# Archive 2013

**December 18, 2013 Ronald Meester**

*The shooting problem*

When: Wednesday December 18th, 15.45h

Place: TU Delft, Faculty EWI, Mekelweg 4 - Snijderszaal (1st floor)

Abstract: The starting point (time t=0) is a crowd of n people in a room, all having a gun. At time t=1, all people in the room shoot a randomly chosen person in the room; it is possible that two people shoot at each other, but no one can shoot him or herself. We assume that every shot will be fatal and will kill the person shot at. After this first shooting round, some random number of people has survived, and at time t=2 we repeat the procedure with all survivors. We continue to do so, until we have reached the situation that either no one survived, or exactly one person survived. We denote by p(n) the probability that eventually there are no survivors. We are interested in the asymptotics of p(n), as n tends to infinity.

(Joint work with Wouter Kager)

**December 11, 2013 Martijn Pistorius **

*Optimal timing to sell a stock under a spectrally negative Levy model with a jump-to-default*

When: Wednesday December 11th, 15.45h

Place: TU Delft, Faculty EWI, Mekelweg 4 - Snijderszaal (1st floor)

We consider the problem to identity the optimal time to sell a

defaultable asset in the sense of minimizing the ``prophet's

drawdown'', which is the ratio of the ultimate maximum and the

value of the asset price at the moment of sale.

We assume that default occurs at

a constant rate, and that at the moment of default there is

recovery value of R%. This problem is phrased as an

optimal stopping problem which we solve explicitly in the case that

the asset price before default is modelled by a spectrally

negative exponential L\'{e}vy process. We provide a detailed discussion of

the structure of the optimal solution. We will also discuss a number of possible

extensions.

**December 4, 2013 Jean-Louis Marchand**

*Conditioning diffusions with respect to partial **observations*

When: Wednesday December 4th, 15.45h

Place: TU Delft, Faculty EWI, Mekelweg 4 - Snijderszaal (1st floor)

The aim of this work is to describe the conditional law of a multidimensional diffusion process with

respect to some observed coordinates at some deterministic times. The parameters of the conditional

process may be described. However, its drift is non explicit. In order to be able to sample the conditional

law, we propose an auxiliary process, whose law is equivalent to the targeted one. Moreover, this auxiliary

process possesses explicit parameters which allows simple simulations.

An application of this result is presented in the case of the reconstruction of fluid motions by using

Videoās.

**November 27, 2013 Angelika Rohde**

*A new scheme for locally adaptive bandwidth selection*

When: Wednesday November 27th, 15.45h

Place: TU Delft, Faculty EWI, Mekelweg 4 - Snijderszaal (1st floor)

A new scheme for locally adaptive bandwidth selection is proposed which sensitively shrinks the bandwidth of a kernel estimator at lowest density regions such as the support boundary which are unknown to the statistician. In case of a H\"older continuous density, this locally minimax-optimal bandwidth is shown to be smaller than the usual rate, even in case of homogeneous smoothness. Besides the classical minimax risk bounds at some fixed point, new pointwise risk bounds along a shrinking neighborhood of lowest density regions are derived, which demonstrate the superiority of the new estimator as compared to classical adaptive estimators. Our bounds are complemented by a local minimax lower bound. This lower bound splits into three regimes depending on the value of the density. The new estimator adapts to the first two regimes, and it is shown that simultaneous adaptation to the fastest regime is not possible in principal. The results are fully non-asymptotic. Consequences on plug-in rules for support recovery based on the new estimator are worked out in detail. In contrast to those built with classical density estimators, the plug-in rules based on the new construction are minimax-optimal, up to some logarithmic factor. As a by-product, we demonstrate that the rates on support estimation obtained in Cuevas and Fraiman (1997, Ann. Statist.) are always suboptimal in case of H\"older continuous densities.

This is a joint work with Tim Patschkowski.

**November 20, 2013 Diego Garlaschelli (University of Leiden)**

*Early-warning signals of topological collapse in interbank networks*

When: Wednesday November 20th, 15.45h

Place: TU Delft, Faculty EWI, Mekelweg 4 - Snijderszaal (1st floor)

The financial crisis clearly illustrated the importance of

characterizing the level of `systemic' risk associated with an entire

credit network, rather than with single institutions. However, the

interplay between financial distress and topological changes is still

poorly understood. Here we analyze the quarterly interbank exposures

among Dutch banks over the period 1998-2008, ending with the crisis.

After controlling for the link density, many topological properties

display an abrupt change in 2008, providing a clear - but

unpredictable - signature of the crisis. By contrast, if the

heterogeneity of banks' connectivity is controlled for, the same

properties show a gradual transition to the crisis, starting in 2005

and preceded by an even earlier period during which anomalous debt

loops presumably favored the underestimation of counter-party risk.

These early-warning signals are undetectable if the network is

reconstructed from partial bank-specific data, as routinely done. We

discuss important implications for bank regulatory policies.

Reference:

Tiziano Squartini, Iman van Lelyveld, Diego Garlaschelli,

http://arxiv.org/abs/1302.2063.

**October 23, 2013 Johan Segers (Universite catholique de Louvain)**

*Semiparametric Gaussian copula models: Geometry and rank-based efficient estimation*

When: Wednesday October 23, 15.45h

Place: TU Delft, Faculty EWI, Mekelweg 4 - Snijderszaal (1st floor)

For multivariate Gaussian copula models with unknown margins and structured correlation matrices, a rank-based, semiparametrically efficient estimator is proposed for the Euclidean copula parameter. This estimator is defined as a one-step update of a rank-based pilot estimator in the direction of the efficient influence function, which is calculated explicitly. Moreover, finite-dimensional algebraic conditions are given that completely characterize adaptivity of the model with respect to the unknown marginal distributions and of efficiency of the pseudo-likelihood estimator. For correlation matrices structured according to a factor model, the pseudo-likelihood estimator turns out to be semiparametrically efficient. On the other hand, for Toeplitz correlation matrices, the asymptotic relative efficiency of the pseudo-likelihood estimator with respect to our one-step estimator can be as low as 20%. These findings are confirmed by Monte Carlo simulations.

**October 16, 2013 Christos Pelekis (TU Delft)**

*How to poison your mother-in-law*

When: Wednesday October 16, 15.45h

Place: TU Delft, Faculty EWI, Mekelweg 4 - Snijderszaal (1st floor)

Abstract: Suppose you want to poison your mother-in-law.

She comes over for tea and eats s biscuits from a tray that contains n biscuits in total.

She has no preference and chooses her biscuits uniformly at random.

You posses a bottle of arsenic containing h grams of it and the lethal dose is, say, 1 gram.

Unfortunately, you cannot put the poison in her tea, you have to put it in the biscuits.

Which distribution of poison has the highest probability of doing the "oude taart" in?

In this talk I will explain how to optimally get rid of people you dislike in certain instances of the above scenario.

I will also discuss the "cyclic version" of the problem.

**October 9, 2013****Aad van der Vaart (Universiteit van Leiden) **

*Asymptotic analysis of Bayesian methods for sparse models*

When: Wednesday October 9, 15.45

Place: TU Delft, Faculty EWI, Mekelweg 4 - Snijderszaal (1st floor)

We consider fitting a linear regression model in the situation that there

are more columns than rows in the regression matrix, but it is known that

for most of the columns the parameter is zero or very small. A Bayesian approach

to this problem is to specify prior distributions for the number of nonzero

parameters, the set of nonzero parameters, and the values of the nonzero

parameters. We discuss the ability of the resulting posterior distribution to

reconstruct the true model, as a function of the choice of priors, with reference

to optimal minimax reconstruction rates and model choice consistency. We also

give an introduction to other Bayesian and empirical Bayesian approaches.

(joint work with Ismael Castillo and Johannes Schmidt-Hieber)

**October 25, 2013 Alex Opoku - EWI (TU Delft)**

*The critical curve for a copolymer near a selective interface*

When: Wednesday October 25, 15.45h

Place: TU Delft, Faculty EWI, Mekelweg 4 - Snijderszaal (1st floor)

A polymer is a large molecule that is made up of smaller units called monomers that are joined together by chemical bonds. A homopolymer has identical monomers (e.g. polyethylene) while a copolymer has non-identical monomers (e.g. DNA). Mathematical models for describing various phenomena exhibited by polymers interacting with themselves and/or with the media surrounding them are referred to as (random) polymer models.

In this talk I will discuss one of such models for a copolymer interacting with an interface separating two immiscible media. Each monomer type has an affinity for one of the media and the monomer types are randomly arranged along the polymer chain. This model undergoes a localisation-delocalisation phase transition in the parameter space of the model. I will discuss the phase diagrams for the quenched (monomer types fixed) and the annealed (average over monomer types) versions of the model.

This talk is based on joint work with Professor Frank den Hollander (Leiden University) and Professor Erwin Bolthausen (Zurich University).

**September 25, 2013 Pasquale Cirillo - EWI (TU Delft)**

*Prior distributions and processes via urns*

When: Wednesday September 25, 15.45h

Place: TU Delft, Faculty EWI, Mekelweg 4 - Snijderszaal (1st floor)

Urn schemes have been an important part of the theory of probability since the publication by Jakob Bernoulli of his Ars conjectandi [1] in 1713. Their most interesting characteristic is the possibility of simplifying complex probabilistic ideas, making them intuitive and concrete, and yet guaranteeing a good level of abstraction, that allows for general, elegant results.

An important feature of urn schemes, which is rarely found in the literature (two exceptions, even if incomplete, are [3] and [4]), is the possibility of easily generating prior distributions for Bayesian nonparametric purposes.

The aim of this talk, which is based on and extends the results of [2] and [3], is to give an introduction to the use of urns to build priors. In particular, Dirichlet, beta-Stacy and neutral to the right processes will be discussed and constructed through the use of basic urn models, Polya trees and reinforced urn processes.

References

1) Bernoulli J., (1713). Ars Conjectandi. Reprinted in Die Werke von Jakob Bernoulli (1975), BirkĆ¤user.

2) Cirillo P., (2012). Some selected papers on urn models. Habilitationsschrift Statistik, Bern University.

3) Cirillo P., (2013). From Bernoulli to Bayes: building priors with urns. Working paper.

4) Ghosh J.K., Ramamoorthi R.V., (2003). Bayesian Nonparametrics. Springer-Verlag, New York.

5) Hjort N.L., Holmes C., MĆ¼ller P., Walker S.G., (2010). Bayesian Nonparametrics. Cambridge University Press, Cambridge.

**September 18, 2013 Moritz Schauer (TU Delft) **

*Guided proposals for simulating diffusions *

When: Wednesday September 18, 15.45h

Place: TU Delft, Faculty EWI, Mekelweg 4 - Snijderszaal (1st floor)

In this talk a Monte Carlo method to simulate from a multidimensional diffusion process conditioned on hitting a fixed point at a future time is presented.

Proposals for such diffusion bridges are obtained by superimposing an additional guiding term to the drift of the process under consideration. The guiding term is derived via approximation of the target process by a simpler diffusion processes with known transition densities. Acceptance of a proposal can be determined by computing the likelihood ratio between the proposal and the target bridge. This is illustrated for class of proposals with guiding term obtained from linear processes.

**June 12, 2013 Juan-Juan Cai (TU Delft)**

*Two Estimation Problems in Multivariate Extreme Value Theory *

When: Wednesday June 12, 15.45h

Place: TUDelft, Faculty EWI, Mekelweg 4 - Timmanzaal (LB.01.170)

Part I: When considering *d* possibly dependent random variables, one is often interested in extreme risk regions, with very small probability *p*.We consider risk regions of the form {z ā R^d ā¶f (z)ā¤ Ī²} , where *f* is the joint density and Ī² a small number. Estimation of such an extreme risk region is difficult since it contains hardly any or no data. Using extreme value theory, we construct a natural estimator of an extreme risk region and prove a refined form of consistency, given a random sample of multivariate regularly varying random vectors.

Part II: Denote the loss return on the equity of a financial institution as *x* and that of the entire market as *Y*. For a given very small probability *p*, the marginal expected shortfall (MES) is defined as E(X | Y > y_p) , where* y_p* is the (1-p)-th quantile of the distribution of *Y* . The MES is an important factor when measuring the systemic risk of financial institutions. For a wide nonparametric class of bivariate distributions, we construct an estimator of the MES and establish the asymptotic normality of the estimator when pā0 , as the sample size nāā .

The performances of both estimators are demonstrated through detailed simulations and application studies

**June 5, 2013 Gaia Becheri (TU Delft) **

*Limits of Experiments: an application to Panel Unit Root Tests *

When: Wednesday June 5, 15.45h

Place: TU Delft, Faculty EWI, Mekelweg 4 - **Snijderszaal **(1st floor)

One of the problems of the mathematical statistics is to construct, for a given experiment, optimal statistical decisions based on the observed data. The limit of experiments theory provides useful tools to construct asymptotically optimal decisions and to compare the performances of different decisions. In this talk, I give a brief review of Le Cam's theory and show how it can be effectively used to tackle problems such as the unit root test in panel data.

**May 29, 2013 Lex Oversteegen (University of Alabama, Birmingham) **

*Extending Isotopies of Planar Compacta *

When: Wednesday May 29, 15.45h

Place: TU Delft, Faculty EWI, Mekelweg 4 - **Snijderszaal **(LB.01.010 - 1st floor)

Lex will talk about his recent work with Hoehn and Tymchatyn on the Cartwright-Littlewood conjecture on fixed points in the plane. The abstract is enclosed.

**May 8, 2013 Cristian Giardina (University of Modena and Reggio Emilia & University of Nijmegen) **

*Algebraic approach to self-duality of the exclusion process *

When: Wednesday May 8, 15.45h

Place: TU Delft, Faculty EWI, Mekelweg 4 ā **Snijderszaal** (1st floor)

Using the structure of a Lie-algebra it is possible to construct Markov processes having symmetries, i.e. operators commuting with the generator. It is then possible to use those symmetries to obtain self-duality functions, that greatly simplify the analysis of the process. The scheme will be reviewed for the exclusion process, and applications of duality will be discussed for the boundary driven process coupled to particle reservoirs.

**May 1, 2013 Juan-Juan Cai (TU Delft) (Cancelled!)**

*Two Estimation Problems in Multivariate Extreme Value Theory*

When: Wednesday May 1, 15.45h

Place: TU Delft, Faculty EWI, Mekelweg 4 ā **Snijderszaal** (1st floor)

Part I: When considering *d* possibly dependent random variables, one is often interested in extreme risk regions, with very small probability *p*.We consider risk regions of the form {z ā R^d ā¶f (z)ā¤ Ī²} , where *f* is the joint density and Ī² a small number. Estimation of such an extreme risk region is difficult since it contains hardly any or no data. Using extreme value theory, we construct a natural estimator of an extreme risk region and prove a refined form of consistency, given a random sample of multivariate regularly varying random vectors.

Part II: Denote the loss return on the equity of a financial institution as *x* and that of the entire market as *Y*. For a given very small probability *p*, the marginal expected shortfall (MES) is defined as E(X | Y > y_p) , where* y_p* is the (1-p)-th quantile of the distribution of *Y* . The MES is an important factor when measuring the systemic risk of financial institutions. For a wide nonparametric class of bivariate distributions, we construct an estimator of the MES and establish the asymptotic normality of the estimator when pā0 , as the sample size nāā .

The performances of both estimators are demonstrated through detailed simulations and application studies

**April 24, 2013 Wioletta Ruszel (TU Delft)**

*Transitions in particle models*

When: Wednesday, April 24, 15.45

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderszaal (first floor)

The talk will consist of two parts. In the first part I would like to explain Gibbs-non Gibbs transitions for continuous spin models. We consider a system of interacting particles, sitting on a d-dimensional lattice and evolving in time. At time zero the system can be described by a Gibbs measure. The question is now under which conditions on the initial measure and the dynamics, the time-evolved measure (at a fixed time t) is still a Gibbs measure.

In the second part of the talk I would like to explain some results for sandpile models on random trees. Consider a BTW-sandpile model on a random tree. One of the questions is for example how does the distribution of avalanche sizes depend on the underlying tree?

**March 27, 2013 Alberto Manconi (Tilburg)**

*Learning by Doing: The Value of Experience and the Origins of Skill for Mutual Fund Managers.*

When: Wednesday March 27, 2013 15:45-16:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderszaal (first floor)

This talk provides evidence for substantial learning by doing effects among professional investors in a large and highly competitive segment of financial markets. We develop a new methodology to show that experienced mutual fund managers outperform their nonexperienced counterparts by up to 67bps per quarter on a risk-adjusted basis. The key to our identification strategy is that we look āinsideā funds and exploit heterogeneity in experience for the same manager at a given point in time across industries. In addition to highlighting a previously underemphasized source of observed mutual fund manager skill, our approach circumvents some of the main obstacles for the empirical literature on learning by doing effects in economics.

Keywords: Panel data analysis, performance evaluation, finance.

**March 20, 2013 Emilio N.M. Cirillo (Universitadi Roma ``La Sapienza'')**

*Multiple metastable states in the Blume-Capel model *

When: Wednesday March 20, 2013 15:45-16:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderszaal (first floor)

The study of systems with multiple (not necessarily degenerate)

metastable states presents subtle difficulties from the mathematical point of

view related to the variational problem that has to be solved in these cases.

In this talk I shall first discuss how to prove sufficient conditions to

identify multiple metastable states. Then I will show how to apply

these condition to the case of the Blume--Capel model with zero chemical

potential.

**March 13, 2013 Christian Maes (Instituut voor Theoretische Fysica KU Leuven)**

*Variational principles and Lyapunov functions for characterizing the nonequilibrium condition. *

When: Wednesday March 13, 2013 15:45-16:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderszaal (first floor)

For a probabilist, variational principles follow from large deviation theory. That makes contact with statistical mechanics when realizing that the free energy in the Gibbs variational principle is a large deviation functional. For steady nonequilibria it appears useful to interpret the Donsker-Varadhan fluctuation functional for Markov processes. We will also discuss the corresponding presence of Lyapunov functions, for example functions of the density profile that are monotone in time under a rescaled (hydrodynamic) evolution.

**March 1, 2013 Piet Groeneboom (TU Delft)**

*Second lecture in his series of three lectures on Nonparametric Estimation under Shape Constraints.*

When: Wednesday March 6, 2013 15:45-16:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Lipkenszaal (first floor)

After pioneering work of (among others) Brunk, Chernoāµ and Prakasa Rao,

summarized in the book of the āfour Bāsā (Barlow, Bartholomew, Bremner and Brunk),

the field of isotonic regression and shape constrained inference temporarily received less

attention. But there was a revival of interest because of several factors.

Firstly, there was analytic progress when it became clear how to compute the āChernoffian

distributionā, first studied by Chernoāµ in a study of an estimator of the mode

of a distribution. This arose from a study of the connection between Brownian motion

with a parabolic drift and Airy functions. Secondly, the relevance of the theory for nonparametric

estimates of distribution functions in inverse problem became apparent, in

particular for deconvolution and interval censoring models. And thirdly, fast algorithms

became available for computing the shape-constrained estimates. In my lectures I will

discuss all three angles to these problems, with an emphasis on recent results and open

problems.

**February 27, 2013 Tanja Eisner (University of Amsterdam) **

*A Generalisation of the Wiener-Wintner Theorem*

When: Wednesday February 27, 2013 15:45-16:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderszaal (first floor)

We discuss a nilsequence version of the classical Wiener-Wintner theorem on convergence of weighted ergodic averages due to Host and Kra and present a uniform version of this result. This is a joint work with Pavel Zorin-Kranich.

**February 20,** 2013 Piet Groeneboom (TU Delft)

*Nonparametric estimation under shape constraints. *

When: Wednesday February 20, 2013 15:45-16:45

Where: TU Delft, Faculty EWI, Mekelweg 4, **Timmanzaal ** LB 01.170 (first floor)

After pioneering work of (among others) Brunk, Cherno and Prakasa Rao,summarized in the book of the \four B's" (Barlow, Bartholomew, Bremner and Brunk),the eld of isotonic regression and shape constrained inference temporarily received lessattention. But there was a survival of interest because of several factors.Firstly, there was analytic progress when it became clear how to compute the \Cher-noan distribution", rst studied by Cherno in a study of an estimator of the modeof a distribution. This arose from a study of the connection between Brownian motionwith a parabolic drift and Airy functions. Secondly, the relevance of the theory for non-parametric estimates of distribution functions in inverse problem became apparent, inparticular for deconvolution and interval censoring models. And thirdly, fast algorithmsbecame available for computing the shape-constrained estimates. In my lectures I willdiscuss all three angles to these problems, with an emphasis on recent results and openproblems.

**February 13,** 2013 Aernout van Enter (Rijksuniversiteit Groningen)

*Gibbs-non-Gibbs transitions for measures on Cayley trees *

When: Wednesday February 13, 2013 15:45-16:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderszaal (first floor)

We consider Gibbs measures for Ising models on Cayley trees, subjected to an infinite-temperature Glauber dynamics (independent spin flips). We discuss similarities and differences with the situation on regular lattices. In particular we find that on trees there is the possibility of different Gibbs measures acquiring different Gibbsian properties, and the possibility of measures becoming "totally non-Gibbsian" in the sense that all spin configurations become points of discontinuity for some conditional probability.