# The LiU Seminar Series in Statistics and Mathematical Statistics

Spring 2012

### Tuesday, January 17, 3.15 pm, 2012. Seminar in Statistics

**Profile Analysis with Random-Effects Covariance Structure**

Martin Singull, Mathematical Statistics, Linköping University.

Martin Singull

*Abstract*: In this talk, we will consider a parallel profile model for several groups. Given the parallel profile model we construct tests based on the likelihood ratio, without any restrictions on the parameter space, testing the covariance matrix for random-effects structure or sphericity. Furthermore, given both the parallel profile and random-effects covariance structure the level hypothesis is tested. The attained significance levels and the empirical powers for the given tests are compared with the restricted tests given by Yokoyama and Fujikoshi (1993) and Yokoyama (1995).

Location: John von Neumann

### Tuesday, January 31, 3.15 pm, 2012. Seminar in Mathematical Statistics

**Small deviation probabilities and their interplay with operator theory and Bayesian statistics**

Mikhail Lifshits, MAI, LiU and S:t Petersburg State University

Mikhail Lifshits

*Abstract*: TBA

Location: Kompakta rummet, MAI.

### Tuesday, February 14, 3.15 pm, 2012. Seminar in Statistics

**Large-scale network modeling, data integration and experimental planning, with applications to cancer genomics**

Rebecka Jörnsten, Mathematical Sciences, Chalmers

Rebecka Jörnsten

*Abstract*: Aberration of a gene's copy number (CNA) is known to affect the mRNA level of that gene. CNAs are also known to be prevalent in cancer genomes. We construct CNA-mRNA network models to investigate the global effects of copy number changes on gene expression. The network models allow us to identify CNA-hubs that appear to drive the gene expression. Using regularized regression we uncover network modules that are predictive of clinical outcome (survival).

Time permitting, we will also discuss an experimental planning problem in cancer genomics. We present a novel computational-experimental framework for efficient identification of interacting target pairs (genes or drugs), applicable for screening of large systems (>1000 targets). This framework exploits the fact that the response of a target pair in a given system can be partly predicted by computational means from (i) a small set of experimentally determined target pairs, and (ii) pre-existing data (e.g. drug-response databases, gene ontology, PPI) on the similarities between targets. We demonstrate the efficiency of the proposed method on several public, gold-standard data sets, and show that our protocol increases the rate of discovery of interactions by up to 7-fold compared with standard screening.

Location: Alan Turing

### Tuesday, February 28, 3.15 pm, 2012. Seminar in Statistics

**Local Influence Analysis and Cross-over Studies**

Chengcheng Hao, Department of Statistics, Stockholm University

Chengcheng Hao

*Abstract*: With a special reference to cross-over design models with random individual effects, the purpose of this dissertation is to develop new methodology to detect influential observations in the context of mixed linear models with explicit maximum likelihood estimators (MLEs). Case-weighted perturbation schemes within and between subjects in mixed models are constructed. It is emphasised that perturbations should be performed under the restriction that explicit MLEs can be obtained in the perturbed model. Two influence functions, the delta-beta influence and variance-ratio influence, are tools to evaluate the influence on the estimates of mean parameters and variance parameters, respectively, with respect to the used perturbations. The proposed approach, named the delta-beta-based local influence approach, derives the expressions of the delta-beta and variance-ratio influences for two specific cross-over designs. In both the AB|BA design (2 X 2 cross-over design) and the ABBA|BAAB design, the applied influence functions turn out to have closed-form expressions of residuals from the unperturbed models. Some graphical tools are also presented.

Location: Alan Turing

### Tuesday, March 13, 3.15 pm, 2012. Seminar in Mathematical Statistics

**On optimality of neighbor designs under interference models**

Augustyn Markiewicz, Department of Mathematical and Statistical Methods, Poznań University of Life Sciences

Augustyn Markiewicz

*Abstract*: The concept of neighbor designs was introduced and defined by Rees (1967) who gave also some methods of their construction. Henceforth many methods of construction of neighbor designs as well as of their generalizations are available in the literature. However there are only few results on their optimality. Therefore the aim of the talk is to give an overview of study on this problem. It will include some recent results on optimality of specified neighbor designs under various linear models.

Location: Kompakta rummet, MAI.

### Tuesday, March 27, 3.15 pm, 2011. Seminar in Mathematical Statistics

**On sequential change-point detection**

Allan Gut, Department of Mathematics, Uppsala University

Allan Gut

*Abstract*A typical situation in a series of observations is that if everything is in order, then the observations follow some kind of common pattern, whereas if something goes astray at some time point, then, from there on, the observations follow a different pattern. One obviously wishes to find out as soon as possible if something goes wrong---that is, if there is a change-point---in order to take appropriate action, and, at the same time, minimize the probability of taking action if nothing is wrong. The typical analysis in change-point theory is based on samples of fixed size. In a series of paper, together with Josef Steinebach at the University of Cologne, we have taken an alternative view point. Namely, instead one observes the random phenomenon in question sequentially in order to take action as soon as one observes some statistically significant deviation from ``normal'' behaviour. Based on this idea we have analyzed the counting process related to the original processes. In this talk I will review some results of our joint efforts. The main ingredients in the proofs are strong invariance principles for renewal processes and extreme value asymptotics for Gaussian processes.

Location: Kompakta rummet, MAI.

### Tuesday, April 10, 3.15 pm, 2011. Seminar in Mathematical Statistics

**Bi-stability in an age structured Hepatitis B model**

Nelson Owuor Onyango, University of Nairobi, Kenya and SLU Uppsala.

Nelson Owuor Onyango

*Abstract*The Basic Reproduction Number, R0, associated with epidemic models is a threshold condition for determining disease extinction (R0<1) or endemicity (R0>1). Under normal circumstances, there is a forward bifurcation at R0=1, and the emerging endemic solution is unique. We however seek to establish within the context of an age structured model, conditions for which bi-stability (also called backward bifurcation) may occur. Previous simulation studies indicate that in hyper-endemic populations, with high carrier prevalence, bi-stable dynamics are highly likely (Medley G.F. et al, 2001).

Key words: Backward bifurcation, Stability of PDE models in epidemiology, Hepatitis B, Basic Reproduction Number.

Location: Kompakta rummet, MAI.

### Tuesday, April 24, 3.15 pm, 2012. Seminar in Mathematical Statistics

**Quasi equilibrium methods in population genetics**

Ola Hössjer, Mathematical Statistics, Stockholm University

Ola Hössjer

*Abstract*: We consider time evolvement of a population with some kind (geographical, social, ethnic, ...) of substructure. It is assumed that a limited amount of migration takes place between the subpopulations. Two classical questions in population genetics are to quantify the degree of spatial heterogeneity between the subpopulations (fixation index) and the degree of inbreeding (effective population size). In this talk we introduce a general framework for answering these (and other) questions. The idea is to model the spatio-temporal variation at a number of genetic markers as vector valued autoregressive processes and consider their quasistationary behaviour, conditional on that no variant (allele) at each marker of interest has taken over the whole population.

Location: Kompakta rummet, MAI.

### Tuesday, May 8, 1.15 pm, 2012. Seminar in Statistics ** Note the time!**

**Functional Data Analysis, Causal Inference and Brain Connectivity**

Martin A. Lindquist, Department of Statistics, Columbia University, U.S.A.

Martin A. Lindquist

*Abstract*: Functional data analysis (FDA) and causal inference are two areas that have received substantial interest in the statistics literature lately. However, to date, both remain relatively underutilized in the neuroimaging community. This talk illustrates several neuroimaging applications in which both FDA and causal inference promise to play an important role. We conclude with the introduction of a functional path analysis model for studying brain connectivity, which extends the standard structural equation model framework to the functional data setting. We use the potential outcomes notation of causal inference to determine the assumptions required to obtain a valid estimate of the average causal effect from the functional path analysis model.

Paper

Location: Alan Turing

### Tuesday, May 22, 3.15 pm, 2012. Seminar in Statistics

**Bayesian inference in Structural Second-Price Auctions With Both Private-value and Common-value Bidders**

Bertil Wegmann, Statistics, Linköping University

Bertil Wegmann

*Abstract*: Auctions with asymmetric bidders have been actively studied in recent years. Tan and Xing (2011) show the existence of monotone pure-strategy equilibrium in auctions with both private-value and common-value bidders. The equilibrium bid function is given as the solution to an ordinary differential equation (ODE). We approximate the ODE and obtain a very accurate, approximate inverse bid as an explicit function of a given bid. We propose a model where the valuations of both common-value and private-value bidders are functions of covariates. The probability of being a common-value bidder is modeled by a logistic regression model with Bayesian variable selection. The model is estimated on a dataset of eBay coin auctions. We analyze the model using Bayesian methods implemented via a Metropolis-within-Gibbs algorithm.

Location: Alan Turing

### Friday, June 8, 1.15 pm, 2012. Licentiate Seminar in Mathematical Statistics ** Note the time!**

**Estimation in Multivariate Linear Models with Linearly Structured Covariance Matrices**

Joseph Nzabanita, Mathematical Statistics, Linköping University.

Joseph Nzabanita

Discussant: Dr. Daniel Klein, Faculty of Sciences, P.J. Safarik University in Kosice, Slovakia.

Location: BL32 (Nobel)

Page responsible: Mattias Villani

Last updated: 2012-06-06