Statistics Across Campuses

  Central Limit Theorem for Linear Spectral Statistics of Large Dimensional Kendall's Rank Correlation Matrices and its Applications Date:  Thursday, 1 April 2021 Time:   2 -3pm Speaker:  Assoc. Professor Zeng Li   ( Southern University of Science and Technology ) . Abstract:  I n this talk we will talk about the limiting spectral behaviors of large dimensional Kendall’s rank correlation matrices generated by samples with independent and continuous components. The statistical setting covers a wide range of highly skewed and heavy-tailed distributions since we do not require the components to be identically distributed, and do not need any moment conditions. We establish the central limit theorem (CLT) for the linear spectral statistics (LSS) of the Kendall’s rank correlation matrices under the Marchenko-Pastur asymptotic regime, in which the dimension diverges to infinity proportionally with the sample size. We further pro...

  Estimation, diagnostics, and extensions of nonparametric Hawkes processes.   Date:  Friday, 26 March 2021 Time:   3-4pm Speaker:  Assoc. Professor Jiancang Zhuang   (The Institute of Statistical Mathematics Japan and Department of Statistical Sciences, the Graduate University for Advanced Studies) . Abstract:   The Hawkes self-exciting model has become one of the most popular point-process models in many research areas in the natural and social sciences because of its capacity for investigating the clustering effect and positive interactions among individual events/particles. This talk discusses a general nonparametric framework for the estimation, extensions, and post-estimation diagnostics of Hawkes models. For illustration, I use the kernel function as the basic smoothing tool and the earthquake data and crime data as two application examples, to show how a Hawkes model is formulated from scratch. Zoom Link:  https://macquarie.zoom.us/j/84842...

Statistical inference for high dimensional principal components Date: 25 March 2021, Thursday Time: 10am AEDT Speaker: Dr Xiucai Ding (University of California, Davis) Abstract: In this talk, I will present some recent results on the asymptotic behavior of the extreme eigenvalues and eigenvectors of the high dimensional spiked sample covariance matrices, in the supercritical case when a reliable detection of spikes is possible. Especially, we derive the joint distribution of the extreme eigenvalues and the generalized components of the associated eigenvectors, i.e., the projections of the eigenvectors onto arbitrary given direction, assuming that the dimension and sample size are comparably large. In general, the joint distribution is given in terms of linear combinations of finitely many Gaussian and Chi-square variables, with parameters depending on the projection direction and the spikes. We also apply the results to various high dimensional statistical hypothesis testing problems...

  Order Selection with Confidence for Mixture Models Date:  Friday 19 March 2021 Time:  3pm Speaker:  Dr Hien Nguyen ( La Trobe University) Abstract: Finite mixture models are distribution models that are defined by convex combinations of a finite number of elements (components) from some base distribution class, where the number of elements dictates the complexity of the mixture model. Given that data arise from a class of finite mixture models, where the number of components is unknown, an important problem that arises is choice of the number of components that one should use to model the data. We present a hypothesis test-based algorithm to selecting the number of components of a mixture model that yields a lower bound on the number of components, with confidence. We demonstrate that in special circumstances, the approach also yields a method that consistently selects the correct number of components, and we demonstrate the effectiveness of the approach via a stud...

Random FPUT Lattices   Date: Thursday 11 March 2021 Time: 10am Speaker:   Professor J. Douglas Wright (Drexel University) Abstract: We consider a linear Fermi-Pasta-Ulam-Tsingou lattice with random spatially varying material coefficients. Using the methods of stochastic homogenization we show that solutions with long wave initial data converge in an appropriate sense to solutions of a wave equation. The convergence is both strong and almost sure, but the rate of convergence is quite slow. The technique combines energy estimates with powerful classical results about random walks, specifically the law of the iterated logarithm. This work is joint with Drexel PhD student, Josh McGinnis. Zoom Link:  https://macquarie.zoom.us/j/83753405912?pwd=VU96LzJqbnhVODQwMnhhTS9VNEc5Zz09

Improving the appeal of variational approximations Date: 12 March 2021, Friday Time: 4pm AEDT Speaker: Dr Luca Maestrini (University of Technology Sydney) Abstract: Variational approximations facilitate approximate inference for the parameters of a variety of statistical models. However, they are sometimes criticized for being hard to implement, hindered by the sizes of model design matrices and potentially inaccurate. First, we show how the notion of variational message passing on factor graph fragments allows for repeated use of algorithmic primitives, representing enormous savings in terms of algebra and computer coding. We illustrate this concept on applications that can be modelled as inverse problems. We also explain how streamlined solutions to sparse matrix problems can be used for making fast variational inference for models with a high number of random effects and provide an illustration for multilevel models with penalized regression coefficients. Last, we show a simple rem...