract:
In this work, we propose an additive time-varying (or partially
time-varying) structure where a time-dependent component is added to
the extended vector GARCH process for modelling the dynamics of
volatility interactions. In this setting, codependence in volatility is
allowed to change smoothly between two extreme states and financial
contagion is identified from these crisis-contingent structural
changes. The estimation of the new time-varying vector GARCH process is
simplified using an equation by equation estimator for the volatility
equations in the first step, and estimating the correlation matrix in
the second step. A Lagrange multiplier test of volatility contagion is
also presented for testing the null hypothesis of constancy
codependence against a smoothly time-varying interdependence. The
proposed statistical test allows us to investigate volatility contagion
by testing a significant increase in cross-market volatility
transmissions. Finite sample properties of the proposed test statistic
are investigated by Monte Carlo experiments. An empirical application
of the modelling and testing procedure to sovereign bond yields is also
provided. This is joint work with Susana Martins.
Keywords: Multivariate time-varying GARCH; Volatility
spillovers; Structural change; Lagrange multiplier test;
Volatility-based contagion.
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11:30-12:15
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Carlos Daniel Paulino (Centro de
Estatística e Aplicações da Universidade de Lisboa)
Abstract:
Estimation of microorganism concentration in ballast water tanks is
important to evaluate and possibly to prevent the introduction of
invasive species in stable ecosystems. For such purpose, the number of
organisms in ballast water aliquots are counted and used to estimate
their concentration with some precision requirement in order to verify
compliance with international standards. We consider Poisson and
negative binomial models under a
Bayesian approach to determine minimum sample sizes required to
construct HPD credible intervals satisfying average coverage and
average length criteria.
Keywords: sample size, average coverage criterion,
average length criterion, Poisson distribution, negative binomial
distribution.
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12:15-13:00
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Carmen Minuesa Abril (University of
Extremadura)
Abstract:
Population-size-dependent branching processes (PSDBPs) are models which
describe the evolution of populations where individuals in the same
generation produce their offspring independently according to a
probability law which depends on the current population size. One
important class of PSDBPs are branching processes with a carrying
capacity; these are appropriate for modelling populations that exhibit
logistic growth, where the population size tends to fluctuate, for a
long period of time, around a threshold value corresponding to the
maximum number of individuals that the ecosystem can support in view of
its resources. In this work, we consider discrete-time PSDBPs and
assume that we observe the total population size at every generation up
to some time. We propose an estimator for the mean of the offspring
distribution at each population size by using the maximum likelihood
method, and we derive its asymptotic properties. Since the processes
that we consider eventually become extinct with probability one, for
the analysis of the limiting behaviour of the estimators it is needed
to condition on the survival of the process in a distant future and to
study the corresponding estimator in the Q-process associated with the
original branching process. This leads to a new concept of consistency,
which we name Q-consistency. We show that our estimators are
Q-consistent and that their conditional limit is close to the targeted
quantity. Finally, we illustrate our results numerically. This is joint
work with Peter Braunsteins (University of Melbourne) and Sophie
Hautphenne (University of Melbourne).
Keywords: branching process; population-size-dependence;
maximum likelihood estimator; carrying capacity
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14:15-15:00
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Cláudia Santos (Coimbra College of
Agriculture, Polytechnic Institute of Coimbra and CIDMA, University of
Aveiro)
In
this work a multivariate integer-valued autoregressive model of order
one with periodic time-varying parameters, and driven by a periodic
innovations sequence of independent random vectors is introduced.
Emphasis is placed on models with periodic multivariate negative
binomial innovations. Aiming to reduce computational burden arising
from the use of the conditional maximum likelihood method a composite
likelihood-based approach is adopted. The performance of such method is
compared with that of some traditional competitors, namely moment
estimators and conditional maximum likelihood estimators. An
application to a multivariate data set of time series concerning the
monthly number of fires in three districts in mainland Portugal is also
presented.
Keywords: Multivariate models, binomial thinning
operator, composite likelihood.
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15:05-15:45
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Sandra Dias (CEMAT, Departamento de
Matemática, ECT, Universidade de Trás-os-Montes e Alto Douro)
Abstract:
As, for environment data, the averages and extremes are available to
researchers, many authors have been interested in the limiting joint
distribution of the sum and maximum. For instance, Chow and Teugels
(1978) studied the limiting joint distribution of the sum and maximum
of n independent and identically distributed (i.i.d.) random variables
when the underling marginal distributions are attracted to a stable and
max-stable distribution, Anderson and Turkman (1991) extended the
results to stationary strong mixing sequences with finite variance and
McCormick and Sun (1993) obtained lower and upper bounds for the
limiting distribution considering stationary strong mixing sequences
with margins belonging to Anderson's class. In this work, we study the
limit joint distribution of the sum and maximum of k_n random
variables, where k_n is an integer-valued geometric growing sequence
and the underling marginal distributions are attracted to a semistable
and max-semistable distribution, in both i.i.d. and stationary
approaches. We also consider the case where we have stationary strong
mixing sequences, whose margins are positive integer random variables
belonging to Anderson's class. Some applications of these results are
presented. Join work with Maria da Graça Temido (CMUC, Departamento de
Matemática, Faculdade de Ciências e Tecnologia, Universidade de
Coimbra)
References:
Anderson, C. W., Turkman, K. F. (1991). The joint limiting distribution
of sums and maxima of stationary sequences. J. Appl. Probab. 28, 33-44
Chow, T. L., Teugels, J. L. (1978). The sum and the maximum of i.i.d.
random variables.
Proceeding of the Second Prague Symposium on Asymptotic Statistics
(Hadrec Králové), 81-92
McCormick, W. P., Sun J. (1993). Sums and maxima of discrete stationary
processes. J. Appl. Probab. 40, 863-876
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15:45-16:30
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Luís Meira-Machado (Department of
Mathematics, University of Minho, Portugal)
Abstract:
In many medical studies, patients may experience several events across
a follow-up period. Analysis in such studies is often performed using
multi-state models. These models can be successfully used for
describing complex event history data, for example, describing stages
in the disease progression of a patient. The so-called ?illness-death?
model plays a central role in the theory and practice of these models.
Many time-to-event data sets from medical studies with multiple end
points can be reduced to this generic structure. In these models one
important goal is the modeling of transition rates but biomedical
researchers are also interested in reporting interpretable results in a
simple and summarized manner. These include estimates of predictive
probabilities, such as the transition probabilities, occupation
probabilities, cumulative incidence functions, prevalence and the
sojourn time distributions. We aim to introduce feasible estimation
methods for all these quantities in an illness-death model
conditionally (or not) on current or past covariate measures. The
proposed methods are illustrated using real data. Software in the form
of an R package has been developed implementing all methods.
Keywords: Kaplan-Meier; Landmarking; Markov condition;
Multi-state model; Survival analysis.
References:
Meira-Machado L, Sestelo M (2019). Estimation in the progressive
illness-death model: A nonexhaustive review. Biometrics, 61(2):
245-263.
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The One Day Meeting on Statistics and Applied
Probability 2019 is organized by the CMAT-SAPOR of the Centre of
Mathematics at University of Minho. It is dedicated to topics of
Bayesian Statistics, Branching Processes, Extreme Values Analysis,
Survival Analysis and Time Series Models. A short-course on Bayesian
Statistics will be lectured by Carlos Daniel Paulino (U. Lisboa) and
Giovani Silva (U. Lisboa) on October 3rd.
Invited speakers: 
Local Organizing Committee:
