# Archive 2016

**December 13, 2016: Dimitris Rizopoulos (Erasmus University Medical Center)**

When: Tuesday December 13th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Room D@ta.

*Personalized screening intervals for biomarkers using joint models for longitudinal and survival data*

Screening and surveillance are routinely used in medicine for early detection of disease and close monitoring of progression. Motivated by a study of patients who received a human tissue valve in the aortic position, in this work we are interested in personalizing screening intervals for longitudinal biomarker measurements. Our aim in this paper is to select the optimal time point to plan the next measurement. To achieve this we combine information theory measures with optimal design concepts for the posterior predictive distribution of the survival process given the longitudinal history of the subject.

**December 06, 2016: Francesca Collet (TU Delft)**

When: Tuesday December 6th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Room D@ta.

*Rhythmic collective behavior in stochastic systems*

One of the fundamental problems in Statistical Mechanics is to understand how systems composed by many interacting units organize to produce “coherent” behavior at a macroscopic level. Basic examples include polarization (e.g. spin alignments in Ising-like models) and synchronization (e.g. phase locking in interacting rotators). In this talk we deal with a different, and less understood, phenomenon of self-organization: the emergence of periodic behavior in systems whose units have no tendency to evolve periodically. We will show how the interplay between dissipation and noise can be responsible for self-sustained oscillations. This idea will be implemented in details in some stochastic models with mean-field interaction.

**November 29, 2016: Joris Bierkens (TU Delft)**

When: Tuesday November 29th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Room D@ta.

*The Zig-Zag Process and Super-Efficient Sampling for Bayesian Analysis of Big Data*

Standard MCMC methods can scale poorly to big data settings due to the need to evaluate the likelihood at each iteration. There have been a number of approximate MCMC algorithms that use sub-sampling ideas to reduce this computational burden, but with the drawback that these algorithms no longer target the true posterior distribution. We introduce a new family of Monte Carlo methods based upon a multi-dimensional version of the Zig-Zag process of (Bierkens, Roberts, 2016), a continuous time piecewise deterministic Markov process. While traditional MCMC methods are reversible by construction the Zig-Zag process offers a flexible non-reversible alternative. The dynamics of the Zig-Zag process correspond to a constant velocity model, with the velocity of the process switching at events from a point process. The rate of this point process can be related to the invariant distribution of the process. If we wish to target a given posterior distribution, then rates need to be set equal to the gradient of the log of the posterior. Unlike traditional MCMC, we show how the Zig-Zag process can be simulated without discretisation error, and give conditions for the process to be ergodic. Most importantly, we introduce a sub-sampling version of the Zig-Zag process that is an example of an exact approximate scheme. That is, if we replace the true gradient of the log posterior with an unbiased estimator, obtained by sub-sampling, then the resulting approximate process still has the posterior as its stationary distribution. Furthermore, if we use a control-variate idea to reduce the variance of our unbiased estimator, then both heuristic arguments and empirical observations show that Zig-Zag can be super-efficient: after an initial pre-processing step, essentially independent samples from the posterior distribution are obtained at a computational cost which does not depend on the size of the data.

**November 22, 2016: René Conijn (Utrecht University)**

When: Tuesday November 22nd, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Room D@ta.

*Largest clusters in Percolation and Conformal Measure Ensembles*

Consider an n x n-box in the triangular lattice. The asymptotic behaviour, as n tends to infinity, of the largest percolation clusters in this box was well studied by Borgs, Chayes, Kesten and Spencer in (1999 and 2001). However some questions remained open. If we restrict ourself to critical percolation the size of the largest cluster is of the order n^(91/48). The first natural question is: does there exist a limiting distribution for the size of the largest cluster scaled by its order? In this talk we discuss the existence of the limiting distribution and introduce conformal measure ensembles as a key ingredient. Furthermore we will see an interesting application of these measure ensembles to the FK-Ising model.

Based on joint work with Rob van den Berg, Federico Camia and Demeter Kiss.

**November 15, 2016: No Seminar -> Lunteren Stochastics Meeting**

**November 8, 2016: Marco Formentin (University of Padua)**

When: Tuesday November 8th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Room D@ta.

*Rank-based Markov chains for complex systems*

In this talk, we will take a look at some systems of interacting particles on the real line, where the only spatial structure that is relevant for the dynamics is the relative order of the particles. They have possible applications in diverse fields ranging from biology (Bak-Sneppen model) to economics (Stigler model). We will move from data to modeling and mathematical description of such systems with strong focus on human written communication where a simple ranked-based Markov chain may account for regular patterns in response time statistics across media (letters, emails, sms). All these systems employ a version of the rule "kill the lowest particle" and seem to exhibit self-organized criticality.

**November 1, 2016: Anastasia Borovykh (University of Bologna)**

When: Tuesday November 1st, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Room D@ta.

*Pricing options under defaultable local Lévy models*

In financial mathematics, the fast and accurate pricing of financial derivatives is an important branch of research. Depending on the type of financial derivative, the mathematical task is essentially the computation of integrals. For many stochastic processes that model the financial assets, these integrals can be most efficiently computed in the Fourier domain. However, for some relevant and recent stochastic models the Fourier domain computations are not at all straightforward, as these computations rely on the availability of the characteristic function of the stochastic process, which is not known. In this talk we consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Lévy-type martingale. This class of models allows for a local volatility, a local default intensity and locally dependent jumps in the asset price. Due to the inavailibility of the characteristic function for this process, we present an approximation using an advanced Taylor-based expansion in such a way that the resulting characteristic function exhibits favorable properties for the pricing methods.

**October 25, 2016: Joris Mulder (Tilburg University)**

When: Tuesday October 25th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Room D@ta.

*Bayesian hypothesis testing in social science research*

Researchers in the social and behavioral sciences often formulate competing hypotheses with equality and/or order constraints on the parameters of interest. The goal is then to test these hypotheses using the observed data. Bayes factors have proven useful for this testing problem because (i) Bayes factors can be straightforwardly used for testing multiple nonnested hypotheses in a direct manner; (ii) Bayes factors automatically balance between fit and complexity; and (iii) Bayes factors have an intuitive interpretation as the relative evidence in the data between two hypotheses. All these properties are not shared by the Fisherian p-value, the dominant testing criterion in social research. In this talk a new Bayes factor test is proposed, referred to as the prior adjusted default Bayes factor. The method is compared to existing Bayes factors by looking at various criteria such as information (in)consistency, the incorporation of model complexity of order-constrained hypotheses, and the rate of evidence for a true hypothesis.

**October 18, 2016: Qian Feng (CWI)**

When: Tuesday October 18th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Room D@ta.

*Efficient Computation of Exposure Profiles On Real-World and Risk-Neutral Scenarios for Bermudan Swaptions*

We present a computationally efficient technique for the computation of exposure distributions at any future time under the risk-neutral and some observed real-world probability measures, needed for computation of credit valuation adjustment (CVA) and potential future exposure (PFE). In particular, we present a valuation framework for Bermudan swaptions. The essential idea is to approximate the required value function via a set of risk-neutral scenarios and use this approximated value function on the set of observed real-world scenarios. This technique significantly improves the computational efficiency by avoiding nested Monte Carlo simulation and by using only basic methods such as regression. We demonstrate the benefits of this technique by computing exposure distributions for Bermudan swaptions under the Hull-White and the G2++ models.

**October 11, 2016: No Seminar**

**October 4, 2016: Alex Opoku (University of Energy and Natural Resources - Ghana)**

When: Tuesday October 4th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Room D@ta.

*Opinion formation in stylized society: A view from statistical mechanical window*

In most societies, like ours in Ghana, views on issues such as political party one will vote for in an election is sharply divided along ethnical lines. For some of these people it does not matter how convincing the opposing view may be, they will always stick

to their view.

In this context, formation of a dominant opinion or lack of it is dependent on the proportions of individuals who have fixed their views and those who are yet to decide and other environmental conditions.

In this talk we will propose a class of spin models that will give insights into how consensus or lack of is formed in such a society.

**September 27, 2016: Bas Kleijn (University of Amsterdam)**

When: Tuesday September 27th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Room D@ta.

*Four Bayesian limit theorems for frequentists*

Four frequentist theorems on the large-sample limit behaviour of posterior distributions are proved, for posterior consistency in metric or weak topologies; for posterior rates of convergence in metric topologies; for consistency of the Bayes Factor for hypothesis testing or model selection; and a new theorem that explains how credible sets are to be transformed to become asymptotic confidence sets. Proofs require the existence of suitable test sequences and priors that give rise to a property of local prior predictive distributions called remote contiguity, which generalizes Schwartz's Kullback-Leibler condition as a weakened form of Le Cam's contiguity. All results remain valid if the data is non-i.i.d. and are applied in a range of examples and counterexamples.

**September 20, 2016: Jakob Soehl (TU Delft)**

When: Tuesday September 20th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Room D@ta.

*Nonparametric Bayesian posterior contraction rates for discretely observed scalar diffusions*

We consider nonparametric Bayesian inference in a reflected diffusion model, with discretely sampled observations X_0, X_Δ,..., X_nΔ. We analyse the nonlinear inverse problem corresponding to the "low-frequency sampling" regime where Δ>0 is fixed and n tends to infinity. A general theorem is proved that gives conditions for prior distributions Π, on the diffusion coefficient σ and the drift function b that ensure minimax optimal contraction rates of the posterior distribution over Hölder-Sobolev smoothness classes. These conditions are verified for natural examples of nonparametric random wavelet series priors. For the proofs we derive new concentration inequalities for empirical processes arising from discretely observed diffusions that are of independent interest.

September 13, 2016: Wilbert Samuel Rossi (University of Twente)

When: Tuesday September 13th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Room D@ta.

*Threshold Models in large-scale networks: local mean-field approximation and optimal control.*

The spread of new behaviors and technologies in social and economic networks is often driven by cascading mechanisms. In the talk, I focus on the Linear Threshold Model (LTM) of cascades, first introduced by Granovetter (1978). In a network where agents can choose between two actions, the LTM provides a simple, local decision making law. Each agent is equipped with an individual threshold that represents how many of its neighbors must adopt a certain action before it becomes the agent’s chosen action. The choices are revised during synchronous rounds and multiple switch are allowed.

I present our analysis of the LTM on large-scale directed networks with heterogeneous agents, using a local mean-field approach. We obtain a nonlinear, one-dimensional, recursive equation that approximates the actual fraction of adopters of a given action and we prove a concentration theorem. Remarkably, the approach remains valid even if the threshold distribution is dynamically adjusted. This allows the formulation of optimal control problems: in the talk I discuss a case study.

**September 6, 2016: Charlene Kalle (Leiden University)**

When: Tuesday September 6th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Timmanzaal (LB 01.170).

*From symmetric doubling maps to alpha-continued fractions to obtain invariant measures.*

We introduce a family of symmetric doubling maps generating binary expansions with digits -1,0 and 1. We are interested in determining the frequency of the digit 0 in typical expansions, using the Ergodic Theorem. Therefore, we determine that for a full measure set of parameters, the invariant measure of the symmetric doubling map is piecewise smooth. This is done by exploiting a relation with another family of maps, namely the alpha-continued fraction maps.

This is joint work with Karma Dajani.

**June 14, 2016: Rodrigo Bissacot (University of Sao Paolo) - LAST SEMINAR 2015/2016**

When: Tuesday June 14th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderszaal (LB 01.010).

*Phase Transitions and Large Deviations at Zero Temperature in Countable Markov Shifts*

We discuss the existence of a large deviation principle for a family of equilibrium measures µ_{ß }when the temperature goes to zero on countable Markov shifts. The proof works in the setting where the equilibrium measures have the Gibbs property. We explore the connection between the existence of maximizing measures (from the ergodic optimization point of view) and the absence of phase transitions in Renewal shifts to obtain a characterization for the phase transitions in this class of shifts.

**June 7, 2016: Liu Manxia (University of Nijmegen)**

When: Tuesday June 7th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderszaal (LB 01.010).

*Capturing heterogeneous dynamics*

Capturing heterogeneous dynamic systems in a probabilistic model is a challenging problem. A single time granularity, such as employed by dynamic Bayesian networks, provides insufficient flexibility to capture the dynamics of many real-world processes. The alternative is to assume that time is continuous, giving rise to continuous time Bayesian networks. Here the problem is that the level of temporal detail is too precise to match available probabilistic knowledge.

We present a novel class of models, called hybrid time Bayesian networks(HTBNs), which combine discrete-time and continuous-time Bayesian networks. The new formalism allows us to more naturally model dynamic systems with regular and irregularly changing variables. We also present a mechanism to construct discrete-time versions of hybrid models and an EM-based algorithm to learn the parameters of the resulting BNs. To learn parameters of HTBNs where some irregularly changing variables are partially unobserved, we use Markov chain Monte Carlo sampling to estimate the posterior distribution of the parameters.

**May 31, 2016: Cancelled.**

**May 24, 2016: Sylvia Wenmackers**** (Catholic University of Leuven)**

When: Tuesday May 24th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderszaal (LB 01.010).

*Infinitesimal probabilities and ultra-additivity*

In this presentation, I will discuss the motivations for a particular set of axioms for non-Archimedean probability theory (developed together with Vieri Benci and Leon Horsten), which allows us to assign non-zero infinitesimal probabilities to remote contingencies. I will also address some criticisms that have been raised against this approach in the recent literature.

References:

Benci, V., Horsten, L., and Wenmackers, S. [2013]: ‘Non-Archimedean Probability’, Milan Journal of Mathematics, 81, 121–51.

Benci, V., Horsten, L., and Wenmackers, S. [forthcoming]: ‘Infinitesimal Probabilities’, British Journal for the Philosophy of Science.

**May 17, 2016: Wioletta Ruszel ****(TU Delft)**

When: Tuesday May 17th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderszaal (LB 01.010).

*Sandpiles and bi-Laplacians*

The concept of self-organized criticality was introduced in Bak et al. (1987) as a lattice model with a fairly elementary dynamics. Despite its simplicity, this model exhibits a very complex structure: the dynamics drives the system towards a stationary state which shares several properties of equilibrium systems at the critical point, e.g. power law decay of cluster sizes and of correlations of the height-variables. The model was generalised by Dhar (1990) in the so-called Abelian sandpile model (ASP). Several modifications were proposed, such as a continuum version where each lattice site can have a “real” height instead of a natural one. This is the so-called divisible sandpile model introduced by Levine and Peres in 2009.

In a recent work Levine et al.(2015) prove that the odometer function (which measures in some sense the average amount of mass which is exciting at a fixed site) of a divisible sandpile model on a finite graph can be expressed as a shifted discrete bi-Laplacian Gaussian field. For the discrete torus, they suggest the possibility that the scaling limit of the odometer may be related to the continuum bi-Laplacian field. In this work we show that in any dimension the rescaled odometer converges to the continuum bi-Laplacian field on the unit torus. As a by-product we are able to determine the kernel of the continuum bi-Laplacian on the torus.

This is joint work with Alessandra Cipriani (WIAS Berlin) and Rajat Hazra (IST Kolkata).

May 10, 2016: **Kim Hendrickx**** (University of Hasselt)**

When: Tuesday May 10th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderszaal (LB 01.010).

*Current status linear regression via maximum likelihood estimation *

We discuss estimators for the finite-dimensional regression parameter in the current status linear regression model. It is shown that, using a simple truncation device, one can construct n-consistent and asymptotically normal estimates of the finite-dimensional regression parameter. We discuss the efficiency or almost efficiency of estimators and illustrate this with a simulation study.

Joint work with Piet Groeneboom.

**The talk of Thomas Manfredi**** (OECD), scheduled on Tuesday May 10, has been postponed.**

May 3, 2016: Alexandre Lazarescu** (University of Luxembourg)**

When: Tuesday May 3rd, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderszaal (LB 01.010).

*Combinatorial and integrable aspects of the asymmetric simple exclusion process*

The asymmetric simple exclusion process, or ASEP, is a continuous time Markov process where particles jump stochastically on a 1D lattice, preferentially to one side, and with hard-core interactions. It is possibly the most studied model in non-equilibrium statistical mechanics, for a number of reasons: it is relatively simple and elegant in its definition and has a complex and physically insightful behaviour, it is connected to many other models or mathematical objects, and it is integrable and therefore exactly solvable, at least in principle.

In this seminar, I will go over some of the results pertaining to the integrability of this model. I will first describe its steady state, which can be expressed as a matrix product and involves Dyck paths and q-oscillators. I will then focus on the statistics of the current of particles flowing through the system and show how they can be calculated from studying special random walks on N^k. Finally, I will show how that same result can be obtained more rigorously through methods from quantum integrability, such as the Q-operator method and the functional Bethe Ansatz.

**April 26, 2016: Eni Musta**** (TU Delft)**

When: Tuesday April 26th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderszaal (LB 01.010).

*Smooth estimation of a monotone baseline hazard in the Cox model*

A frequently encountered problem in the context of nonparametric estimation under shape constraints is the estimation of the hazard or failure rate. We consider smooth estimators for a monotone baseline hazard rate in the Cox model. Varying the choice of the isotonic estimator and the order of smoothing and isotonization, four different estimators can be obtained. We analyze their asymptotic behavior and show that they are normal at rate n^(2/5). It turns out that the kernel smoothed versions of the Grenander-type and of maximum likelihood estimator together with the Grenander-type smoothed estimator are asymptotically equivalent, while the maximum smoothed likelihood estimator exhibits the same asymptotic variance but a different bias. Numerical results on pointwise confidence intervals emphasize the comparable behavior of the four methods.

This is joint work with H.P. Lopuhaä

**April 19 , 2016: Jan Boronski**** (IT4I Ostrava & AGH Krakow)**

When: Tuesday April 12th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Timmanzaal (LB01.170).

*On dynamics of the Sierpinski Carpet*

In 1993, Aarts and Oversteegen proved that the Sierpinski carpet S admits a transitive homeomorphism, answering a question of Gottschalk. They also showed that it does not admit a minimal one. Earlier, in 1991 Kato proved that S does not admit expansive homeomorphisms. In 2007 Bis, Nakayama and Walczak proved that S admits a homeomorphism with positive entropy, and that it admits a minimal group action. We show that S admits homeomorphisms with strong mixing properties. Namely, there is a homeomorphism H : S → S that has a fully supported measure m, such that (H, m) is Bernoulli, H has a dense set of periodic points, and H does not have Bowen's specification property. In particular, S admits a topologically mixing homeomorphism. The starting point of our construction is Arnold's cat map.

This is joint work with P. Oprocha.

**April 12 , 2016: Omiros Papaspiliopoulos (Pompeu Fabra University)**

When: Tuesday April 12th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Timmanzaal (LB01.170).

*Scalable Bayesian variable selection and model averaging **under block orthogonal design*

A new approach to Bayesian variable selection is introduced that is computationally efficient for Big Data (both *N* and *p* large) that operates under the assumption that the Gram matrix is block-diagonal. The methodology allows fully Bayesian inference with respect to important parameters and hyperparameters of the linear regression model, such as residual variance and prior shrinkage parameters.

Joint work with D. Rossell (Warwick).

**April 5 , 2016: Irène Marcovici (Université de Lorraine)**

When: Tuesday April 5th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderszaal (LB 01.010).

*Ergodicity of noisy cellular automata: the coupling method and beyond*

When perturbating a cellular automaton by a random noise (positive probability of error, for each cell independently), the system is generally expected to be ergodic, meaning that during its evolution, it eventually forgets about its initial condition. For a high noise, this can be shown by coupling. However, for a small noise, ergodicity is often very difficult to prove. We present extensions of the coupling method to small noises when the cellular automaton has some specific properties (hardcore exclusion, nilpotency, permutivity).

**March 31, 2016: Stochastics Analysis Day at TU Delft (Workshop)**

When: Thursday March 31st, 10:30-17:30

Where: TU Delft, Faculty EWI, Mekelweg 4, Room F.

March 29, 2016: No seminar - Easter Break

March 22 , 2016: Seminar Cancelled and Postponed

March 15 , 2016: Yi He (Tilburg University)

When: Tuesday March 15th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Timmanzaal (LB01.170).

*Asymptotic Normality in Extreme Depth-base Quantile Region Estimation*

Consider the small-probability multivariate quantile regions consisting of extremely outlying points with nearly zero data depth value. We extend the extreme-value-theory based estimation method proposed in Cai, Einmahl and de Haan (2011) and He and Einmahl (2016) to incorporate general depth functions. Under weak regular variation conditions, both the consistency and asymptotic normality results are derived. A refined asymptotic normality result is established for half-space depth. The simulation study clearly demonstrates the good performance of our refined asymptotic approximation in finite samples. We use our method for risk management by applying it to financial data. In this talk, depending on the time constraints, we may only cover the results for half-space depth.

**March 8 , 2016: Daan Crommelin (CWI and University of Amsterdam) **

When: Tuesday March 8th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Timmanzaal (LB01.170).

*Stochastic models for multiscale dynamical systems*

Modeling and simulation of multiscale dynamical systems such as the climate system is challenging due to the wide range of spatiotemporal scales that need to be taken into account. A promising avenue to tackle this multiscale challenge is to use stochastic methods to represent dynamical processes at the small/fast scales. The feedback from microscopic (small-scale) processes is represented by a network of Markov processes conditioned on macroscopic model variables. I will discuss some of the work from this research direction. A systematic derivation of appropriate stochastic processes from first principles is often difficult, and statistical inference from suitable datasets can provide an interesting alternative.

**March 1 , 2016: Ronald Meester (Vrije Universiteit Amsterdam)**

When: Tuesday March 1st, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Timmanzaal (LB01.170).

*New axiomatization for degrees of belief via a betting interpretation.*

It has been recognized by many researchers that the classical axioms of probability are not always suitable for epistemic interpretations of probability, that is, when uncertainly relates to e.g. belief, provability and knowledge of facts, rather than to facts themselves. Until recently no axiomatization of such epistemic probability existed which can be related to betting interpretations analogous to the Dutch Book arguments for classical probability. We provide such axiomatization, and show that this leads to so called Shafer belief functions, the theory of which we are currently developing.

**February 16 , 2016: Fei Cong (TU Delft)**

When: Tuesday February 16th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Timmanzaal (LB01.170).

*Constrained Multi-period Mean-Variance Portfolio Optimization.*

We propose a simulation-based approach for solving the constrained dynamic mean-variance portfolio management problem. For this dynamic optimization problem, we first consider a sub-optimal strategy, called the multi-stage strategy, which can be utilized in a forward fashion. Then, based on this fast yet sub-optimal strategy, we propose a backward recursive programming approach to improve it. We design the backward recursion algorithm such that the result is guaranteed to converge to a solution, which is at least as good as the one generated by the multi-stage strategy. In our numerical tests, highly satisfactory asset allocations are obtained for dynamic portfolio management problems with realistic constraints on the control variables.

**February 9 , 2016: Daniel Rodrigues Valesin (Groningen University)**

When: Tuesday February 9th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderszaal (LB 01.010).

*Extinction time of the contact process on general graphs.*

Complementing earlier work by Mountford, Mourrat, Valesin and Yao, we study metastable behavior of the contact process on general finite and connected graphs. For the contact process with infection rate $\lambda$ on a graph $G$, the extinction time is the random amount of time until the process started from all individuals infected reaches the trap state in which the infection is absent. We prove, without any restriction on $G$, that if $\lambda$ is larger than the critical rate of the one-dimensional process, then the extinction time grows faster than $\exp(|G|/(\log |G|)^a)$ for any constant $a > 1$, where $|G|$ denotes the number of vertices of $G$. Also for general graphs, we show that the extinction time divided by its expectation converges in distribution, as the number of vertices tends to infinity, to the exponential distribution with parameter 1.

Joint work with Bruno Schapira.

**February 2 , 2016: Chen Zhou (DNB and Erasmus University)**

When: Tuesday February 2nd, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderszaal (LB 01.010).

*Statistics of heteroscedastic extremes.*

We extend classical extreme value theory to non-identically distributed observations. When the tails of the distribution are proportional much of extreme value statistics remains valid. The proportionality function for the tails can be estimated non-parametrically along with the (common) extreme value index. For a positive extreme value index, joint asymptotic normality of both estimators is shown; they are asymptotically independent. We also establish asymptotic normality of a forecasted high quantile and develop tests for the proportionality function and for the validity of the model. We show through simulations the good performance of the procedures and also present an application to stock market returns. A main tool is the weak convergence of a weighted sequential tail empirical process.

**January 26, 2016: Aurelius Zilko (TU Delft)**

When: Tuesday January 26th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, v/d Poelzaal (LB 01.220).

*Dependence Modelling with Copula in A Mixed Discrete - Continuous Problem.*

A recent application requires a dependence model to be constructed between discrete and continuous variables. To do so, we intend to use copula. The use of copula is well studied and applied mostly in fully continuous setting. Therefore, we study its behavior when copula is applied in, first, fully discrete setting and, secondly, mixed discrete and continuous setting. Further on, we investigate how the graphical structure called vines can be used to construct better, but more complex, copula model in this case. An application on the railway traffic management is considered as an example.

**January 12, 2016: Milton D. Jara V. ****(Leiden University)**

When: Tuesday January 12th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderszaal (LB 01.010).

*The fractional KPZ equation and the strong universality KPZ conjecture.*

We consider an exclusion process with long jumps and we prove convergence along subsequences of the density fluctuations of this model to an energy solution of a fractional KPZ equation. We conjecture that this equation, which is still not well understood, also governs the behaviour of the density of particles of general particle systems, like the TASEP or the TAZRP.

Joint work with Patricia Gonçalves.