# Program STAR-workshop

10.00-10.05 | Opening and welcome (Rob van der Mei) |

10.05-10.20 | Organizational matters STAR (Onno Boxma) |

10.20-11.10 | Keynote lecture by Mark Girolami (University College London) |

11.10-11.30 | Coffee break |

11.30-12.15 | Invited lecture by Johan van Leeuwaarden (TUE and EURANDOM) |

12.15-12.45 | Short presentations by Wioletta Ruszel (TUE), Moritz Schauer (TUD and TUE) and Beata Ros (VU) |

12.45-13.30 | Lunch |

13.30-14.15 | Invited lecture by Wouter Kager (VU University Amsterdam) |

14.30-15.00 | Short presentations by Jan-Pieter Dorsman (TUE and CWI) and Siamak Taati (RUG) |

15.00-15.15 | Coffee break |

15.15-16.00 | Invited lecture by Martijn Pistorius (University of Amsterdam) |

16.00-16.05 | Closing (Rob van der Mei) |

16.05-17.00 | Borrel |

# Titles and abstracts

**Mark Girolami (University College London)**

**Keynote talk:** Diffusions and Geodesic Flows on Manifolds: The Differential Geometry of Markov chain Monte Carlo

**Abstract:** Markov chain Monte Carlo (MCMC) provides the dominant methodology for inference over statistical models with non-conjugate priors. Despite a wealth of theoretical characterisation of mixing times, geometric ergodicity, and asymptotic step-sizes, the design and implementation of MCMC methods remains something of an artisan art-form. An attempt to address this issue in a systematic manner leads one to consider the geometry of probability distributions, as has been the case previously in the study of e.g. higher-order efficiency in statistical estimators. By considering the natural Riemannian geometry of probability distributions MCMC proposal mechanisms based on Langevin diffusions that are characterised by the metric tensor and associated manifold connections are proposed and studied. Furthermore, optimal proposals that follow the geodesic paths related to the metric are defined via the Hamilton-Jacobi approach and these are empirically evaluated on some challenging modern-day inference tasks.

This talk is based on work that was presented as a Discussion Paper to the Royal Statistical Society and a dedicated website with Matlab codes is available at www.ucl.ac.uk/statistics/research/rmhmc.

**Johan van Leeuwaarden (TU Eindhoven and EURANDOM)**

**Invited talk:** Large systems with admission control

**Abstract:** We consider many-server systems with admission control, and obtain heavy traffic limit theorems. Rejected jobs are either lost or allowed to attempt again later. These repeated attempts give rise to interesting system behavior, also in the limiting regime.

**Wioletta Ruszel (TU Eindhoven) **

**Talk:** Sandpile models on random graphs

**Abstract:** I want to review some recent developments in studying sandpile-type models on random trees and the complete graph.

**Moritz Schauer (TU Delft and TU Eindhoven)**

**Talk:** Nonparametric Bayesian inference for scalar diffusions using MCMC

**Abstract:** An MCMC algorithm for Bayesian inference on the drift function of a discretely observed scalar diffusion is presented. The drift function will be equipped with a nonparametric sieve prior. Each of the nested models corresponds to a series approximation of the drift with respect to a hierarchical Schauder basis of growing resolution. This prior isknown to have good asymptotic properties in the continuous time case. The implementation applies Gaussian conjugacy and uses sparse matrix techniques, which take advantage of the nested and compact supports of the Schauder functions.

**Beata Ros (VU University Amsterdam)**

**Talk:** Existence and uniqueness of maximum likelihood estimators for covariance models with Kronecker product structure

**Abstract:** In many studies data is measured in multiple domains, like space and time. We focus on the situation where data is measured in two domains, which is the case for EEG. For the random matrix X we assume that the covariance between two elements is a product of spacial and temporal components. This implies that the covariance matrix of a vector built from columns of X is a Kronecker product of two matrices. We discuss existence and uniqueness of the maximum likelihood estimator for these matrices.

**Wouter Kager (VU University Amsterdam)**

**Invited talk:** Combinatorics of even subgraphs

**Abstract:** For a given graph G, consider the following question: how many subgraphs are there with exactly r edges and only vertices of even degree? This kind of information can be encoded in a generating function. I will discuss a remarkable identity between this generating function and the sum of signed weights of all possible loops on the graph G, which arises out of the so-called combinatorial method for the Ising model.

**Jan-Pieter Dorsman (TU Eindhoven and CWI) **

**Talk:** Layered queueing networks: marginal queue length approximations and light traffic behaviour

**Abstract:** We study a two-layered queueing network where the servers of the first-layer queues act as customers for second-layer servers, introducing interaction between the layers. This network finds its applications in for example production environments, where a machine processing products breaks down and faces competition for repair facilities with other machines. In this talk, we briefly discuss marginal queue length approximations for the first-layer queues in this network, as well as the light-traffic behaviour of the joint queue length distribution.

**Talk:** Random-cluster representation of some variants of the Potts model

**Abstract:** I will discuss a random-cluster representation of two closely related variants of the ferromagnetic Potts model. The first allows neutral (‘invisible’) colours along with the ordinary ferromagnetic colours, and was introduced by Tamura, Tanaka and Kawashima (2010) to demonstrate that a first-order transition may occur in two dimensions, even when the transition of the ordinary Potts model is of second order. The other model, introduced by Berker, Ostlund and Putnam (1978), allows vacancies (uncoloured sites) controlled by a chemical potential, and was devised to study phase transitions in the absorption of krypton atoms onto a graphite surface. The random-cluster representation provides a clear-cut distinction between the ordered and disordered regions, and allows us to prove the occurrence of a first-order transition in the regime that the number of neutral colours is large, or the chemical potential is small. The proof, based on the Pirogov-Sinai theory, is an adaptation of a similar proof, by Laanait et al (1991), for the ordinary Potts model with a large number of colours. This is a joint work with Aernout van Enter and Giulio Iacobelli.

**Martijn Pistorius (University of Amsterdam)**

**Invited talk:** Optimal selling of a defaultable stock in a spectrally negative Levy model

**Abstract: ** The relative drawdown process is the ratio of the running maximum and the current value of a stochastic process. The relative drawdown process turns up in several areas of mathematical finance. In the context of portfolio risk management, for instance, the maximum relative drawdown has been proposed as an investment performance criterion. Also, some of the popular trading strategies are based on the relative drawdown.
In this talk we consider the problem to identity the optimal time to sell a stock in the sense of minimizing the relative drawdown. We assume that the price of the stock is given by an exponential Lévy process, which is a model that captures the features of fat tails and asymmetry, which are commonly observed in financial returns data. In this study we restrict ourselves to spectrally negative Lévy processes, which have no positive jumps. We assume furthermore that the stock is subject to a possibility of default. This problem is phrased as an optimal stopping problem which we solve explicitly.
This talk is based on joint work with A. Mijatovic.