VVS-SMS AiO lectures 2005
VVS-SMS AiO lectures 2005
| The section Mathematical Statistics organises special lecture afternoons where AiO's (Ph.D. students) who are close to finishing their theses present their work. The previous SMS-VVS AiO afternoon was held on 29 January 2004. |
| The afternoon is organised at the Korteweg-de Vries Institute for Mathematics of the Universiteit van Amsterdam under the auspices of the Section Mathematical Statistics (SMS) of the Dutch Society for Statistics and Operations Research (VVS) |
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Travel directions: From metro station Weesperplein, you walk to the East in Sarphatistraat (ascending numbers). After about 200 meters, you turn left into Roetersstraat. You'll find Gebouw A after 50 meters on your right.
Directions in the building: Climb the staircase in the entrance hall. On the first floor you follow the signs "Gebouw B". Half way you will see the window of the "Facilitheek", where you take a right. At the end of the corridor you turn left. After about 20 meters you'll see the elevators on your right. Go to the 2nd floor. When you leave the elevator, you have almost arrived at B.240. |
| 13.30-14.15 | Wouter Kager | Reflected Brownian motions in generic triangles with uniform exit distributions |
| 14.15-15.00 | Frank van der Meulen | Convergence rates of posterior distributions for Brownian semimartingale models |
| 15.00-15.30 | Coffee break | |
| 15.30-16.15 | Jasper Anderluh | Pricing Parisian Options by inverting Fourier transforms |
| 16.15-17.00 | Jelle Goeman | Analyzing microarray data at the level of the pathway |
| 17.00 | Drinks |
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Jasper Anderluh: Pricing Parisian Options by inverting Fourier transforms
As an introduction the talk will start explaining the reason of mathematics being involved in the financial field and especially the connection between stochastics and derivative trading. Something will be said about quatities that need to bo computed for practical relevance. After the introduction we will introduce the Parisian Option contract and give an overview of ways for pricing it. Then we will focuss on the the Fourier Transform of the Parisian Option and the inversion of it, in order to obtain the relevant numbers. The talk will conclude with a numerical example. |
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Jelle Goeman: Analyzing microarray data at the level of the pathway
The microarray is a recent technological innovation in molecular biology, which allows simultaneous measurement of the expression of thousands of genes in a tissue sample. The microarray has become very popular as an experimental technique in medical science. It is used to find associations between genes and disease and to improve diagnosis and prognosis of patients. Statistically, however, problems arise due to the extreme high-dimensionality of the data (tens of thousands of measurements per individual) combined with only moderate sample sizes (tens or hundreds of individuals). Aside from problems, the high dimensionality of the data also offers statistical opportunities. I will present a method which studies the microarray by setting "pathways" (sets of genes with similar role or function) in stead of single genes at the level of analysis. The method tests directly whether these pathways are associated with disease variables of interest, so that the analysis can more immediately address biologically interesting questions. The test I use is a score test in a generalized linear model, which has some interesting locally optimal power properties. |
| Wouter Kager:
Reflected Brownian motions in generic triangles with uniform exit distributions Let T be any triangle in the upper half of the complex plane such that one side of the triangle is the interval (0,1). In this presentation I will show that there exists a Brownian motion in T, started from the top and reflected instantaneously on the left and right sides of the triangle at fixed reflection angles, such that this Brownian motion lands on the interval (0,1) with the uniform distribution. The proof proceeds by a carefull construction of a discrete random walk having the desired properties. I will also discuss some intriguing properties of the reflected Brownian motions and, if there is time, connections with critical percolation. |
| Frank van der Meulen:
Convergence rates of posterior distributions for Brownian semimartingale models Suppose we continuously observe a process, which is defined by a Brownian semimartingale model. This model includes a wide class of processes, for example diffusions generated by a stochastic differential equation. We assume that the drift-coefficient of the process is parametrized by an unknown (possibly infinite-dimensional) parameter theta. The Bayesian approach consists of putting a prior distribution on theta and making inference based on the posterior distribution, which is the conditional distribution of theta given the observations. We study the asymptotic behavior of the posterior from a frequentist point of view. Our main result gives lower bounds for the (Bayesian) rate at which the posterior converges to the true underlying distribution. I will subsequently discuss: the general Brownian semimartingale model + some examples - Bayesian estimation - Bayesian convergence rates - the main result. (Joint work with Aad van der Vaart and Harry van Zanten) |