Statistics Across Campuses

  The geometry of forecast reconciliation Date:  Friday 28  August 2020 Time: 3 pm Speaker:  Prof Rob J Hyndman (Monash University) Abstract: It is common to forecast at different levels of aggregation. For example, a retail company will want national forecasts, state forecasts, and store-level forecasts. And they will want them for all products, for groups of products, and for individual products. Forecast reconciliation methods allow for the forecasts at all levels of aggregation to be adjusted so they are consistent with each other. I will describe a geometric interpretation for reconciliation methods used to forecast time series that adhere to known linear constraints. In particular, a general framework is established nesting many existing popular reconciliation methods within the class of projections. This interpretation facilitates the derivation of novel results that explain why and how reconciliation via projection is guaranteed to improve forecast accur...

Vintage Factor Analysis with Varimax Performs Statistical Inference Slides Date: 04 September 2020, Friday Time: 11am Speaker: Dr Karl Rohe  (University of Wisconsin–Madison) Abstract: Psychologists developed Multiple Factor Analysis to decompose multivariate data into a small number of interpretable factors without any a priori knowledge about those factors [Thurstone, 1935]. In this form of factor analysis, the Varimax "factor rotation" is a key step to make the factors interpretable [Kaiser, 1958]. Charles Spearman and many others objected to factor rotations because the factors seem to be rotationally invariant [Thurstone, 1947, Anderson and Rubin, 1956]. These objections are still reported in all contemporary multivariate statistics textbooks. This is an engima because this vintage form of factor analysis has survived and is widely popular because, empirically, the factor rotation often makes the factors easier to interpret. In a recent paper, we overturned a great dea...

Composite likelihood and logistic regression models for aggregated data Date: 14 August 2020, Friday Time: 1pm Speaker:  Dr Boris Beranger  (UNSW Sydney) Abstract: Symbolic data analysis (SDA) is an emerging technique for the analysis of large and complex datasets where individual level data are summarised into group-based distributional summaries (symbols) such as random rectangles or histograms.Likelihood-based methods have been recently developed, allowing to fit models for the underlying data while only observing distributional summaries. However, while powerful, when working with random histograms this approach rapidly becomes computationally intractable as the dimension of the underlying data increases. In this talk we first introduce a composite likelihood setting for the analysis of random histograms in K dimensions using lower-dimensional marginal histograms. We apply this approach to bypass the well known computational issues in the analysis of spatial extremes over ...

Network Influence Analysis Date: 20 August 2020, Thursday Time: 10am Speaker: Dr Tao Zou  (ANU) Abstract: Due to the rapid development of social networking sites, the spatial autoregressive (SAR) model has played an important role in social network studies. However, the underlying structure of SAR implicitly assumes that all nodes (or actors or users) within the network have the same influential power measured by the common autocorrelation parameter. Hence, the classical SAR is unable to identify influential nodes. This paper proposes the adaptive SAR model by introducing the network influence index, which includes the classical SAR model as a special case. Using this proposed model without imposing any specific error distribution, we apply Lee’s (2004) quasi-maximum likelihood approach to estimate the unknown parameters of the index, which can then be used to characterize the influential power of each node. The asymptotic properties of parameter estimates are established and three...

Conditional Normal Extreme-Value Copulas Date: 14 August 2020, Friday Time: 4pm Speaker:  Dr Pavel Krupskiy  (University of Melbourne) Abstract: We propose a new class of extreme-value copulas which are extreme-value limits of conditional normal models. Conditional normal models are generalizations of conditional independence models, where the dependence among observed variables is modeled using one unobserved factor. Conditional on this factor, the distribution of these variables is given by the Gaussian copula. This structure allows one to build flexible and parsimonious models for data with complex dependence structures, such as data with spatial or temporal dependence. We study the extreme-value limits of these models and show some interesting special cases of the proposed class of copulas. We develop estimation methods for the proposed models and conduct a simulation study to assess the performance of these algorithms. Finally, we a...

Subsampling Sequential Monte Carlo for Static Bayesian Models   Date: 14th August 2020 Friday  Time: 2-3pm  Speaker: Dr. Khue-Dung Dang (UTS)  joint work David Gunawan, Matias Quiroz, Robert Kohn, and Minh Ngoc Tran Abstract:  We show how to speed up Sequential Monte Carlo (SMC) for Bayesian inference in large data problems by data subsampling. SMC sequentially updates a cloud of particles through a sequence of distributions, beginning with a distribution that is easy to sample from such as the prior and ending with the posterior distribution. Each update of the particle cloud consists of three steps: reweighting, resampling, and moving. In the move step, each particle is moved using a Markov kernel; this is typically the most computationally expensive part, particularly when the dataset is large. It is crucial to have an efficient move step to ensure particle diversity. Our article makes two important contributions. First, in order to speed up the SMC computati...

Can we trust PCA on non-stationary Data? Date: 13 August 2020, Thursday Time: 10am Speaker: Dr Yanrong Yang (ANU) Abstract: This paper establishes asymptotic properties for spiked empirical eigenvalues for high dimensional data with both cross-sectional dependence and dependent sample structure. A new finding from the established theoretical results is that spiked empirical eigenvalues will reflect dependent sample structure instead of cross-sectional structure under some scenarios, which indicates that principal component analysis (PCA) may provide inaccurate inference for cross-sectional structure. An illustrated example is provided to show that some commonly used statistics based on spiked empirical eigenvalues mis-estimate the true number of common factors. As an application on high dimensional time series, we propose a test statistic to distinguish unit root from factor structure, and demonstrate its effective finite sample performance on simulated data. Our results are then appl...

STREAMLINED VARIATIONAL INFERENCE FOR RANDOM EFFECTS MODELS   Date:  Friday  7 August 2020  Time: 3 pm Speaker:  Prof  Matt Wand (University of Technology Sydney) Abstract: Variational inference offers fast approximate inference for graphical models arising in computer science and statistics. However, for models containing random effects, direct application of variational inference principles is not sufficient for fast inference due to the sizes of the relevant design matrices. We explain how the notion of matrix algebraic streamlining is crucial for making variational inference practical for models containing very high numbers of random effects. Both nested higher level and crossed random effect structures are discussed. Zoom Link:  https://macquarie.zoom.us/j/99218303144