Statistics Across Campuses

  Weak Subordination of Multivariate Levy Processes Date: 4 August 2022, Thursday Time: 5pm AEST Statistics and Stochastic colloquium (part of the Colloquium Series of the Department of Mathematics and Statistics) at La Trobe University jointly organized with the Probability Victoria Seminar. Contact the organizers: Kostya Borovkov kostya.borovkov@gmail.com, Andriy Olenko a.olenko@latrobe.edu.au Speaker: Dr Boris Buchmann, ANU Abstract: Subordination is the operation which evaluates a Levy process at a subordinator, giving rise to a pathwise construction of a "time-changed" process. Originating with Bochner in the context of probability semigroups, subordination was applied by Madan and Seneta to create the variance gamma process, which is prominently used in financial modelling. However, unless the subordinate has independent components or the subordinator has indistinguishable components, subordination may not produce a Levy process.     We introduce a new op...

Bayesian learning of graph substructures  Date: 5 August 2022, Friday Time: 4pm AEDT Speaker: Willem van den Boom (National University of Singapore) Abstract:  Graphical models provide a powerful methodology for learning the conditional independence structure in multivariate data. Inference is often focused on estimating individual edges in the latent graph. Nonetheless, there is increasing interest in inferring more complex structures, such as communities, for multiple reasons, including more effective information retrieval and better interpretability. Stochastic blockmodels offer a powerful tool to detect such structure in a network. We thus propose to exploit advances in random graph theory and embed them within the graphical models framework. A consequence of this approach is the propagation of the uncertainty in graph estimation to large-scale structure learning. We consider Bayesian nonparametric stochastic blockmodels as priors o...

Model-Assisted Uniformly Honest Inference for Optimal Treatment Regimes in High Dimension Date :  Thursday, 28 July 2022 Time:   10:00  - 11:00 am Speaker:   Dr Yunan Wu   (University of Texas at Dallas)  Abstract: We develop new tools to quantify uncertainty in optimal decision making and to gain insight into which variables one should collect information about given the potential cost of measuring a large number of variables. We investigate simultaneous inference to determine if a group of variables is relevant for estimating an optimal decision rule in a high-dimensional semiparametric framework. The unknown link function permits flexible modeling of the interactions between the treatment and the covariates, but leads to nonconvex estimation in high dimension and imposes significant challenges for inference.  We first establish that a local restricted strong convexity condition holds with high probability and that any feasible local sparse solu...

An Ensemble Kalman-Bucy filter for correlated observation noise Date: 8 July 2022, Friday Time: 4pm AEDT Speaker:  Sebastian Ertel  (Technical University of Berlin, Germany) Abstract:  In this talk we aim to derive an Ensemble Kalman–Bucy filter (EnKBF) for  continuous time filtering problems, where the signal and the observation noise  are correlated.   To achieve this goal we first characterize a large class of mean-field diffusion  processes, that give a consistent representation of the desired posterior distribution.   A kinetic interpretation of these processes is discussed.   Next we use this representation to derive an EnKBF for the correlated noise  framework. We then discuss bounds for the (empirical) covariance matrix of  both the EnKBF and its mean-field limit, that can be used to establish the well- posedness of these equations.   Finally we discuss the convergence of the EnKBF to its mean-field ...