Home
Speakers
Timetable
Sponsors
Poster
Contact and venue
Photos

Expected time span: 10:00  15:00
Kjersti Aas, Norwegian Computing Center, Oslo

Title: Paircopula constructions  even more flexible than copulas
Abstract:
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 copulabased structures have been proposed as an alternative to the standard copula
methodology. One of the most promising of these structures is the paircopula construction (PCC).
Paircopula constructions are also called regular vines (Rvines). 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 paircopula constructions and apply the methodology to a 19
dimensional financial data set.

Ágnes Backhausz, Eötvös Loránd University, Budapest

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
realworld networks [1]. 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 vertexvertex 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 timesteps that is based on 3interactions
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./B09/KMR20100003.

Alexander Bulinski, Lomonosov Moscow State University

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 nongenetic risk factors are examined to assess the risks of complex diseases
such as cardiovascular ones.

Probal Chaudhuri, Indian Statistical Institute, Calcutta

Title: Comparison of Multivariate Distributions Using QuantileQuantile Plots and Related Tests
Abstract: The univariate quantilequantile (QQ) plot is a wellknown 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 QQ 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 QQ plots and study their
asymptotic properties. The performance of those tests are compared with that of some
other wellknown tests for multivariate distributions available in the literature. This
is joint work with Subhra S. Dhar (Cambridge University) and Biman Chakraborty
(University of Birmingham).

László Martinek, Eötvös Loránd University, Budapest

Title: Estimation of Claim Numbers in Automobile Insurance
Abstract:
The use of bonusmalus 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 bonusmalus 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 goodnessoffit we will use scores, similar to better known divergence measures. The detailed method is also suitable to compare bonusmalus 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/B09/KMR20100003.

Axel Munk, University of Göttingen
Fabrizio Ruggeri, Consiglio Nazionale delle Ricerche  Istituto di Matematica Applicata e Tecnologie Informatiche, Milano

Title: Bayesian Estimation in Stochastic PredatorPrey Models
Abstract: Parameter estimation for the functional response of predatorprey 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.

Michael Sorensen, University of Copenhagen, Department of Mathematical Sciences

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
concrete examples.

Charles Taylor, University of Leeds

Title: Regression models on the torus
Abstract:
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 realline and circular predictors.
Secondly, we consider various parametric models for the circularcircular
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.

Rasmus Plenge Waagepetersen, University of Aalborg

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 firstorder 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 quasilikelihood for binary spatial data.


