# The LiU Seminar Series in Statistics and Mathematical Statistics

### Tuesday, September 8, 3.15 pm, 2015. Seminar in Mathematical Statistics.

**Multivariate tests with censored data**

Måns Thulin, Department of Statistics, Uppsala University

Måns Thulin

*Abstract*: The one-way MANOVA problem of testing whether the mean vectors of several populations differ is common in many fields of research. In medicine, the rapid advance of high-throughput technologies has led to an increased interest in multivariate sets of biomarkers in e.g. blood samples. Such biomarkers can be used to understand different diseases and how they are affected by treatments and covariates. Biomarker data is often left-censored because some measurements fall below the laboratory's detection limit. I will discuss some problems caused by censoring; in particular how censoring affects multivariate two-sample and one-way MANOVA tests, in terms of size and power. Classical parametric tests are found to perform better than nonparametric alternatives, which means that the current recommendations for analysis of censored multivariate data have to be revised. The good performance of the classical parametric tests can at least partially be explained by some asymptotic results related to multivariate skewness and kurtosis. If time permits, I will also discuss MANOVA for multivariate survival data.

Location: Hopningspunkten.

### Tuesday, September 22, 3.15 pm, 2015. Seminar in Statistics.

**A Framework for MCMC by Data Subsampling**

Matias Quiroz, Statistics and Machine Learning, Linköping University and Sveriges Riksbank.

Matias Quiroz

*Abstract*: The complexity of Markov Chain Monte Carlo (MCMC) algorithms arises from the requirement of a likelihood evaluation for the full data set in each iteration. In this talk we will present a framework for speeding up MCMC algorithms by estimating the likelihood based on a small sample of the data. The likelihood estimate is obtained by the highly efficient difference estimator from the survey sampling literature. The estimate is subsequently used in a pseudo-marginal Metropolis-Hastings algorithm. However, since the estimate is slightly biased, the proposed algorithm is approximate. We prove that the approximate posterior targeted by our algorithm is close to the true posterior. We compare our algorithm to recent subsampling approaches in the machine learning literature and find promising results.

Location: Alan Turing

### Tuesday, October 6, 3.15 pm, 2015. Seminar in Mathematical Statistics.

**Outbreak detection in the presence of reporting delays**

Michael Höhle, Mathematical Statistics, Stockholm University.

Michael Höhle

*Abstract*: Outbreak detection algorithms are statistical process control based procedures for the on-line identification of change-points in count time series, e.g., representing weekly reported cases of a particular disease. Inherent reporting delays in the underlying surveillance system collecting these data are here an impediment towards timely detection of outbreaks. In this talk, I'll present a novel statistical algorithm, which considers the obtained time series as an incomplete two-way contingency table to be analyses by a negative binomial regression model. Bayesian inference based on the predictive posterior is performed both by asymptotic Bayes and integrated nested Laplace approximations. Simulation studies as well as the time series of reported Salmonella Newport cases in Germany in 2011 are then used to evaluate and illustrate the method.

Location: Hopningspunkten.

### Tuesday, October 20, 3.15 pm, 2015. Seminar in Statistics.

**Dietrich von Rosen, Department of Energy and Technology, Swedish University of Agricultural Sciences (SLU), and Linköping University**

Partial least squares and multivariate linear models

Partial least squares and multivariate linear models

*Abstract*: Many real life applications produce "near-collinear" data which among others causes prediction problems. It is therefore often natural to apply some kind of regularized regression methods when analysing them. For example, sub-set selection, ridge regression, lasso regression, principal components regression or partial least squares regression (PLS). Most of the methods are defined in an iterative algorithmic fashion. In each step a component (basis vector) is identified and thereafter residuals are formed which are taken as inputs in the next step. Cross validation is often used to choose the optimal number of components. The predictor of interest is in many applications a projection of the response variable on the space generated by the components. In the special case of PLS the space is Krylov structured. In the talk we show how to tie PLS to bilinear models. The advantage with the approach is that mean and dispersion structures can be handled.

Location: Alan Turing

### Tuesday, November 3, 3.15 pm, 2015. Seminar in Mathematical Statistics.

**Thinning and branching-stable point processes as a model for bursty spatial data**

Sergey Zuev, Mathematical Statistics, Chalmers University.

Sergey Zuev

*Abstract*: Thinning-stable point processes are important class of generally infinite intensity point processes since they are exactly the processes arising as a limit in superposition-thinning schemes. It can shown that these processes are exactly Cox (doubly stochastic Poisson) processes with strictly stable random intensity measures and, in a regular case, they are cluster processes with a specific heavy tailed distribution of cluster size. The cluster representation uses the so-called Sibuya point processes that constitute a new family of purely random point processes. Based on this facts, we develop statistical inference for stable processes and also discuss their generalisation when the thinning operation is replaced by a stochastic operation based on branching.

Location: Hopningspunkten.

### Tuesday, November 17, 3.15 pm, 2015. Seminar in Statistics.

**Bayesian Predictive Classifier for Gaussian data with Block-Diagonal Dependence Structure**

Tatjana Pavlenko, Mathematical Statistics, KTH Royal Institute of Technology.

Tatjana Pavlenko

*Abstract*: The talk will present an approach for constructing Bayesian predictive classifier for high-dimensional data. Our approach assumes that classes are represented by Gaussian distributions with the block-diagonal dependence structure and provides a closed form expression for the posterior predictive distribution of the data. Due to factorization of this distribution, the resulting Bayesian predictive classifier yields an efficient solution to the high-dimensional problem by splitting it into smaller tractable problems. Numerical studies will be presented demonstrating that the suggested predictive classifier outperforms its competitors such as linear discriminant analysis based on the block-wise inverse covariance estimators and the shrunken centroids regularized linear discriminant analysis. Albeit our approach relies on a given dependence structure, we also present some efficient methods of learning this structure from the data.

Location: Alan Turing

### Tuesday, December 1, 3.15 pm, 2015. Seminar in Mathematical Statistics.

**Random permutations related to quantum Heisenberg models**

Jakob Björnberg, Mathematical Statistics, University of Copenhagen.

Jakob Björnberg

*Abstract*: The interchange process (or random-transposition random walk) is a model for random permutations which is closely related to a model from quantum statistical physics (the ferromagnetic Heisenberg model). In fact, certain 'cycle-weighted' interchange processes are equivalent to the latter, and in this talk we present results on such processes. Magnetic ordering in the physical model translates to the occurrence of large cycles in the random permutation. We focus on the case when the underlying graph is the complete graph (i.e. the 'mean-field' case in physical jargon). By a combination of probabilistic techniques and some group character theory we can obtain nice formulas for expectation values in the model, and then use these to identify the critical point.

Location: Hopningspunkten.

### Tuesday, December 9, 1.15 pm, 2015. Seminar in Mathematical Statistics.

**Stochastic differential equations for sticky reflecting Brownian motion**

Hans Jürgen Engelbert, Friedrich-Schiller-University, Jena, Germany.

Hans Jürgen Engelbert

*Abstract*: Available here.

Location: Hopningspunkten.

### Tuesday, December 15, 3.15 pm, 2015. Seminar in Statistics.

**Minimax optimum experimental design for choosing between models for enzyme inhibition**

Ellinor Fackle-Fornius, Department of Statistics, Stockholm University.

Ellinor Fackle-Fornius, Department of Statistics, Stockholm University.

*Abstract*: An optimum design is found by minimizing some suitable criterion function. The criterion function is chosen to reflect the aim of the experiment, often to estimate model parameters. However, the optimum design for a nonlinear model is parameter dependent, that is, in order to find the best design to estimate the model parameters, the very same parameters have to be known. One way to deal with this issue is to use a minimax design, which seeks the minimum of the maximum criterion function for a set of plausible parameter values. In this application a minimax as well as a maximin efficient (where design efficiency is the criterion) design are derived for choosing between two types of enzyme inhibition; competetive and non-competetive inhibition. An extended version of the Michaelis-Menten model is used to take account of the two inhibition types. We use the same setup as in Atkinson and Bogacka (2013) where another type of design is used as a solution to the parameter dependence issue. We evaluate the minimax and maximin efficient designs and compare those to the robust design of Atkinson and Bogacka (2013).

Location: Alan Turing

Page responsible: Mattias Villani

Last updated: 2016-01-30