# Seminars

### Seminar Series in Probability and Statistics

Seminars are held on Mondays from 4pm to 5pm.

The usual location for the seminars is: TU Delft, Faculty EWI, Mekelweg 4.

**February 25, 2019**: Ayan Bhattacharya (CWI Amsterdam)

When: Monday, February 25

**February 11, 2019**: Jaron Sanders (TU Delft)

When: Monday, February 11

*Clustering in Block Markov Chains*

In this talk, I will discuss our recent paper that considers cluster detection in Block Markov Chains (BMCs). These Markov chains are characterized by a block structure in their transition matrix. More precisely, the n possible states are divided into a finite number of K groups or clusters, such that states in the same cluster exhibit the same transition rates to other states. One observes a trajectory of the Markov chain, and the objective is to recover, from this observation only, the (initially unknown) clusters. In this paper we devise a clustering procedure that accurately, efficiently, and provably detects the clusters. We first derive a fundamental information-theoretical lower bound on the detection error rate satisfied under any clustering algorithm. This bound identifies the parameters of the BMC, and trajectory lengths, for which it is possible to accurately detect the clusters. We next develop two clustering algorithms that can together accurately recover the cluster structure from the shortest possible trajectories, whenever the parameters allow detection. These algorithms thus reach the fundamental detectability limit, and are optimal in that sense.

This is joint work with Alexandre Proutière and Se-Young Yun.

**January 28, 2019**: Pasquale Cirillo (Tu Delft)

When: Monday, January 28th

Where: TU Delft, EWI-Lecture hall F

*The arithmetic of finance*

Take finance, remove the trendy words, remove the acronyms and the obscure jargon, admit you will not be rich, but be happy because you will not lose money either. What do you get? Interestingly you discover that all those changes of measure, those coherent risk measures, even the pay-off of a European option, not to mention utility theory in its many declinations, are nothing but the result of sums and products. So, let’s come back to basics.

**January 14, 2019**: Lixue Pang (TU Delft)

When: Monday, January 14th

Where: TU Delft, EWI-Lecture hall F

*Bayesian estimation of a decreasing density*

Consider the problem of estimating a decreasing density function, with special interest in zero. It is well known that the maximum likelihood estimator is inconsistent at zero. This has led several authors to propose alternative estimators which are consistent. As any decreasing density can be represented as a scale mixture of uniform densities, a Bayesian estimator is obtained by endowing the mixture distribution with the Dirichlet process prior. Assuming this prior, we derive contraction rates of the posterior density at zero. Several choices of base measure are numerically evaluated and compared. In a simulation various frequentist methods and a Bayesian estimator are compared. Finally, the Bayesian procedure is applied to current durations data.

**December 17, 2018**: Barbara Terhal (TU Delft, QuTech)

When: Monday December 17th, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, EWI-Lecture hall F

*The sign problem in quantum physics: room for algorithms and optimization*

Quantum physical problems are described by a sparse Hermitian matrix called a Hamiltonian which obeys a certain locality structure allowing for an efficient description. A subset of such Hamiltonians have been called sign-problem free or "stoquastic" as their smallest eigenvector is the largest eigenvector of a nonnegative matrix. The connection with nonnegative matrices has allowed for the development of various Quantum Monte Carlo methods to simulate features of these Hamiltonians in the quantum physics community over the past 30 years. As the non-negativity of a matrix is basis-dependent, local basis changes which preserve the locality structure of the Hamiltonian can remove the sign problem. We report on our new results of finding such local basis changes algorithmically for subclasses of Hamiltonians.

**December 03, 2018**: Frank van der Meulen (Tu Delft)

When: Monday December 03th, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, EWI-Lecture hall D@ta

*Simulation of hypo-elliptic conditioned diffusions*

Consider a diffusion that is constructed as a strong solution to a stochastic differential equation (SDE). Parameter estimation of discrete time data is hard, due to intractability of the likelihood. To deal with this problem, a popular approach is to use a data-augmentation method, where the latent path is imputed. This imputation boils down to simulation of conditioned diffusions. Over the past decade this area of research has received considerable attention. Virtually all of the proposed methods assume that each component of the SDE is driven by its own Brownian motion. Unfortunately, if this is not the case, they break down. I will discuss how this problem can be dealt with for a wide class of SDE-models.

**November 19, 2018**: Marton Balasz (Bristol University)

When: Monday November 19th, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, EWI-Lecture hall D@ta

*Jacobi triple product via the exclusion process*

I will give a brief overview of very simple, hence maybe less investigated

structures in interacting particle systems: reversible product blocking

measures. These turn out to be more general than most people would think, in

particular asymmetric simple exclusion and nearest-neighbour asymmetric zero

range processes both enjoy them. But a careful look reveals that these two are

really the same process. Exploitation of this fact gives rise to the Jacobi

triple product formula - an identity previously known from number theory and

combinatorics. I will show you the main steps of deriving it from pure

probability this time, and I hope to surprise my audience as much as we got

surprised when this identity first popped up in our notebooks.

**October 29, 2018**: Joe P. Chen (Colgate University)

When: Monday October 29th, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, EWI-Lecture hall D@ta

*Hydrodynamic limit of the boundary-driven exclusion process on the Sierpinski gasket*

The exclusion process is a well-known interacting particle system which exhibits a rich variety of phenomena. In particular, limit theorems for the asymmetric exclusion process on 1D have been studied intensely over the past few years. A natural question is whether similar analysis can be made on higher-dimensional state spaces.

To be precise, fix a state space *Χ* with a finite boundary set ∂*Χ*. Let (*G _{N }) *be a sequence of graph approximations of

*Χ*. Consider the (asymmetric) exclusion process on

*G*, and in addition, add to each boundary point

_{N}*α*∈ ∂

*Χ*a birth-and-death chain, which models the injection or extraction of particles at well-defined rates. Then under the diffusive scaling limit (if known), the empirical density will concentrate on a hydrodynamic trajectory governed by a nonlinear heat equation. In addition, one may also establish a large deviations principle, characterizing the fluctuations about the hydrodynamic trajectory.

When *Χ = *[0,1] and ∂*Χ = *{0,1}, this has been proved by Bertini, De Sole, Gabrielli, Jona-Lasinio, and Landim. In this talk I will describe joint work with Michael Hinz (Bielefeld) and Alexander Teplyaev (Connecticut) on establishing the corresponding results when *Χ* is the Sierpinski gasket and ∂*Χ *is the set of 3 boundary vertices of the gasket. Our results pave the way for further studies of non-equilibrium fluctuations in the presence of 3+ boundary components.

Our proofs are based on the "entropy method" of Guo, Papanicolaou, and Varadhan, and in adopting this method we had to overcome a number of technical difficulties, most notably the lack of translational invariance. This led to an auxilliary study of functional inequalities for the exclusion process on a "resistance space," which includes trees, fractals, and random graphs as examples. I will briefly mention my own work proving a "moving particle lemma" on a finite connected weighted graph, which is used to facilitate a local coarse-graining argument in passing to the macroscopic limit.

**October 22, 2018**: Bert Kappen (Radboud University Nijmegen,Gatsby Computational Neuroscience Unit UCL London)

When: Monday October 22nd, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, Lecture hall F.

*The Quantum Boltzmann Machine*

We propose to generalise classical maximum likelihood learning to density matrices. As the objective function, we propose a quantum likelihood that is related to the cross entropy between density matrices. We apply this learning criterion to the quantum Boltzmann machine (QBM), previously proposed by Amin et al.. We demonstrate for the first time learning a quantum Hamiltonian from quantum statistics using this approach. For the anti-ferromagnetic Heisenberg and XYZ model we recover the true ground state wave function and Hamiltonian. The second contribution is to apply quantum learning to learn from classical data. Quantum learning uses in addition to the classical statistics also quantum statistics for learning. These statistics may violate the Bell inequality, as in the quantum case. Maximizing the quantum likelihood yields results that are significantly more accurate than the classical maximum likelihood approach in several cases. We give an example how the QBM can learn a strongly non-linear problem such as the parity problem. The solution shows entanglement, quantified by the entanglement entropy.

https://arxiv.org/abs/1803.11278

Bio: http://www.snn.ru.nl/~bertk/biograph2

**October 08, 2018**: Extreme TiDE seminar

When: Monday October 8th, 15:00 - 17:00

Where: TU Delft, Faculty EWI, Mekelweg 4, Lecture hall Snijderzaal (LB 01.010).

**15:00-15:45** Hanna Ahmed (Tilburg University)

*Improved estimation of the extreme value index using a related variables*

Heavy tailed phenomena are naturally analyzed by extreme value statistics. A crucial step in such an analysis is the estimation of the extreme value index, which describes the tail heaviness of the underlying probability distribution. We consider the situation where we have next to the n observations of interest another n + m observations of one or more related variables, like, e.g., financial losses due to earthquakes and the related amounts of energy released, for a longer period than that of the losses. Based on such a data set, we present an adapted version of the Hill estimator that shows greatly improved behavior and we establish the asymptotic normality of this estimator. For this adaptation the tail dependence between the variable of interest and the related variable(s) plays an important role. A simulation study confirms the substantially improved performance of our adapted estimator relative to the Hill estimator. We also present an application to the aforementioned earthquake losses.

This is a joint work with John H.J. Einmahl.

**16:00-17:00** Clément Dombry (*University of Franche-Comté*)

*Analysis of the proportional tail model for extreme quantile regression via a coupling approach*

Extreme quantile regression is a fundamental problem in extreme value theory. Assume that we observe an n-sample (x_{1},y_{1}) ,...,(x_{n},y_{n}) of a random variable *Υ*∈*R *together with covariates *X*∈*R*.

Our goal is to estimate the conditional quantile of order 1-*p* of *Y* given *X* = *x*. When *p* is small, there is not enough observations and extrapolation further in the tail distribution is needed. We face an extreme value problem.

The purpose of the talk is to present an ongoing joint work with B.Bobbia and D.Varron on the proportional tail model where we assume that the conditional tails are asymptotically proportional to the unconditional tail, that is P(*Y*>*y*|*X*=*x*) ∼ *σ*(*x*)P(*Y*>*y*) as* y* → *y*^{* },the upper endpoint of the distribution. This framework was introduced in the slightly different context of heteroscedastic extremes in Einmahl et al. (JRSSB 2016) and the function *σ* was coined the skedasis function. Assuming an extreme value condition for *Y* together with the proportional tail model, the extreme quantile regression is reduced to the estimation of the skedasis function and the extreme value index. We present our results for such an estimation. Interestingly, we introduce different techniques for the proof as Einmahl et al.: we introduce coupling arguments relying on total variation and Wasserstein distances, whereas the original proof relies mostly on empirical process theory.

The *seminar room* will be **Snijderszaal (LB 01.010** ) at the first floor of EWI Faculty (Building 36). Full address: Mekelweg 4, 2628 CD Delft.

**September 24, 2018**: Pierre Nyquist (TU Eindhoven)

When: Monday September 24th, 16:00

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

The infinite swapping algorithm: Properties and applications.

Infinite swapping is a Monte Carlo method originally developed by Doll, Dupuis and co-authors using empirical measure large deviations. The method is designed to overcome the problem of rare-event sampling, and thus speed up convergence, in the setting of computing integrals with respect to Gibbs measures. In our subsequent work the properties of infinite swapping were studied further using a combination of empirical measure large deviations and stochastic ergodic control problems, revealing explicit information on the convergence properties of the sampling scheme. This talk will focus on the properties of infinite swapping, and the associated large deviations analysis, and (non-standard) applications in quantum dynamics and machine learning. Given time we will also discuss briefly the use of empirical measure large deviations to study convergence rates for MCMC methods, and possible implications of the comparison between parallel tempering and infinite swapping for training RBMs.

This is based on joint work with Paul Dupuis, Jim Doll (Brown University), Henrik Hult and Carl Ringqvist (KTH).

**September 17, 2018**: Maki Furukado (Yokohama National University)

When: Monday September 17th, 16:00

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

The generation of the stepped surface in terms of the modified Jacobi-Perron algorithm

For a substitution σ satisfying some conditions, it is known the way how to define a map which maps an unit face to some unit faces on a stepped surface, which are constructed by three kinds of unit faces U, of a plane related with σ. It seems that we can generate the stepped surface by applying σ to U infinitely many times. In this talk, we would like to treat the substitutions in terms of the modified Jacobi-Perron algorithm and to discuss about the generation of the stepped surface.

This work is in collaboration with Shunji Ito (Kanazawa University) and Shin-ichi Yasutomi (Toho University).

**September 10, 2018**: Mike Keane (TU Delft)

When: Monday September 10th, 16:00

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

*The World of Bernoulli Schemes*

The study of random processes is a central element of

probability and statistics. In this lecture I wish to concentrate on the

understanding which has been developed of Bernoulli schemes, named after

the seminal work of Jacob and Johan Bernoulli in the 17th century in

Basel and Groningen, and in particular to explain simple methods which

algorithmically convert sequences of random "coin" tosses of a coin to

such random sequences of another, different "coin", both in the

classical and quantum domains. There is at present a hope that the new

"coins", sometimes called "quantum coins", will provide solutions to yet

intractable questions using classical Bernoulli techniques.

June 11, 2018: **Rajat Hazra (Indian Statistical Institute, Kolkata)**

When: Monday June 11th, 16:00

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

*Branching random walk: a tale of two tails.*

Branching random walk with regularly varying displacements is a heavy-tailed random field indexed by a Galton-Watson tree. We shall survey some results on rightmost position of the particle and also describe the point process associated to it. These results were obtained when the mean of the branching random variable is finite and satisfies the Kesten-Stigum condition. We extend these results to the case when the mean is infinite in the underlying GW tree (which can happen when the branching random variable has heavy tails). The weak limit of the rightmost particle, the associated cloud speed, the point process of displacements all can be described explicitly. If time permits we shall also describe the case when displacements have exponentially decaying tails.

The talk is based on the master thesis of Souvik Ray (ISI, Kolkata) and also joint works with Ayan Bhattacharya (CWI, Amsterdam), Parthanil Roy (ISI Bangalore), Philippe Soulier (Universite Paris Nanterre).

**May 14, 2018: ****Eni Musta (TU Delft)**

When: Monday May 14th, 16:00

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

*Central limit theorems for global errors of smooth isotonic estimators*

A typical problem in nonparametric statistics is estimation of an unknown function on the real line, which may, for instance, be a probability density, a regression function or a failure rate. In many cases, it is natural to assume that this function is monotone and incorporating such a prior knowledge in the estimation procedure leads to more accurate results. We consider smooth isotonic estimators, constructed by combining an isotonization step with a smoothing step. We investigate the global behavior of these estimators and obtain central limit theorems for their L_p losses. We also perform a simulation study for testing monotonicity on the basis of the L_2 distance between the kernel estimator and a smooth isotonic estimator.

Joint work with Hendrik P. Lopuhaä.

**May 07, 2018: ****Federico Sau (TU Delft)**

When: Monday May 7th, 16:00

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

E*xclusion process in symmetric dynamic environment: quenched hydrodynamics.*

For the simple exclusion process evolving in a symmetric dynamic random environment, we derive the hydrodynamic limit from the quenched invariance principle of the corresponding random walk. For instance, if the limiting behavior of a test particle resembles that of Brownian motion on a diffusive scale, the empirical density, in the limit and suitably rescaled, evolves according to the heat equation.

In this talk we make this connection explicit for the simple exclusion process and show how self-duality of the process enters the problem. This allows us to extend the result to other conservative particle systems (e.g. IRW, SIP) which share a similar property.

Work in progress with F. Collet, F. Redig and E. Saada.

**April 23, 2018: Tim van Erven (Leiden University)**

When: Monday April 23rd, 16:00

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

*MetaGrad: Multiple Learning Rates in Online Learning*

In online sequential prediction it is well known that certain subclasses

of loss functions are much easier than arbitrary convex functions.

We are interested in designing adaptive methods that can automatically

get fast rates in as many such subclasses as possible, without any

manual tuning. Previous adaptive methods are able to interpolate between

strongly convex and general convex functions. We present a new method,

MetaGrad, that adapts to a much broader class of functions, including

exp-concave and strongly convex functions, but also various types of

stochastic and non-stochastic functions without any curvature. For

instance, MetaGrad can achieve logarithmic regret on the unregularized

hinge loss, even though it has no curvature, if the data come from a

favourable probability distribution. MetaGrad's main feature is that it

simultaneously considers multiple learning rates. Unlike all previous

methods with provable regret guarantees, however, its learning rates are

not monotonically decreasing over time and are not tuned based on a

theoretically derived bound on the regret. Instead, they are weighted

directly proportional to their empirical performance on the data using a

tilted exponential weights master algorithm.

References:

T. van Erven and W.M. Koolen. MetaGrad: Multiple Learning Rates in

Online Learning. NIPS 2016.

W.M.Koolen, P. Grünwald and T. van Erven. Combining Adversarial

Guarantees and Stochastic Fast Rates in Online Learning. NIPS 2016.

**April 09, 2018: ****Alessandra Cipriani (TU Delft)**

When: Monday April 09th, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, Lecture hall D@ta.*On two Gaussian random interfaces*

Random interfaces arise naturally as separating surfaces between two different thermodynamic phases or states of matter, for example oil and water. In this talk we will introduce Gaussian models for random interfaces by focusing on two of them: the discrete Gaussian free field (DGFF) and the membrane model (MM). We will present their similarities and differences, in particular we will discuss their 1-dimensional representations, the recent developments on the description of their extremal behavior, and their scaling limits. We will also pose some open problems that arise in the MM setting.

**March 26, 2018: ****Arne Huseby (University of Oslo)**

When: Monday March 26th, 16:00

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

*Environmental contours*

Environmental contours are used as an efficient way of summarizing uncertainty about various environmental variables relevant to marin constructions. They are typically used in the design phase where precise knowledge about the construction is not yet available. The traditional approach to environmental contours is based on the well-known Rosenblatt transformation. However, due to the effects of this transformation the probabilistic properties of the resulting environmental contour can be difficult to interpret. An alternative approach to environmental contours uses Monte Carlo simulations on the joint environmental model, and thus obtain a contour without the need for the Rosenblatt transformation. This contour have well-defined probabilistic properties, but may sometimes be overly conservative in certain areas. In this presentation we review the main approaches to environmental contours, and show how to evaluate the probabilistic properties of such contours.

**March 19, 2018: ****Bruno Kimura (TU Delft)**

When: Monday March 19th, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, Lecture hall D@ta.*Phase transition in the one-dimensional long range Ising model under the presence of decaying external fields*

The long range Ising models differs from the classical ones by the fact that the spin-spin interaction decays spatially. Since long range models often behaves like short range models in higher dimension, we studied the phase diagram of one-dimensional Ising models in d=1 and proved that even in the presence of certain external fields there is phase transition at low temperatures. The techniques used to prove such result were based contour arguments developped by Froehlich, Spencer, Cassandro, Presutti et al.

**March 12, 2018: ****Dennis Dobler**** (VU Amsterdam)**

When: Monday March 12th, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, Lecture hall D@ta.*Nonparametric inference on transition probabilities in right-censored multi-state models*

When analyzing times of occurences of certain events, e.g. individuals' transitions from a healthy to a disease state or vice versa, many medical studies need to face the problem of incomplete data due to independent right-censoring. That is, from certain points in time, observation of some events is not possible any more. Because of this, the use of empirical distributions for estimating event probabilities would lead to a systematic bias.

Instead, products of estimated hazard functions yield estimators of probabilities of state transitions. This well-known Aalen-Johansen estimator is applicable if the Markov assumption for the processes of individual state trajectories is satisfied, i.e. given the present state, visited past and future states are independent. Considered as a process in time, this estimator has a complicated Gaussian limit distribution when the sample size tends to infinity. This makes the use of resampling techniques necessary. We will discuss related conditional central limit theorems which enable the construction of confidence bands for state transition probabilities.

When there is reason to discard the Markov assumption, the Aalen-Johansen estimator loses its justification. We will discuss recently proposed estimators of transition probabilities in this situation as well as their drawbacks and advantages.

March 05, 2018: Cees de Valk (**Royal Netherlands Meteorological Institute KNMI****)**

When: Monday March 05rd, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, Lecture hall D@ta.*Tail behaviour of a transport-based multivariate quantile*

The talk addresses joint work with Johan Segers at the Université catholique de Louvain. Recently, an attractive multivariate quantile based on Monge-Kantorovitch optimal transport was proposed: a map transforming a spherical reference distribution function to the distribution function of interest is sought which minimises the mean square of the size of the displacement. We explore this idea further, in particular to define and estimate a multivariate tail quantile. Starting from the assumption of multivariate regular variation, we derive limit relations satisfied by the optimal map and the associated quantile. Estimators and examples of applications are discussed.

February 26, 2018: Jan H. van Schuppen (TU Delft)

When: Monday February 26th, 16:00

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

Control and Prediction of Traffic Flow in a Large-Scale Road Network

The research is motivated by control of the motorway network of The Netherlands. Six traffic control centers receive online data about the traffic flow and activate the control measures of routing control, dynamic speed limits, incident warnings, and ramp-metering.

There is first a need for an algorithm to predict the traffic flow in a large-scale network for a period of 30 minutes into the future.

The predictions are needed to evaluate control measures. The short prediction time, less than a second, is needed for control purposes.

The prediction algorithm is based on parallel processing at the local level with a coordination at the network level.

For this an iterative procedure has been formulated.

It is then possible to predict the traffic flow in a 145 km network in about 0.04 s with an elementary computer.

Control objectives for a large-scale road network require a new approach. The reader may think for the scale of the network of the range of 100 to 2.000 km, most of the Western part of The Netherlands with about 6 to 10 million inhabitants.

For this purpose, a multilevel control system is proposed that is currently in development. So far one distinguishes the levels of a section, a link, a subnetwork, a network, a region, etc. Control objectives are assigned to each level and control algorithms for each level are synthesized.

Control synthesis of a multilevel control system requires the development of an appropriate procedure.

The research is based on scientific cooperation with:

Yubin Wang and Jos L.M. Vrancken.

**February 19, 2018: ****Bas Janssens (TU Delft)**

When: Monday February 19th, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, Lecture hall D@ta.*Reflection positivity for parafermions*

If you interchange two bosons, nothing happens. If you interchange two fermions, you get a minus sign. More generally, if you interchange two parafermions (or "anyons"), you get a complex pth root of unity. Inspired by recent interest in the use of parafermions in statistical physics, we give necessary and sufficient conditions on parafermionic hamiltonians in order for the the corresponding Gibbs state to be reflection positive. (Joint w. Arthur Jaffe, J. Funct.

Analysis 272:8, 3506-3557)

February 12, 2018: **Cristian Giardinà (Università di Modena e Reggio Emilia)**

When: Monday February 12th, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, Lecture hall D@ta.*Boundary driven 2D Ising model*

I will discuss properties of the non-equilibrium stationary state of the two-dimensional Ising model coupled to magnetization reservoirs. When the boundaries impose magnetization values corresponding to opposite phases, a free boundary problem (of Stefan type) describes the evolution of the interface in the hydrodynamic limit. I will argue that the stationary solutions in the metastable or unstable phase may sustain a current that is going uphill, i.e. from the reservoir with lower magnetization to the one with larger magnetization.

February 05, 2018: **Ivan S. Yaroslavtsev (TU Delft)**

When: Monday February 05th, 16:00

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

The canonical decomposition of local martingales in infinite dimensions

The canonical decomposition of local martingales was invented by Yoeurp in 1976 and partly by Meyer in 1976, and it has the following form: a local martingale has the canonical decomposition if it can be decomposed into a sum of a continuous local martingale (a Wiener-like part), a purely discontinuous quasi-left continuous local martingale (a Poisson-like part, which does not jump at predictable stopping times), and a purely discontinuous local martingale with accessible jumps (a discrete-like part, which jumps only at certain predictable stopping times). Due to Yoeurp the canonical decomposition of a real-valued local martingale always exists and is unique. In the current talk we will extend this result to infinite dimensions and show that the canonical decomposition of an arbitrary $X$-valued local martingale exists if and only if $X$ is a UMD Banach space; moreover, if this is the case, then the corresponding $L^p$ ($1<p<\infty$) and weak $L^1$ estimates for the decomposition terms hold.

The canonical decomposition plays a significant role in vector-valued stochastic integration theory. For instance one can show sharp estimates for an $L^p$-norm of an $L^q$-valued stochastic integral with respect to a general local martingale. An important tool for obtaining these estimates are the recently proven Burkholder-Rosenthal-type inequalities for discrete $L^q$-valued martingales.

This talk is partly based on joint work with Sjoerd Dirksen (RWTH Aachen University).

**January 29, 2018: ****Wolter Groenevelt (TU Delft)**

When: Monday January 29th, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, Lecture hall D@ta.*Stochastic duality, orthogonal polynomials and Lie algebras*

Recently it has been shown that stochastic duality functions for several Markov processes can be given in terms of orthogonal polynomials. In this talk I explain how this results can be obtained from representation theory of Lie algebras.**January 22, 2018: No seminar**

**January 15, 2018: ****Rob van den Berg (CWI Amsterdam)**

When: Monday January 15th, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, Lecture hall D@ta.*Near-critical percolation and applications*

Motivated by sol-gel transitions, David Aldous (2000) introduced and analysed an interesting percolation model on a tree where clusters stop growing (`freeze') as soon as they become infinite. I will discuss recent work with Demeter Kiss and Pierre Nolin (and current work with Pierre Nolin) on processes of similar flavour on planar lattices. We focus on the question whether or not the `gel' (i.e. the union of the frozen clusters) occupies a negligible fraction of space. Sharp versions of some classical scaling results by Harry Kesten for near-critical percolation were needed, and developed, to answer this question. I also plan to present a modification of the model which may be interpreted as a `self-organized critical' sensor/communication network. The study of it leads naturally to a more general framework of near-critical percolation with `heavy-tailed' impurities.

**January 08, 2018: ****Marjan Bakker (Tilburg University)**

When: Monday January 08th, 16:00

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

*Human factors in statistics: an example with outliers.*

I’m part of the Meta-Research Center of Tilburg University, School of Social and Behavioral Sciences and our research focuses on investigating research practices and problems in the scientific system. I will first present a short overview of our work, after which I will continue to discuss a specific research practice, namely the detection and handling of outliers. In psychology, outliers are often excluded before running an independent sample *t* test and data are often non-normal because of the use of sum scores based on tests and questionnaires. After reviewing common practice, I present results of simulations of artificial and actual psychological data, which show that the removal of outliers based on commonly used *Z* value thresholds severely increases the Type I error rate. Result show that removing outliers with a threshold-value of *Z* of 2 in a short and difficult test, increases Type I error rates up to .222. Inflations of Type I error rates are particularly severe when researchers are given the freedom to alter threshold-values of *Z* after having seen the effects thereof on outcomes. I recommend the use of non-parametric or robust tests instead.

December 18, 2017:** ****NO SEMINAR**

**December 11, 2017: Chen Zhou (Erasmus University Rotterdam)**

When: Monday December 11th, 15:05

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderzaal (LB01.010)

*Trends in extreme value indices*

We consider extreme value analysis for independent but non-identically distributed observations. In particular, the observations do not share the same extreme value index. This situation is related to, but differs from, heteroscedastic extremes in Einmahl et al. (2016). Compared to the heteroscedastic extremes, our model allows for a broader class in which tails of the probability distributions of different observations are of different order. In other words, we are dealing with distributions that differ much more than the heteroscedastic extremes. Assuming continuously changing extreme value indices, we provide a non-parametric estimate for the functional extreme value index. Besides estimating the extreme value index locally, we also provide a global estimator for the trend and its joint asymptotic property. The global asymptotic property can be used for testing a pre-specified parametric trend in the extreme value indices. In particular, it can be applied to test whether the extreme value index remains at a constant level across all observations.

December 11, 2017:**Jan Beirlant (KU Leuven)**

When: Monday December 11th, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderzaal (LB01.010)

*Bias reduced estimation of the extreme value index*

A lot of attention has been paid to bias reduced estimation of the extreme value index in case of heavy-tailed distributions. In this talk we present some proposals for all max-domains of attraction. A first method is based on ridge regression for generalized quantiles. Secondly we discuss the use of Bernstein polynomials for estimating the bias in the Peaks over Threshold method.

**December 4, 2017:** **Pierre Monmarché (Université Pierre et Marie Curie)**

When: Monday December 4th, 16:00

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

*Sampling with kinetic processes*

Given a target probability measure mu, a MCMC algorithm relies on an ergodic Markov process with invariant measure mu. There exist many such processes and, in order to chose the best one, one should understand at which speed they converge to their equilibrium. We will motivate the use of kinetic processes, and present some results on two different dynamics: the kinetic Langevin process, which is a hypoelliptic diffusion, and velocity jump processes, which are piecewise deterministic processes.

**November 27:****Ludolf Meester (TU Delft)**When: Monday November 27th, 16:00

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

*Exponential convergence of adaptive importance sampling algorithms for Markov chains *

These algorithms orginate in the field of particle transport analysis, but the structure of the problems is quite general: a Markov chain is run and per transition a "reward" is earned; this continues until the process hits a "graveyard set." Quantity of interest is the expected total reward. In the original problem the reward is energy dissipated, but other problems also fit in: rare event simulations in various settings (reward is 1 for the transition into the graveyard and 0 otherwise); finding the largest eigenvalue of a nonnegative matrix.

A recent paper answers the following question: for which of this kind of Markov chain problems can a so-called filtered estimator be found in combination with a Markov importance measure under which this estimator has variance zero. Adaptive importance sampling algorithms aim to approach this zero variance measure on-the-fly and already two special cases were known for which this works: the resulting sequence of estimates converges at an exponential rate. For a while I thought that finding a general convergence proof would be impossible, but in recent months I have made some progress with this. In the talk I will describe the proof including the part where the conditions are not weak enough to my liking---maybe you have an idea.... **November 20, 2017: **Michael Vogt** (University of Bonn)**

When: Monday November 20th, 16:00

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

*Multiscale Clustering of Nonparametric Regression Curves *

We study a longitudinal data model with nonparametric regression functions that may vary across the observed subjects. In a wide range of applications, it is natural to assume that not every subject has a completely different regression function. We may rather suppose that the observed subjects can be grouped into a small number of classes whose members share the same regression curve. We develop a bandwidth-free clustering method to estimate the unknown group structure from the data. More specifically, we construct estimators of the unknown classes and their unknown number which are free of classical bandwidth or smoothing parameters. In the talk, we analyze the statistical properties of the proposed estimation method and illustrate it by an application to temperature anomaly data.

**November 13, 2017:**** **** Stochastics Meeting Lunteren**

**November 6, 2017:** Nan van Geloven (Leiden University Medical Center)

When: Monday November 6th, 16:00

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

*Univariate frailty models for the evaluation of treatments*

Doctors often have to choose between starting treatment immediately or first introducing a wait-and-see period during which a patient might recover without the treatment. In this presentation I show that the effect of such a treatment delay period on the time to recovery depends on the heterogeneity between patients’ recovery chances. I study this effect using univariate frailty models, assuming different distributions for the frailty. In a frailty model with constant (i.e, exponential) baseline hazard and a proportional treatment effect that is common over patients, a treatment delay period hardly compromises cumulative recovery rates if the population is heterogeneous. In a homogeneous population however, cumulative recovery rates are directly compromised by treatment delay.

Estimating the effect of treatment delay from data can be done in several ways. We show that the conventional Cox proportional hazard model overestimates the effect of treatment delay. Including a frailty term in the model could improve the estimation, but frailties are generally hard to estimate in univariate survival data. I present alternative approaches accommodating the effect of heterogeneity on treatment delay using treatment by time interaction terms. Estimation results are presented both through simulations and in two motivating applications evaluating the effect of delaying fertility treatments on time-to-pregnancy in couples with unexplained subfertility.

October 30, 2017:** ****Eric-Jan Wagenmakers**** ****(University of Amsterdam)**

When: Monday October 30th, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, Lecture hall Chip.

*The Why and How of Testing a Point-Null Hypothesis Within a **Bayesian Framework*

In the first part of this presentation I will describe the

history of the Bayesian point-null hypothesis test as developed by

Harold Jeffreys. The conclusion --which appears to have been largely

forgotten-- is that in order to have any confidence in the existence

of an invariance or a general law, one needs to assign it a separate

prior probability. I will contrast Jeffreys's methodology with a

beguiling alternative, which is to assess the extent to which the

posterior distribution overlaps with the point of interest.

**October 23, 2017:** **Aernout van Enter**** ****(University of Groningen)**

When: Monday October 23th, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, Lecture hall G.

*One-sided versus two-sided points of view*

Finite-state, discrete-time Markov chains coincide with Markov fields on $\mathbb Z$, (which are nearest-neighbour Gibbs measures in one dimension). That is, the one-sided Markov property and the two-sided Markov property are equivalent.

We discuss to what extent this remains true if we try to weaken the Markov property to the almost Markov property, which is a form of continuity of conditional probabilities. The generalization of the one-sided Markov measures leads to the so-called "g-measures" (aka "chains with complete connection", "uniform martingales",..), whereas the two-sided generalization leads to the class of Gibbs or DLR measures, as studied in statistical mechanics. It was known before that there exist g-measures which are not Gibbs measures. It is shown here that neither class includes the other.

We consider this issue in particular on the example of long-range, Dyson model, Gibbs measures.

(Work with R.Bissacot, E.Endo and A. Le Ny)**October 18, 2017: **Erik Broman** (Chalmers University of Technology and University of Gothenburg)**

**When: Wednesday October 18th, 13:45**

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

Covering a subset of R^d by Poissonian random sets The problem of covering a set A by a collection of random sets dates back to Dvoretzky in 1954. Since then, a host of papers have been written on the subject. In this talk we shall review some of this history and discuss two directions in which progress have recently been made. In the first case we consider a statistically scale invariant collection of subsets of R^d, which are chosen at random according to a Poisson process of intensity lambda. The complement of the union of these sets is then a random fractal that we denote by C. Such random fractals have been studied in many contexts, but here we are interested in the critical value of lambda for which the set C is almost surely empty (so that R^d is completely covered). Such problems were earlier studied and solved in one dimension, while here we shall present recent progress which solves it in all dimensions. This part is based on joint work with J. Jonasson and J. Tykesson.

In the second direction we consider a dynamic version of coverings. For instance,

the set A could be a box of side lengths n, and then balls are raining from the

sky at unit rate. One then asks for the time at which A is covered. Together with

F. Mussini I have recently studied a variant in which the balls are replaced by

bi-infinite cylinders. This makes the problem fundamentally different as one no

longer have independence between well separated regions. Thus, new methods

and techniques must be used. Our main result is that we find the correct asymptotics for the cover time as the set A grows.

October 16, 2017:** ****Carlo Lancia**** ****(Leiden University Medical Center)**

When: Monday October 16rd, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, Lecture hall G.

*Modelling inbound air traffic with pre-scheduled random arrivals: analytical and applied results*

*Pre-scheduled random arrivals* (PSRA) are obtained by superimposing i.i.d. random delays to a deterministic stream of customers. This point process is very fit for modelling vehicular and logistics streams, where structured arrivals are inherently subject to random fluctuations. Yet, the use of PSRA for modelling air-traffic demand is scarce, and Poisson

processes are preferred because of mathematical tractability.

Using data from some important European airports, I will construct a PSRA process and show that it describes well the inbound demand. Further, I will show that this PSRA can capture air-space capapacityconstraints, which are observed as a negative autocorrelation between arrivals in two consecutive time windows.

Next, I will move to a stochastic operations research setting and study a single-server queue with deterministic service time. Such a model is motivated by the landing operations of a large hub, like London Heathrow. I will consider the special case of a PSRA with exponential delays, called exponentially delayed arrivals (EDA). In Kendall's notation the queue system is then EDA/D/1.

I will show how to model EDA/D/1 as a bivariate Markov chain in the quarter plane. This chain has a unique equilibrium distribution, which can be found by solving a bivariate functional equation for the generating function of the stationary state. The functional equation is hard to solve but admit an easy solution on a subspace of the complex bi-plane. Using that solution, I will derive asymptotic bounds for the equilibrium distribution of EDA/D/1 and propose an easy-yet-efficient approximation scheme.

October 9, 2017:**Paulo Serra**** ****(TU Eindhoven)**

When: Monday October 9th, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, Lecture hall G.

*Bayesian preventive maintenance*

Motivated by industrial practice, we model the condition of an asset using a stochastic process. We assume that as soon as the condition of the asset exceeds a predefi ned safety threshold, the asset is shut down and costly corrective reparations must ensue. The condition of the asset is regularly inspected (at pre-determined moments, with a fi xed inspection cost), and the goal is to decide based on the history of the inspections and taking into account all costs, if preventive maintenance (which is less costly) should be performed.

We consider the class of so called control limit (threshold-type) policies: maintenance is performed if a certain threshold (depending on the collected data, preventive maintenance- and corrective repair costs) is exceeded, at which point the asset is restored to a "good-as-new" condition. We work with a loss function that corresponds to the costs of each action (repair, maintenance, inspection). The model parameters are endowed with a prior, and the threshold is chosen so as to minimise the Bayesian expected loss.

The asymptotic distribution of the model parameters, of the duration of each maintenance cycle, and of the proposed threshold is also discussed.

I also present some numerical results, and address issues relating to the optimality of the approach.

This is joint work with Stella Kapodistria (Eindhoven University of Technology).**October 2, 2017:** **Lorenzo Federico**** ****(TU Eindhoven)**

When: Monday October 2nd, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, Lecture hall G.

*CRITICAL PERCOLATION ON THE HAMMING GRAPH*

Percolation on fInite graphs is known to exhibit a phase transition similar to the Erdos-Renyi Random Graph in presence of sufficiently weak geometry. We focus on the Hamming graph $H(d,n)$ (the cartesian product of d complete graphs on $n$ vertices each) when $d$ is fixed and $n \to \infty$. We identify the critical point $p^{(d)}_c$ at which such phase transition happens and we analyse the structure of the largest connected components at criticality. We prove that the scaling limit of component sizes is identical to the one for critical Erdos-Renyi components, while the number of

surplus edges is much higher. These results are obtained coupling percolation to the trace of branching random walks on the Hamming graph.

Based on joint work with Remco van der Hofstad, Frank den Hollander and Tim Hulshof.

September 25, 2017:**Alisa Kirichenko**** ****(University of Amsterdam)**

When: Monday September 25th, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, Lecture hall G.

*Function estimation on a large graph using Bayesian Laplacian regularization.*

We consider a Bayesian approach to estimating a smooth function in the context of regression or classification problems on large graphs. We present a mathematical framework that allows to study the performance of nonparametric function estimation methods on large graphs. We also present minimax convergence rates for these problems within the framework. We show how asymptotically optimal Bayesian regularization can be achieved under an asymptotic shape assumption on the underlying graph and a smoothness condition on the target function, both formulated in terms of the graph Laplacian. The priors we study are randomly scaled Gaussians with precision operators involving the Laplacian of the graph.**September 18, 2017:** **Conrado Freitas Paulo Da Costa**** ****(Leiden University)**

When: Monday September 18th, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, Lecture hall G.

*From particle systems to reaction-diffusion equations*

In this talk I will present how to use birth and death chains on a graph to derive solutions of a family of non-linear finite dimensional SDE's of Reaction-Diffusion type. In one dimension, this family corresponds to the fluctuations around a stable point of an ODE, and can be seen as arising either from taylor-made particle systems or from scaling limits of a canonical particle system. For multi-dimensional SDE's, the approach of taylor-making the particle systems is more general and allows for a broader family of SDE's.The derivation of these solutions, in the spirit of Stroock and Varadhan martingale methods, is based on using the equivalence between weak solutions of SDE's and solutions of Martingale problems.

Abstract

September 11, 2017:**William Yoo**** ****(Leiden University)**

When: Monday September 11th, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, Lecture hall G.

*Bayes Lepski’s method and credible bands through volume of tubular neighborhoods*

For a class of priors based on random series basis expansion, we develop a Bayesian Lepski’s method to estimate unknown regression function. In this approach, the series truncation point is determined based on a stopping rule that balances the posterior mean bias and the posterior standard deviation. Armed with this mechanism, we discuss an interesting method to construct Bayesian credible bands, where this statistical task is reformulated into a problem in geometry, and the band’s radius is calculated based on finding the volume of certain tubular neighborhoods embedded on a unit sphere. We discuss two special cases involving B-splines and wavelets, and will touch upon some interesting consequences such as the uncertainty principle and self-similarity.**July 4, 2017: Emilio Cirillo (****Rome 1****)**

When: Tuesday July 4th, 12:45

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

* Particle-based modelling of flows through obstacles*

The presence of obstacles modifies the way in which particles diffuse. In cells it is observed that the mean-square displacement of biomolecules scales as a power law with exponent smaller than one. This behavior, called anomalous diffusion, is due to the presence of macromolecules playing the role of obstacles. We discuss the effect of fixed macroscopic obstacles on the time needed by particles to cross a strip and we consider both a diffusive and a ballistic regime. We find that in some regimes this residence time is not monotonic with respect to the size and the location of the obstacles. We discuss our results for particles performing random walks on a two dimensional strip considering also the effect of an exclusion rule. Results obtained in collaboration with A. Ciallella (Rome), O. Krehel (Eindhoven), A. Muntean (Karlstadt), R. van Santen (Eindhoven), and A. Sengar (Eindhoven) will be discussed.

June 27, 2017: Christoph Hofer-Temmel** (NLDA)**

When: Tuesday June 27th, 12:45

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

Disagreement percolation for marked Gibbs point processes Disagreement percolation is a technique to control the differing boundary conditions in a Gibbs specification by a simpler percolation model. In the high temperature regime, the percolation model does not percolate and implies the uniqueness of the Gibbs measure. If the percolation has exponentially decaying connection probabilities, then exponential decay of correlations for the Gibbs measure follows, too. We extend this technique from the discrete case and bounded range interaction simple Gibbs point processes to finite range interaction marked Gibbs point process and general Boolean models. A core building block is a dependent thinning from a Poisson point process to a dominated Gibbs point process within a finite volume, where the thinning probability is related to the derivative of the free energy of the Gibbs point process.

June 20, 2017: Matthias Gorny** (Université Paris-Sud)**

When: Tuesday June 20th, 12:45

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

*A Curie-Weiss model of self-organized criticality*

In their famous 1987 article, Per Bak, Chao Tang and Kurt Wiesenfeld showed that certain complex systems, composed of a large number of dynamically interacting elements, are naturally attracted by critical points, without any external intervention. This phenomenon, called self-organized criticality (SOC), can be observed empirically or simulated on a computer in various models. However the mathematical analysis of these models turns out to be extremely difficult. Even models whose definition seems simple, such as the models describing the dynamics of a sandpile, are not well understood mathematically. In my presentation, I will introduce a model of SOC which is built by modifying the generalized Ising Curie-Weiss model. I will present a fluctuation theorem which proves that this model indeed exhibits SOC: the sum $S_{n}$ of the random variables behaves as in the typical critical generalized Ising Curie-Weiss model, i.e., the fluctuations are of order $n^{3/4}$ and the limiting law is $C \exp(-\lambda x^{4})\,dx$ where $C$ and $\lambda$ are suitable positive constants. Finally I will introduce associated dynamic models of SOC.

June 13, 2017: No Seminar

June 9, 2017: Rob Ross** (TU Delft)**

When: Friday June 9th, 12:45

Where: TBA

*Reliability in High Voltage networks – Effective asset management of a strategic infrastructure*

The transmission electrical network is the backbone of the electrical grid. It connects large scale power generation to the regional distribution electrical networks and to large customers. Of growing importance are also the interconnections between neighbouring countries and between countries through submarine cable systems.

TenneT is the transmission utility in the Netherlands and a large part of Germany. With a security of supply of 99.9999% and 41 million end-users the challenge is how to preform effective asset management, i.e. how to warrant and make optimal use of the many thousands of objects that together shape the grid. On the one hand billions of euros are invested in the development of grids that embrace sustainable energy. On the other hand a considerable part of the grid is over 30 years of age and still functioning well, but the challenge is to timely detect the need for inspection, refurbishment and replacement. Too early replacement is a waste of public money, but too late replacement may lead to large damage. Asset management aims at doing the right thing at the right time against minimum costs. The underlying evaluation and decision-making are based on expertise and optimized with statistics.

This colloquium will focus on the various issues that asset strategists of electrical power grids face and the methods that are in place or under development in pursue of the maintaining a high reliability and availability of the electric power supply.**June 6, 2017: **Yining Chen** (LSE)**

When: Tuesday June 6th, 12:45

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

*Detecting multiple local extrema via wild binary segmentation*

We consider the univariate nonparametric regression problem, where given *n* observations, the goal is to detect the number and locations of multiple local maxima and minima in the curve. We propose a new approach that combines the ideas of wild binary segmentation (Fryzlewicz, 2014) and mode estimation using isotone regression. We show that our procedure consistently estimates the number of local extrema, and is minimax optimal (up to a logarithmic factor) in estimating the locations of these points. Moreover, we show that the computational complexity of our method is near-optimal (i.e., up to a logarithmic factor, of order *n*). Finally, we discuss how our approach could be extended to detect other interesting features, such as inflection points.**May 30, 2017: **Stéphanie van der Pas** (LUMC and Leiden University)**

When: Tuesday May 30th, 12:45

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

*Bayesian community detection*

In the stochastic block model, nodes in a graph are partitioned into classes ('communities') and it is assumed that the probability of the presence of an edge between two nodes solely depends on their class labels. We are interested in recovering the class labels, and employ the Bayesian posterior mode for this purpose. We present results on weak consistency (where the fraction of misclassified nodes converges to zero) and strong consistency (where the number of misclassified nodes converges to zero) of the posterior mode, in the 'dense' regime where the probability of an edge occurring between two nodes remains bounded away from zero, and in the 'sparse' regime where this probability does go to zero as the number of nodes increases.

May 23, 2017: Jere Koskela (TU Berlin)

When: Tuesday May 23rd, 12:45

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

*Consistency results for Bayesian nonparametric inference from processes with jumps*

Consistency can informally be thought of as the ability to infer the true data generating model from a sufficiently large amount of data, and has been regarded as a minimal condition for good inference procedures for several decades. It is also notoriously difficult to verify in the Bayesian nonparametric setting. In recent years, positive results have been established for discretely observed, diffusions under restrictive but verifiable conditions on the prior. I will present an introduction to Bayesian nonparametric inference and posterior consistency, and show how these results for diffusions can be generalised to jump-diffusions under an additional identifiability assumption. Similar arguments will also be shown to yield posterior consistency for a separate class of processes called Lambda-Fleming-Viot processes: inhomogeneous, compactly supported compound Poisson processes arising as models of allele frequencies in population genetics. Identifiability can also be verified rather than assumed for Lambda-Fleming-Viot processes, which results in a tractable set of conditions for posterior consistency that is satisfied e.g. by the popular Dirichlet process mixture model prior.

May 16, 2017: Yong Wang (The University of Auckland)

When: Tuesday May 16th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Room D@ta.*Mixture-based Nonparametric Density Estimation*

In this talk, I will describe a general framework for nonparametric density estimation that uses nonparametric or semiparametric mixture distributions. Similar to kernel-based estimation, the proposed approach uses bandwidth to control the density smoothness, but each density estimate for a fixed bandwidth is determined by likelihood maximization, with bandwidth selection carried out as model selection. This leads to much simpler models than the kernel ones, yet with higher accuracy.

Results of simulation studies and real-world data in both the univariate and the multivariate situation will be given, all suggesting that these mixture-based estimators outperform the kernel-based ones.

May 9, 2017: Hakan Güldas (Leiden University)

When: Tuesday May 9th, 12:45

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

*Random walks on dynamic configuration models*

In this talk, first I will introduce dynamic configuration model which is a dynamic random graph model in discrete time. Then, I will go into details of our results about mixing times of simple random walks on dynamic configuration model. The key property of the dynamic configuration model is that the degrees of the vertices do not change over time. Thanks to this property, the notion of stationary distribution for the random walk on the graph makes sense and mixing occurs although the random walk itself is not Markovian. The results I will give identify the behaviour of mixing times in terms of the proportion of edges that changes at every step of graph dynamics when the number of vertices is large.

Result are based on a joint work with Luca Avena, Remco van der Hofstad and Frank den Hollander.

May 2, 2017: Moritz Schauer (Leiden University)

When: Tuesday May 2nd, 12:45

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

*Stochastic monotonicity of Markov processes - A generator approach*

We consider stochastic orders on random variables which can be defined in terms of expectations of test functions. Notable examples are the standard stochastic order induced by the increasing functions or the convex order induced by convex functions, capturing the size and spread of random variables. In general, we consider cones of test functions characterized by Φ f ≥ 0 for some linear operator Φ.

Of particular interest are stochastically monotone Markov processes which preserve stochastic order properties in time. The semigroup {S(t): t ≥ 0} of a monotone Markov processes defined by S(t) f(x) = E [ f(X(t)) | X(0) = x] maps these cones into themselves.

We introduce a new functional analytic technique based on the generator A of the semi-group of a Markov process X(t) and its resolvent to study the property of stochastic monotonicity. We show that the existence of an operator B with positive resolvent such that Φ A - B Φ is a positive operator for a large enough class of functions implies stochastic monotonicity. This establishes a technique for proving stochastic monotonicity and preservation of order for Markov processes that can be applied in a wide range of settings including various orders for diffusion processes with or without boundary conditions and orders for discrete interacting particle systems.

Joint work with Richard C. Kraaij (Ruhr-University of Bochum)

April 25, 2017: Maaneli Derakhshani (Utrecht University)

When: Tuesday April 25th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Room D@ta.*Hints Toward A Stochastic Hidden-Variables Foundation For Quantum Mechanics*

It is well-known that standard quantum theory is plagued by conceptual and technical problems, most notably the quantum measurement problem. The quantum measurement problem indicates that standard quantum theory (whether in non-relativistic or relativistic or quantum-gravitational form) cannot be a fundamental theory of the physical world, and must be replaced by a measurement-problem-free theory of quantum phenomena. Among the viable alternatives to standard quantum theory are nonlocal contextual 'hidden-variable' theories. In this talk, it will be shown that there are tantalizing meta-theoretical hints that the Schroedinger equation and Born-rule interpretation of the wavefunction in standard quantum mechanics have deeper foundations in some nonlocal contextual theory of stochastic hidden-variables. This will be shown by drawing surprising and little-known correspondences between the mathematical structures of Schroedinger's equation and quantum expectation values of physical observables, one the one hand, and the mathematical structures of (1) classical statistical mechanics in the Hamilton-Jacobi representation, (2) the Einstein-Smoluchowski theory of classical Brownian motion, and (3) de Broglie's famous model of a clock particle guided by phase waves, on the other. Finally, it will be suggested that Nelson's stochastic mechanics, and a recent generalization of it proposed by us, constitutes the anticipated theory of stochastic hidden-variables.

April 18, 2017: Easter Break

April 11, 2017: Dutch Math Congress

April 4, 2017: Ronald Meester (VU Amsterdam)

When: Tuesday April 4th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Room D@ta.*Why the law of total probability is sometimes not desirable, and how the the theory of belief functions helps to take care of this*

We discuss some examples of betting situations in which the law of total probability fails. Since this law follows from the axioms of Kolmogorov and the definition of conditional probability, it follows that a more general theory is necessary. I will formulate more flexible axioms which turn out to characterize belief functions, a well known generalisation of probability measures. Within this theory, conditional belief functions can be defined in various ways, corresponding, roughly, to conditioning on either a necessary truth or a contingent truth. As such, the classical theory is extended and refined at the same time. I will argue that when probability is interpreted epistemically, one should always use belief functions rather than Kolmogorov probability.

This is joint work with Timber Kerkvliet.

March 28, 2017: Gourab Ray (Cambridge University)

When: Tuesday March 28th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Room D@ta.*Universality of fluctuation in the dimer model*

The dimer model is a very popular model in statistical physics because of its exact solvability properties. I will try to convince you that the fluctuation in the dimer model is universal in the sense that it is more or less independent of the underlying graph and also the topology the graph is embedded in and is given by a form of Gaussian free field.

Joint work with Nathanael Berestycki and Benoit Laslier.

March 21, 2017: Andrew Duncan (University of Sussex)

When: Tuesday March 21st, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Room D@ta.*Measuring Sample Quality with Diffusions*

To improve the efficiency of Monte Carlo estimators, practitioners are turning to biased Markov chain Monte Carlo procedures that trade off asymptotic exactness for computational speed. While a reduction in variance due to more rapid sampling can outweigh the bias introduced, the inexactness creates new challenges for parameter selection. In particular, standard measures of sample quality, such as effective sample size, do not account for asymptotic bias. To address these challenges, we introduce a new computable quality measure based on Stein's method that quantifies the maximum discrepancy between sample and target expectations over a large class of test functions. We demonstrate this tool by comparing exact, biased, and deterministic sample sequences and illustrate applications to hyperparameter selection, convergence rate assessment, and quantifying bias-variance tradeoffs in posterior inference.

March 14, 2017: Kolyan Ray (Leiden University)

When: Tuesday March 14th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Room D@ta.*Asymptotic equivalence between density estimation and Gaussian white noise revisited*

Asymptotic equivalence between two statistical models means that they have the same asymptotic properties with respect to all decision problems with bounded loss. A key result by Nussbaum states that nonparametric density estimation is asymptotically equivalent to a suitable Gaussian shift model, provided that the densities are smooth enough and uniformly bounded away from zero.

We study the case when the latter assumption does not hold and the density is possibly small. We further derive the optimal Le Cam distance between these models, which quantifies how close they are. As an application, we also consider Poisson intensity estimation with low count data.

This is joint work with Johannes Schmidt-Hieber.**March 7, 2017: **Frank van der Meulen** (TU Delft)**

When: Tuesday March 7th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Room D@ta.*Bayesian estimation for hypo-elliptic diffusions*

Suppose X is a discretely observed diffusion process and we wish to sample from the posterior distribution of parameters appearing in either the drift coefficient or the diffusion coefficient. As the likelihood is intractable a common approach is to derive an MCMC algorithm where the missing diffusion paths in between the observations are augmented to the state space. This requires efficient sampling of diffusion bridges. In recent years some results have appeared in the "uniformly elliptic" case, which is characterised by nondegeneracy of the covariance matrix of the noise. The "hypo-elliptic" case refers to the situation where the covariance matrix of the noise is degenerate and where observations are only made of variables that are not directly forced by white noise. As far as I am aware, not much is known how to sample bridges in this case.

In this talk I will share some recent ideas on extending earlier results with Harry van Zanten (UvA) and Moritz Schauer (Leiden), derived under the assumption of uniformly ellipticity, to this setting.

Joint work with Harry van Zanten (Uva), Moritz Schauer (Leiden) and Omiros Papaspilopoulos (Universitat Pompeu Fabra)

February 28, 2017: No Seminar

February 21, 2017: Pasquale Cirillo (TU Delft) - Cancelled

When: Tuesday February 21st, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Room D@ta.*Interacting Urn Systems and a Financial Application*

February 9 (Extra Thursday!!!), 2017: Gareth Roberts (University of Warwick)

February 9 (Extra Thursday!!!), 2017: Gareth Roberts (University of Warwick)

When: Thursday February 9th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Room D@ta.*Towards not being afraid of the big bad data set*

**February 7, 2017:**Nick Wormald

**(Monash University)**

When: Tuesday February 7th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Room D@ta.*A natural infection model*

Suppose that individuals are randomly placed points in space according to a Poisson process, and have two states, infected or healthy. Any infected individual passes the infection to any other at distance d according to a Poisson process, whose rate is a function f(d) of d that decreases with d. Any infected individual heals at rate 1. Initially, one individual is infected. An epidemic is said to occur when the infection lasts forever. We investigate conditions on f under which the probability of an epidemic is nonzero. This is joint work with Josep Diaz and Xavier Perez Gimenez.

January 31, 2017: Guido Bacciagaluppi (Utrecht University)

When: Tuesday January 31st, 12:45

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

*Quantum probability and contextuality*

In this talk, I shall introduce the generalised theory of probability that arises naturally in quantum mechanics, emphasising its understanding in terms of 'contextuality', and discussing whether and in what sense modelling such phenomena indeed requires going beyond Kolmogorovian probability. **January 24, 2017: Cancelled**

January 17, 2017: Arnaud Le Ny (Université Paris-Est Marne-la-Vallée)

January 17, 2017: Arnaud Le Ny (Université Paris-Est Marne-la-Vallée)

When: Tuesday January 17th, 12:45

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

*(Very) Persistent Random Walks*

In this talk, we shall describe recent works [1] and (maybe) [2] in which we investigate asymptotic properties of one dimensional very Persistent Random Walks (PRW). PRW are correlated walks whose increments are, on the contrary to simple random walks, not i.i.d. but rather dependent in a Markov (finte order) way. They have been widely studied since the mid of last century under different vocables as Goldstein-Kac, correlated or again persistent walks. Due to the extra memory induced by the increments, these random walks are not Marokov proecesses anypore. By very persistent we mean here a model in which even the increments are not Markov, but rather Variable Length Markov Chains whose conditional laws directly depend of the time already spent in the given direction. Equivalently, we are given two independent sequences of i.i.d. persistence times, in a general possibly non-summable framework that extends previous work of Malduin et al. on Directionnally Recurrent Random Walks [3]. Using an extension of Erickson's criteria [4], we provide a general classification of recurrence vs. Transience in term of drift or tail properties depending on the intial laws, and also identify different regime in the scaling limits for persistent times lying in the bassin of attraction of stable laws.

This is a joint work with P. Cénac (Dijon), B. de Loynes (Rennes) and Y. Offret (Dijon).

[1] P. Cénac, A. Le Ny, B. de Loynes, Y. Offret. Persistent Random Walks I : Recurrence vs. Transience. J. of Theo. Probab. 29, 2016/17.

[2] P. Cénac, A. Le Ny, B. de Loynes, Y. Offret. Persistent Random Walks II : Functional Limit Theorems. Preprint arxiv.org/abs/1612.00238.

[3] R. Malduin, M. Monticino, H. von Weisäcker. Directionally Reinforced Random Walks. Adv. In Math. 117, no 2 : 239—252, 1996.

### Organizers:

Dr. Gioia Carinci (Probability)

Dr. Jakob Söhl (Statistics)