Tuesday, January 30, 3.15 pm, 2018. Seminar in Statistics.

Level set Cox processes
Anders Hildeman, Mathematical Sciences, Chalmers University of Technology and University of Gothenburg
Abstract: Our work focuses on modelling point process data that is observed on a spatial domain consisting of several spatial regions with fundamentally different behaviour, and where the classification of the spatial domain in to these regions is unknown. The aim of the analyst might be either to classify the regions, perform Kriging predictions or derive some field parameter properties from one or several of the point pattern classes.
To handle data of this type, we propose an extension to the popular log-Gaussian Cox process (LGCP) model. The LGCP model uses a latent Gaussian random field (GRF) to, a priori, characterize the Poisson intensity. Our extension is based on replacing the latent GRF by a latent spatial mixture model of GRFs. The mixture model is specified using a, categorically valued, random field which represent the classification of the spatial domain. This allows for parametrizing the model through stationary covariance functions and mean value functions specified using covariates. A MCMC method based on the preconditioned Crank-Nicholson MALA algorithm is proposed for Bayesian inference.
Finally, the model is demonstrated on data from the popular Barro Colorado rain forest data set. It is shown that the proposed model is able to capture behavior for which inference based on the LGCP is biased.
Location: Alan Turing.

Tuesday, February 13, 3.15 pm, 2018. Seminar in Mathematical Statistics.

Local law of addition of random matrices on optimal scale
Kevin Schnelli, KTH
Abstract: Describing the eigenvalue distribution of the sum of two general Hermitian matrices is basic question going back to Weyl. If the matrices have high dimensionality and are in general position in the sense that one of them is conjugated by a random Haar unitary matrix, the eigenvalue distribution of the sum is given by the free additive convolution of the respective spectral distributions. This result was obtained by Voiculescu on the macroscopic scale. In this talk, I show that it holds on the microscopic scale all the way down to the eigenvalue spacing. This shows a remarkable rigidity phenomenon for the eigenvalues.
Location: Hopningspunkten.

Tuesday, March 13, 3.15 pm, 2018. Seminar in Mathematical Statistics.

On high dimensional data analysis under errors in variables
Silvelyn Zwanzig, Department of Mathematics, Uppsala University
Abstract: Errors in variables induce additional complications already in models with p< n. The total least squares estimator is theoretically the best estimator in this case. In literature methods are presented for high dimensional sparse models with errors in variables. In the talk I will study the behavior of total least squares estimator for non sparse models with n << p and propose a generalized version of it.
Location: Hopningspunkten.

Tuesday, March 20, 3.15 pm, 2018. Seminar in Mathematical Statistics.

Estimation and residual analysis in the GMANOVA-MANOVA model
Béatrice Byukusenge, Department of Mathematics, Linköping University
Abstract: In this talk we will consider the GMANOVA-MANOVA model, which is a special case of an extended growth curve model, with no assumption of the nested subspace condition. We derive two residuals, establish their properties and give interpretation. Finally, a numerical example on a data set from a study that was conducted to investigate two treatments for patients suffering from multiple sclerosis is performed to validate the theoretical results.
Location: Kompakta rummet.

Tuesday, April 24, 3.15 pm, 2018. Seminar in Statistics.

Data-driven confounder selection for estimating average causal effects
Jenny Häggström, Statistics, Umeå School of Business, Economics and Statistics, Umeå Universitet
Abstract: To unbiasedly estimate a causal effect, on an outcome of interest, unconfoundedness is often assumed. If there is sufficient knowledge on the underlying causal structure then existing confounder selection criteria can be used to select subsets of the observed pretreatment covariates sufficient for unconfoundedness, if such subsets exist. de Luna, Waernbaum and Richardson (Biometrika, 2011), embracing the Neyman-Rubin model, characterized subsets from the original reservoir of covariates that are minimal in the sense that the treatment ceases to be unconfounded given any proper subset of these minimal sets and proposed data-driven algorithms for the selection of minimal sets of covariates. Here, the selection of such target subsets is considered when the underlying causal structure is unknown. Persson, Häggström, Waernbaum and de Luna (CSDA, 2017) implemented the above algorithms using two model free dimension reduction techniques: marginal co-ordinate hypothesis tests and kernel-based smoothing. Häggström (Biometrics, 2017) proposed to model the unknown causal structure by a probabilistic graphical model, e.g. a Bayesian network, estimate this graph from observed data and select the target subsets given the estimated graph. The approaches were evaluated by simulation.
Location: Alan Turing.

Wednesday , May 2, 3.15 pm, 2018. Seminar in Mathematical Statistics.

Testing hypotheses about covariance structures under multi-level multivariate models using Rao score
Katarzyna Filipiak, Poznań University of Technology
Abstract: Modern experimental techniques allow to collect and store multi- level multivariate data in almost all fields such as agriculture, biology, biomedical, medical, environmental and engineering areas, where the observations are collected on more than one response variable at different locations, repeatedly over time, and at different "depths", etc. Before any statistical analysis it is vital to test the appropriate mean and variance-covariance structures on the multi-level multivariate observations.
In this talk the Rao's score test (RST) statistic for testing the hypotheses about variance-covariance structures, such as e.g. separable structures with one component structured or exchangeable structures, is presented. It is shown that the distribution of the RST statistic under the null hypothesis of any separability does not depend on the true values of the mean or the unstructured components of the separable structure. A significant advantage of the RST is that it can be performed for small samples, even smaller than the dimension of the data. Monte Carlo simulations are then used to study the behavior of the empirical type I error as well as the empirical null distribution of the RST statistic with respect to the sample size. It is shown that RST outperforms the commonly used likelihood ratio test in all considered areas.
References:
[1] Roy, A., K. Filipiak, and D. Klein (2018). Testing a block exchangeable covariance matrix. Statistics 52(2), 393-408.
[2] Filipiak, K., D. Klein, and A. Roy (2017). A comparison of likelihood ratio tests and Rao's score test for three separable covariance matrix structures. Biometrical Journal 59, 192-215.
[3] Filipiak, K., D. Klein, and A. Roy (2016). Score test for a separable covariance structure with the first component as compound symmetric correlation matrix. Journal of Multivariate Analysis 150, 105-124.
Location: Kompakta rummet.

Tuesday, May 22, 3.15 pm, 2018. Seminar in Statistics.

Large-scale MCMCsamplers for probabilistic topic models
Måns Magnusson, Department of Computer and Information Science, Linköping University
Abstract: Probabilistic topic models have proven to be an extremely versatile class of mixed-membership models for discovering the thematic structure of text collections. There are many possible applications, covering a broad range of areas of study: technology, natural science, social science and the humanities. New efficient parallel Markov Chain Monte Carlo inference algorithms is proposed for Bayesian inference in large topic models. The proposed methods scale well with the corpus size and can be used for other probabilistic topic models and other natural language processing applications. The proposed methods are fast, efficient, scalable, and will converge to the true posterior distribution.
Location: Alan Turing.

Tuesday, June 5, 3.15 pm, 2018. Seminar in Mathematical Statistics.

Asymptotic integration by parts formula and regularity of probability laws
Vlad Bally, Université Paris-Est Marne-la-Vallée, France
Abstract: download
Location: Hopningspunkten.

Thursday, June 7, 1.15 pm, 2018. Seminar in Statistics.

Strategies for Distributed Bayesian Computation
Alexander Terenin, Imperial College London
Abstract: In this talk, I will discuss two popular approaches for running Markov Chain Monte Carlo methods on parallel and distributed systems: methods based on exchangeability, and asynchronous methods. I will discuss the precise ways in which these are able to take advantage of parallelism, and how that interacts with the system's architecture from a performance and efficiency perspective. I will then discuss how these approaches affect convergence, showcasing recent theoretical analysis of asynchronous methods, and conclude with a discussion on how reliability of Monte Carlo output and performance considerations should be considered when selecting what type of method to deploy in a given setting.
Location: John von Neumann.

Tuesday, June 12, 3.15 pm, 2018. Seminar in Mathematical Statistics.

Stochastic Deformation of Classical Integrability
Jean-Claude Zambrini, Department of Mathematics, University of Lisbon, Portugal
Abstract: Is it possible to deform, along quantum-like trajectories, one of the deepest notions of ODE's theory, the one of integrable systems? We shall start from a classical example, then summarize the method of Stochastic Deformation. It will provide a way to deform Jacobi's strategy to reach this goal in the classical, deterministic, case. This talk is founded on a joint work with C. Léonard (Paris-Ouest Nanterre).
Location: Hopningspunkten.