Tuesday, September 3, 3.15 pm, 2019. Seminar in Statistics.

Rao score test for BCS structured covariance matrix under high-dimensional regime
Jolanta Pielaszkiewicz, Division of Statistics and Machine Learning, Department of Computer and Information Science, Linköping University
Abstract: The Rao score test for hypothesis about the Block Compound Symmetry structure of a covariance matrix will be presented and then modified to version that is appropriate for analysis of high-dimensional data, i.e a data matrix with increasing (at asymptotically constant ratio) numbers of columns and rows will be considered. The asymptotic distribution of modified test statistics will be developed using tools of random matrix theory and will be an extension of earlier results regarding independence and sphericity testing.
Location: Alan Turing.

Tuesday, September 17, 3.15 pm, 2019. Seminar in Mathematical Statistics.

Bayesian learning of weakly structural Markov graph laws using sequential Monte Carlo methods
Jimmy Olsson, Department of Mathematics, KTH
Abstract: We shall discuss a sequential Monte Carlo-based approach to approximation of weakly structural Markov graph laws on spaces of decomposable graphs, or, more generally, spaces of junction (clique) trees associated with such graphs. In particular, we apply a particle Gibbs version of the algorithm to Bayesian structure learning in decomposable graphical models, where the target distribution is a junction tree posterior distribution. Moreover, we use the proposed algorithm for exploring certain fundamental combinatorial properties of decomposable graphs, e.g. clique size distributions. Our approach requires the design of a family of proposal kernels, so-called junction tree expanders, which expand junction trees by connecting randomly new nodes to the underlying graphs. The performance of the estimators is illustrated through a collection of numerical examples demonstrating the feasibility of the suggested approach in high-dimensional domains.
Location: Hopningspunkten.

Tuesday, October 1, 3.15 pm, 2019. Seminar in Statistics.

Hierarchical Bayesian mixture modeling of resting-state functional brain connectivity. Cross-sectional and longitudinal approaches
Tetiana Gorbach, Department of Integrative Medical Biology and Umeå School of Business, Economics and Statistics, Umeå University
Abstract: During the seminar, two studies of functional brain connectivity will be presented. In the first cross-sectional study, we propose a Bayesian hierarchical mixture model to analyze functional brain connectivity where mixture components represent "connected" and "non-connected" brain regions. Mixture modelling provides a data-informed separation of reliable connections from noise in contrast to arbitrary thresholding of a connectivity matrix. The hierarchical structure of the model allows simultaneous inferences for the entire population and each subject separately. We show that the posterior probability of a given pair of brain regions to be connected given the observed correlation of regions' activity might be superior to correlation measure of connectivity. The applicability of the introduced method is exemplified by a study of functional resting-state brain connectivity in older adults based on the data from the Betula project.
In the second study, we extend cross-sectional modeling to a longitudinal data with two scheduled measurements and dropout at the second measurement occasion. We develop a model that provides valid inferences when dropout from the study is not at random. The analysis of longitudinal data demonstrates that longitudinal estimates of connectivity changes may deviate from cross-sectional estimates. The simulation study shows that ignoring dropout mechanism may yield erroneous conclusions regarding connectivity changes.
Location: Alan Turing.

Tuesday, October 15, 3.15 pm, 2019. Seminar in Mathematical Statistics.

Moment constrained optimal dividends: precommitment & consistent planning
Kristoffer Lindensjö, Department of Mathematics, Stockholm University
Abstract: A moment constraint that limits the number of dividends in the optimal dividend problem is suggested. This leads to a new type of time-inconsistent stochastic impulse control problem. First, the optimal solution in the precommitment sense is derived. Second, the problem is formulated as an intrapersonal sequential dynamic game in line with Strotz' consistent planning. In particular, the notions of pure dividend strategies and a (strong) subgame perfect Nash equilibrium are adapted. An equilibrium is derived using a smooth fit condition. The equilibrium is shown to be strong. The uncontrolled state process is a fairly general diffusion.
Location: Hopningspunkten.

Tuesday, October 29, 3.15 pm, 2019. Seminar in Statistics.

Central limit theorems for functionals of large sample covariance matrix and mean vector in matrix-variate location mixture of normal distributions
Stepan Mazur, Örebro University School of Business (jointly with Taras Bodnar and Nestor Parolya)
Abstract: In this talk, we consider the asymptotic distributions of functionals of the sample covariance matrix and the sample mean vector obtained under the assumption that the matrix of observations has a matrix-variate location mixture of normal distributions. The central limit theorem is derived for the product of the sample covariance matrix and the sample mean vector. Moreover, we consider the product of the inverse sample covariance matrix and the mean vector for which the central limit theorem is established as well. All results are obtained under the large-dimensional asymptotic regime, where the dimension p and the sample size n approach infinity such that p/n -> c ∈ [0, +∞) when the sample covariance matrix does not need to be invertible and p/n -> c ∈ [0, 1) otherwise.
Location: Alan Turing.

Tuesday, November 26, 3.15 pm, 2019. Seminar in Statistics.

Adaptive Bayesian SLOPE—High-dimensional Model Selection with Missing Values
Małgorzata Bogdan, Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology
Abstract: We consider the problem of variable selection in high-dimensional settings with missing observations among the covariates. To address this relatively understudied problem, we propose a new synergistic procedure—adaptive Bayesian SLOPE—which effectively combines the SLOPE method (sorted L1 regularization) together with the Spike-and-Slab LASSO method. We position our approach within a Bayesian framework which allows for simultaneous variable selection and parameter estimation, despite the missing values. As with the Spike-and-Slab LASSO, the coefficients are regarded as arising from a hierarchical model consisting of two groups: (1) the spike for the inactive and (2) the slab for the active. However, instead of assigning independent spike priors for each covariate, here we deploy a joint "SLOPE'' spike prior which takes into account the ordering of coefficient magnitudes in order to control for false discoveries. Through extensive simulations, we demonstrate satisfactory performance in terms of power, FDR and estimation bias under a wide range of scenarios. Finally, we analyze a real dataset consisting of patients from Paris hospitals who underwent severe trauma, where we show excellent performance in predicting platelet levels. Our methodology has been implemented in C++ and wrapped into an R package ABSLOPE for public use.
This is a join work with Wei Jiang and Julie Josse from Ecole Polytechnique, Błażej Miasojedow from University of Warsaw, Veronika Rockova from the Chicago Booth School of Business and TraumaBase group from the Hospital Beaujon, APHP, France.
Location: Alan Turing.