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The LiU Seminar Series in Statistics and Mathematical Statistics
Spring 2014
Tuesday, January 28, 3.15 pm, 2014. Seminar in Statistics
Regularized multiple regression: application in genome-wide association studies
Patrik Waldmann, Statistics, LiU.
Abstract: One common characteristic for the new genomic techniques is that data sets are very large, often with many more variables than observations (p >> n).
The goal of genome-wide association studies (GWAS) is to identify the best subset of single-nucleotide polymorphisms (SNPs) that strongly influence a certain trait, for example a disease or production trait.
State of the art GWAS comprise several thousand or even millions of SNPs, scored on a number of individuals on the order of a few thousands.
Most of the GWAS carried out previously are single-SNP studies where each SNP is tested individually for its association to the phenotype.
This presentation will show that regularized multiple regression provides an attractive alternative.
Both classical and Bayesian methods will be presented and compared. Moreover, the effect of intricate correlation patterns between SNPs on the methods will be evaluated.
Location: Alan Turing
Tuesday, February 11, 3.15 pm, 2014. Seminar in Mathematical Statistics
Large deviations for Markov bridges
Xiangfeng Yang, Mathematical Statistics, LiU.
Abstract: Markov bridges have numerous applications, such as the
use of Brownian bridges in the Kolmogorov-Smirnov test in the area of
statistical inference. In this talk I will propose a method to study
large deviations for suitable Markov bridges, including Brownian bridges, Lévy bridges, Bernstein bridges, etc.
The main ingredient of the method is to employ an equivalent form of
large deviations and consider the associated compact level sets instead
of closed sets.
Location: Kompakta rummet.
Tuesday, March 11, 3.15 pm, 2014. Seminar in Mathematical Statistics
Efficient estimation of the number of false positives in high-throughput screening
Holger Rootzén , Mathematical Statistics, Chalmers.
Abstract: This talk is about tail estimation methods to handle false positives in very highly multiple
testing problems where testing is done at extreme significance levels and with low degrees of freedom,
and where the true null distribution may differ from the theoretical one. We show that the number of
false positives, conditional on the total number of positives, approximately has a binomial distribution,
and find estimators of its parameter. We also develop methods for estimation of the true null distribution,
and techniques to compare it with the theoretical one. Analysis is based on a simple polynomial model for
the tail of the distribution of p-values. Asymptotics which motivate the model, properties of the parameter
estimators, and model checking tools are provided. The methods are applied to two large genomic studies and an
fMRI brain scan experiment.
Location: Kompakta rummet.
Tuesday, April 8, 3.15 pm, 2014. Seminar in Mathematical Statistics
Comparison of asymptotic variances of inhomogeneous Markov chains with applications to Markov Chain
Monte Carlo methods
Jimmy Olsson, Mathematical Statistics, KTH.
Abstract: In this talk we will discuss the asymptotic variance of sample path averages
for inhomogeneous Markov chains evolving alternatingly according to
two different pi-reversible Markov transition kernels. More specifically,
we define a partial ordering over the pairs of pi-reversible Markov
kernels that allows us to compare directly the asymptotic variances
for the inhomogeneous Markov chains associated with each pair. As an
important application we use our result for comparing different
data-augmentation-type Metropolis Hastings algorithms. In particular, we
compare some pseudo-marginal algorithms and
propose a novel exact algorithm, referred to as the random refreshment
algorithm, which is more efficient, in terms of asymptotic variance,
than the Grouped Independence Metropolis Hastings algorithm and
has a computational complexity that does not exceed that of the Monte
Carlo Within Metropolis algorithm.
Location: Kompakta rummet.
Tuesday, April 22, 3.15 pm, 2014. Seminar in Statistics
Merging longitudinal datasets from studies in cognition and brain imaging
Anders Lundquist, Statistics, Umeå University.
Abstract: Human cognitive abilities are interesting to investigate from many different aspects, e.g. developmental trajectories during childhood as well as decline during aging,
possibly with pathological components such as dementia. Currently, no single longitudinal dataset covering the human life span exist. However, by merging two available longitudinal datasets,
coming from the Brainchild and Betula studies respectively, we are able to cover an age span of 6-85 years. The primary objective in this talk will be modelling the association between episodic memory performance
and age, which is non-linear across the lifespan. We therefore use Generalized Additive Mixed Models (GAMM:s), permitting the memory performance to be a smooth function of age.
As this is an ongoing project, results are preliminary, and time will be devoted for discussing alternative modelling strategies as well as other issues arising from joining data sets such as these.
Location: Alan Turing
Tuesday, May 6, 3.15 pm, 2014. Seminar in Mathematical Statistics
Using Stein Couplings for the Study of Fringe Trees
Cecilia Holmgren, Mathematical Statistics, SU
Abstract: The binary search tree (in computational science known as Quicksort, the
most used of all sorting algorithms) and the random recursive tree are
important examples of random trees. We have examined fringe trees ("small"
subtrees) in these two types of random trees.
The use of certain couplings based on Stein's method allow provision of
simple proofs showing that in both of these trees, the number of fringe
trees of size k, where k tends to infinity, converges to a Poisson
distribution. Furthermore, combining these results and another version of
Stein's method, we can also show that for k=o(sqrt{n}) (where n is the
size of the whole tree) the number of fringe trees in both types of random
trees converges to a normal distribution.
We can then use these general results on fringe trees to obtain simple
solutions to a broad range of problems relating to random trees; as an
example, we obtain a simple proof showing that the number of protected
nodes in the binary search tree has a normal distribution.
(Joint work with Svante Janson, Uppsala University)
Location: Hopningspunkten.
Tuesday, May 20, 3.15 pm, 2014. Seminar in Statistics
Variational Inference in Factorized Latent Variable Models
Carl Henrik Ek, Computer Science, KTH.
Abstract: In this talk I will discuss variational inference and its application to latent variable models for multi-view learning. We will start with a brief
introduction to the topic and then proceed to introduce recent developments in the field. Given this as a background we will
introduce factorized latent variable models for multi-view data and explain how variational methods are essential to make inference feasible in these model.
We will show experiments on models based on both Dirichlet and Gaussian Process priors.
Location: Alan Turing
Tuesday, May 27, 3.15 pm, 2014. Seminar in Mathematical Statistics
Testing of multivariate data with block compound symmetry covariance
structure
Daniel Klein, P.J. Safarik University, Slovakia
Abstract: It is well-known that Hotelling's T2 test is the conventional method to
test the equality of mean vectors in two populations. However,
Hotelling's T2 statistic is based on the unbiased estimate of the
unstructured variance-covariance matrix. Nevertheless, the
variance-covariance matrix may have some structure, and one should use
an unbiased estimate of that structure to test the equality of mean
vectors. A natural extension of the Hotelling's T2 statistic, called the Block T2 statistic, is obtained for doubly
multivariate data for q response variables at p time points in block
compound symmetric covariance matrix setting. The minimum sample size
needed for this test is only q +1, unlike pq +1 in Hotelling's T2 test.
Location: Hopningspunkten.
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