Contact and venue
Expected time span: 10:00 - 15:00
Kjersti Aas, Norwegian Computing Center, Oslo
Ágnes Backhausz, Eötvös Loránd University, Budapest
Title: Pair-copula constructions - even more flexible than copulas
A copula is a multivariate distribution with standard uniform marginal distributions. While the literature
on copulas is substantial, most of the research is still limited to the bivariate case. However, recently
hierarchical copula-based structures have been proposed as an alternative to the standard copula
methodology. One of the most promising of these structures is the pair-copula construction (PCC).
Pair-copula constructions are also called regular vines (R-vines). The modeling scheme is based on a
decomposition of a multivariate density into a cascade of pair copulae, applied on original variables and
on their conditional and unconditional distribution functions. Each pair copula can be chosen arbitrarily
and the full model exhibit complex dependence patterns such as asymmetry and tail dependence.
In this talk I will give an introduction to pair-copula constructions and apply the methodology to a 19-
dimensional financial data set.
Alexander Bulinski, Lomonosov Moscow State University
Title: A random graph model based on interactions of three vertices.
Abstract: (in PDF)
Random graphs evolving by some “preferential attachment” rule are inevitable in modelling
real-world networks . There is a vast number of publications inventing and studying different
models of that kind, but in most of them the dynamics is only driven by vertex-vertex interactions.
However, one can easily find networks (that is, objects equipped with links) in economy or other
areas where simultaneous interactions can take place among three or even more vertices, and those
interactions determine the evolution of the process.
We consider a random graph model evolving in discrete time-steps that is based on 3-interactions
among vertices. Triangles, edges and vertices have different weights; objects with larger weight are
more likely to participate in future interactions and to increase their weights. Thus it is also a
“preferential attachment” model.
We prove the scale free property of the model, that is, the ratio of weights of weight w tends
to xw almost surely as the number of vertices goes to infinity, where xw is polinomially decreasing
as w \to \infty. Techniques of discrete parameter martingales are applied in the proofs.
The European Union and the European Social Fund have provided financial support to the project under the grant agreement no. TAMOP 4.2.1./B-09/KMR-2010-0003.
Probal Chaudhuri, Indian Statistical Institute, Calcutta
Title: Statistical methods for multidimensional genetic data analysis
Abstract: We concentrate on the new modifications of multifactor dimensionality reduction, logic
regression, random forests and stochastic gradient boosting. Theorems justifying application of
these methods are established. The roles of certain combinations of single nucleotide
polymorphisms and non-genetic risk factors are examined to assess the risks of complex diseases
such as cardiovascular ones.
László Martinek, Eötvös Loránd University, Budapest
Title: Comparison of Multivariate Distributions Using Quantile-Quantile Plots and Related Tests
Abstract: The univariate quantile-quantile (Q-Q) plot is a well-known graphical tool for examining
whether two data sets are generated from the same distribution or not. It is also used to
determine how well a specified probability distribution fits a given sample. We develop
and study a multivariate version of Q-Q plot based on spatial quantiles. The usefulness
of the proposed graphical device is illustrated on different real and simulated data,
some of which have fairly large dimensions. We also develop certain statistical tests
that are related to the proposed multivariate Q-Q plots and study their
asymptotic properties. The performance of those tests are compared with that of some
other well-known tests for multivariate distributions available in the literature. This
is joint work with Subhra S. Dhar (Cambridge University) and Biman Chakraborty
(University of Birmingham).
Axel Munk, University of Göttingen
Fabrizio Ruggeri, Consiglio Nazionale delle Ricerche - Istituto di Matematica Applicata e Tecnologie Informatiche, Milano
Title: Estimation of Claim Numbers in Automobile Insurance
The use of bonus-malus systems in compulsory liability automobile insurance is a worldwide applied method for premium pricing. If certain assumptions hold, like the conditional Poisson distribution of the policyholders claim number, then an interesting task is to evaluate the so called claims frequency of the individuals. Here we introduce 3 techniques, two is based on the bonus-malus class, and the third based on claims history. The article is devoted to choose the method, which fits to the frequency parameters the best for certain input parameters. For measuring the goodness-of-fit we will use scores, similar to better known divergence measures. The detailed method is also suitable to compare bonus-malus systems in the sense that how much information they contain about drivers.
The European Union and the European Social Fund have provided financial support to the project under the grant agreement no. TÁMOP 4.2.1/B-09/KMR-2010-0003.
Michael Sorensen, University of Copenhagen, Department of Mathematical Sciences
Title: Bayesian Estimation in Stochastic Predator-Prey Models
Abstract: Parameter estimation for the functional response of predator-prey systems
is a critical methodological problem in population ecology. Population dynamics is
described by a system of stochastic differential equations in which
behavioural stochasticities are represented by noise terms affecting each
population as well as their interaction. In our work we are interested in
methods for model parameter estimation based on time series of field data.
Charles Taylor, University of Leeds
Title: Martingale estimating functions for diffusions with jumps
Abstract: For discrete time observations of a stochastic differential equation
driven not only by a Wiener process, but also by a Lévy process with
jumps, the likelihood function is not explicitly known and extremely
difficult to calculate numerically. Therefore alternatives like estimating
functions are even more useful for jump diffusions than for classical
diffusions. We present a broad and flexible class of diffusions with jumps
for which explicit optimal martingale estimating functions are available.
Generalizing earlier work with Mathieu Kessler on ordinary diffusion
processes, these estimating functions are based on eigenfunctions of the
generator. A simple condition on the compensator of the jump measure (the
Levy measure) is shown to ensure that explicit optimal martingale
estimating functions can be found. We illustrate the general theory by
Rasmus Plenge Waagepetersen, University of Aalborg
Title: Regression models on the torus
Regression with a circular response is a topic of current interest.
Firstly, we consider a nonparametric estimator, in which
simple adaptations of a weight function enable a unified formulation
for both real-line and circular predictors.
Secondly, we consider various parametric models for the circular-circular
case, in which we propose robust fitting procedures, as well as
potential diagnostic tools to identify influential observations.
Real data examples are used to illustrate the methods.
Title: Optimal estimation of the intensity function of a spatial point process
Abstract: Maximum likelihood estimation for
Cox and cluster point processes can be cumbersome in practice due to the complicated
nature of the likelihood function and the associated score function. It is therefore
of interest to consider alternative more easily computable estimating functions. We
derive the optimal estimating function in a class of first-order estimating functions.
The optimal estimating function depends on the solution of a certain Fredholm integral
equation and reduces to the likelihood score in case of a Poisson process. The Fredholm
equation must be solved numerically and it turns out that the approximated optimal estimating
function is equivalent to a quasi-likelihood for binary spatial data.