The stochastics seminar @ UiS
The seminar series on stochastics is usually held in the lunchroom of IMF at UiS, KE E541.
Anyone interested in the broad range of topics covered by stochastics (statistics, probability theory and applications) are welcome!
To suggest a talk, or for any queries, please contact Stein Andreas Bethuelsen
Past talks
When: Thursday February 20th 2020 at 10:0011:00
Speaker: Aolie Hong (UiS)
Title: Stochastic History Matching and Production Optimization for Hydrocarbon Reservoir Management
Abstract: Reservoir management (RM) is a decisionoriented activity where decision makers use their current knowledge to search for production strategies that maximize the value of hydrocarbon production from a reservoir. Two central
components of RM are history matching (HM) and production optimization (PO). HM draws on information from data. The information is then used to support decisions on production strategies. The optimal production strategy is identified through PO. Decisions will not be good unless they account for relevant and material uncertainties in a given decision context. Uncertainty is a result of not having perfect (i.e., complete) information. Although the oil and gas industry has long been aware of the importance of uncertainty understanding and management, decisiondriven approaches that include consistent uncertainty quantifications are not commonly or comprehensively used. The intent of using decisiondriven approaches is to manage uncertainties for good decision making. This presentation will address some challenges of using decision analysis (DA) tools for managing geological and petrophysical uncertainties in RM.
When: Thursday February 6th 2020 at 10:0011:00
Speaker: Jörn Schulz (UiS/SUS)
Title: Data Beyond the Euclidean Space
Abstract: Complex data such as nonEuclidean or a mixture of Euclidean and nonEuclidean data has gained growing attention recently. However, only few methods are available to do sensitive statistical inferences on these types of data. In this talk, we assume that the nonEuclidean data lives on a smooth manifold and in particular we will focus on directional data, e.g. data that live on a hypersphere. Directional data occur for example in i.) shape representations including directions such as skeletal representations and ii.) dihedral angles of protein structures.
A crucial step in the analysis of those data is principal nested spheres (PNS), a method for decomposition and dimension reduction of directional data. In opposite to principal component analysis, PNS is a backward dimension reduction method. In each step, a submanifold of successively lower dimension, containing the largest total variance, is fitted to the data. A submanifold can be either a smallsphere or a great sphere. The choice of a small or a great sphere is a critical question in the PNS procedure. The fitting of a small sphere to the data might result in an overfitting, e.g. if the data is concentrated around a point. We will discuss a new testing procedure that outperforms alternative testing methods during a simulation study and the analysis of skeletal 3D models of hippocampi. The proposed method is based on a measure of multivariate kurtosis for directional data.
When: Tuesday 17th December 2019 at 13:0014:00
Speaker: Timo Schlüter (Mainz University)
Title: Random walks in dynamic random environments
Abstract: Consider a random walk on the ddimensional integer lattice, moving in a random environment. This environment is defined by a family of Bernoulli random variables for each spacetime coordinate, say w, and a contact process on w. Under certain general conditions on the transition probabilities, e.g. local dependence on the environment and finite range, the random walk satisfies a law of large numbers and an annealed central limit theorem. A useful tool for proving these limit theorems is the construction of regeneration times, which allows to split the random walk into i.d.d. increments.
When: Tuesday 5th November 2019 at 13:0014:00
Speaker: Leander Nikolaus Jehl (UiS)
Title: Reliable Probabilistic Gossip over LargeScale Random Topologies
Abstract: I will talk about the reliability of different probabilistic gossip algorithms over three wellknown largescale random topologies, namely Bernoulli (or ErdösRényi) graph, the random geometric graph, and a scalefree graph. Especially I will focus on fixedfanout and per edge probabilistic gossip and show how to model their reliability based on dependency in neighbors degree.
When: Tuesday 15th October 2019 at 13:0014:00
Speaker: Njål Foldnes (BI)
Title: On ordinal covariance models
Abstract: Ordinalcategorical data are frequently encountered in the social science, e.g., as survey responses to Likertscales. (I.e., Big Five personality tests).
Researchers often want to fit their covariance models (factor models, structural equation models, item response models) to such data.
Since Pearson (1901) a main approach to quantify the correlation between two ordinal variabies has been to assume that the data has been produced by discretizing an underlying bivariate normal distribution. The tetrachoric (dichotomous data) and polychoric (polytomous data) correlation is the correlation of this continuous underlying vector.
We will review this framework, and present results related to the nonidentifiability of the underlying vector. We give sharp bounds on the nonparametric tetrachoric correlation based on copula theory. We show that wellcited papers have employed incorrect simulation methodology for ordinal data generation. This has resulted in the widespread belief that polychoric correlations are quite robust against violations of the normality assumption. We demonstrate that this is not the case, using a new simulation method based on regular vines.
When: Tuesday 1st October 2019 at 13:0014:00
Speaker: Diana Conache (TU Munich)
Title: A model for dislocation lines in 3D solids at low temperature
Abstract: We propose a model for threedimensional solids on a mesoscopic scale with a statistical mechanical description of dislocation lines in thermal equilibrium. The model has a linearized rotational symmetry, which is broken by boundary conditions. We show that this symmetry is spontaneously broken in the thermodynamic limit at small positive temperatures. In particular, we will focus on the statistical mechanical properties of a random Burgers vector configuration. The talk is intended for a general audience. This is joint work with Roland Bauerschmidt, Markus Heydenreich, Franz Merkl and Silke Rolles and is based on https://link.springer.com/article/10.1007/s00023019008299.
When: Tuesday 17th September 2019 at 13:0014:00 in KE E541
Speaker: Berent Lunde (UiS)
Title: An information criterion for gradient boosted trees
Abstract: Gradient boosting has been highly successful in machinelearning competitions for structured/tabular data since the introduction of XGBoost in 2014. Gradient boosting may be seen as a way of doing functional gradient descent to the supervised learning problem. As a consequence, in gradient tree boosting, the functional form of the modelensemble constantly changes during training. To be able to choose the optimal functional complexity, the leading implementations offer a high number of regularization hyperparameters, available for manual tuning. This tuning typically require a combination of computationally costly cross validation on a grid of hyperparameters, coupled with some expert knowledge. To combat this, we propose an information criterion for gradient boosted trees, applicable to both the learning of the topology of trees, and as a stopping criterion for the boosting algorithm. This makes the algorithm adaptive to the dataset at hand; it is completely automatic and with minimal worries of overfitting. Moreover, as the algorithm only has to run once, the computational cost is drastically reduced.
When: Wednesday 4th September 2019 at 13:0014:00
Speaker: Stein Andreas Bethuelsen (UiS)
Title: Loss of memory for the contact process
Abstract: The contact process, or the SIS (SusceptibleInfectedSusceptible) model, is a stochastic process that serves as a toy model for the spreading of an infection in a population. In this model, the social network structure of the population is modelled by a graph. Moreover, each individual of the population can either be healthy or infected. An infected individual recovers from the infection at a unit rate, irrespectively of the state of the other individuals. A healthy individual always remains susceptible to the disease and becomes infected at a rate proportional to the number of infected individuals in its nearest surroundings.
In the first part of the talk, I will review several basic properties of the contact process. Then I will focus on a recent result stating the following: the contact process observed within a partial (and finite) subspace of the population is phimixing, that is, satisfies a strong temporal \emph{loss of memory} property. This mixing property holds under minimal assumptions on the social structure of the population as soon as the rate at which the infection may spread is large enough.
When: Tuesday 20th August 2019 at 14:0015:00
Speaker: Stian Lydersen (NTNU)
Title: Contingency tables: How to choose appropriate methods for analysis
Abstract: Literally hundreds of methods for hypothesis tests and confidence intervals for contingency tables are described in the literature. This is the case even for the seemingly simple 2 × 2 table. Wald intervals, chi squared tests, and the Fisher exact test are examples of widely used methods. Unfortunately, these methods are also commonly used in situations when they perform poorly, and better alternatives exist.
A short description will be given of Wald inference, likelihood ratio inference, and score inference, as well as asymptotic, exact conditional, exact midP, and exact unconditional methods. I will describe the actual significance level and power for a test, and coverage probability, expected interval width, and symmetry for a confidence interval, which will be used as evaluation criteria.
The talk will focus on tests and confidence intervals for the binomial probability, the 2x2 table for independent counts, and the paired 2x2 table. Commonly used methods, and other methods which perform well, will be described and evaluated, and illustrated using data from studies in medicine, health and the social sciences.
Reference: Fagerland MW, Lydersen S, Laake P (2017). Statistical Analysis of Contingency Tables. Chapman and Hall/CRC.
When: Tuesday 23rd July 2019 at 13:0014:00
Speaker: Florian Völlering (Leipzig University)
Title: Inducing geometry on graphs via random walks
Abstract: On a graph we can consider a random walk, which moves in a stochastic manner by
choosing edges to traverse at random. If the graph is equipped with a metric, say the graph distance, then the random walk transition probabilities can be used to define a notion of curvature on the graph, Jan Ollivier's coarse Ricci curvature via transport costs. For practical applications one wants this curvature to be uniformly positive, a condition which is often not satisfied. I will reverse the question, and ask if it is possible to find a metric on the graph for which one has uniformly positive curvature. The perhaps surprising answer that one can find a (pseudo)metric for a given finite graph which has not only uniformly positive, but constant curvature. This distance is in general unique (up to scalar multiplication), and is hence an intrinsic distance of the graph. Preliminary work indicates that this can for example be used for community detection in networks.
When: Friday 24th May 2019 at 09:4511:30
Speaker: Takahiro Hasebe (Hokaido University)
Title: Markov processes, Loewner chains and noncommutative stochastic processes
Abstract: This research establishes a bijection between a class of Markov processes, a class of decreasing Loewner chains on the upper half plane, and noncommutative stochastic processes with monotone independent increments. This is a joint work with Uwe Franz and Sebastian Schleissinger.
When: Tuesday 7th May 2019 at 13:0014:00
Speaker: Inma Castro (University of Extremadura)
Title: Some maintenance models for gamma degrading systems
Abstract: In the past, most mathematical models to describe the uncertainty in ageing of industrial systems were based on random variables. However, as many authors claimed, the temporal variability is not taken into account in these random variable models. In order to properly model the temporal variability, stochastic processes are used. Within these stochastic processes, the gamma process gives a proper model for monotone and random deterioration with time. In this talk, maintenance models for degrading systems with degradation modeled using gamma processes are showed. Firstly, perfect repairs are implemented in a system subject to multiple degradation processes. Secondly, we focus on the implementation of imperfect repairs for these degrading systems. In this case, two models of imperfect repair are explained. In the first model, the repair reduces the system degradation. In the second model, the repair reduces the system age. Comparisons between the two types of imperfect repair are showed.
