Second Term Improvement to Generalised Linear Mixed Model Asymptotics

A recent article on generalised linear mixed model asymptotics, Jiang et al. (2022), derived the rates of convergence for the asymptotic variances of maximum likelihood estimators. If $m$ denotes the number of groups and $n$ is the average within-group sample size then the asymptotic variances have orders $m^{-1}$ and $(mn)^{-1}$, depending on the parameter. We extend this theory to provide explicit forms of the $(mn)^{-1}$ second terms of the asymptotically harder-to-estimate parameters. Improved accuracy of studentised confidence intervals is one consequence of our theory

Tsunami risk modelling for Australia: understanding the impact of data

Modelling the impacts from tsunami events is a complex task. A simplification is obtained by taking a hybrid approach where two different models are combined: relatively simple and fast models are used for simulating the tsunami event and the wave propagation through open water. The impact from tsunami inundation is simulated with another type of model which is suitable for resolving the details of the run-up process and the resulting inundation. The inundation modelling is conducted using the ANUGA model which is a result of collaboration between the Australian National University and Geoscience Australia. It solves the 2D nonlinear shallow water wave equations using a finite volume method. One of the critical requirements for reliable inundation modelling is an accurate model of the earth's surface that extends from the open ocean through the inter-tidal zone into the onshore areas to be studied. Production of a sufficiently accurate elevation model is a complex and difficult process made more difficult because the available elevation data inevitably will come from a number of different sources and will have a range of vintages, resolutions and reliability. There are two questions that arise when data is requested. The first deals with the true variability of the topography. Obviously, a flat surface needn’t be sampled nearly as finely as a highly convoluted surface. The second question relates to sensitivity; how are error bars derived for the impact results if the error bars on each elevation point is known? ANUGA solves the 2D nonlinear shallow water wave equations using a finite volume method and typical models can take days of computational time, so proper sensitivity analyses are often prohibitively expensive in terms of computational resources. The main aim of this project was therefore to understand the uncertainties in the outputs of the inundation model based on possible uncertainty in the input data

Real-time Semiparametric Regression via Sequential Monte Carlo

We develop and describe online algorithms for performing real-time semiparametric regression analyses. Earlier work on this topic is in Luts, Broderick & Wand (J. Comput. Graph. Statist., 2014) where online mean field variational Bayes was employed. In this article we instead develop sequential Monte Carlo approaches to circumvent well-known inaccuracies inherent in variational approaches. Even though sequential Monte Carlo is not as fast as online mean field variational Bayes, it can be a viable alternative for applications where the data rate is not overly high. For Gaussian response semiparametric regression models our new algorithms share the online mean field variational Bayes property of only requiring updating and storage of sufficient statistics quantities of streaming data. In the non-Gaussian case accurate real-time semiparametric regression requires the full data to be kept in storage. The new algorithms allow for new options concerning accuracy/speed trade-offs for real-time semiparametric regression

Semiparametric Regression During 2003–2007

Semiparametric regression is a fusion between parametric regression and nonparametric regression and the title of a book that we published on the topic in early 2003. We review developments in the field during the five year period since the book was written. We find semiparametric regression to be a vibrant field with substantial involvement and activity, continual enhancement and widespread application

Fast approximate inference for multivariate longitudinal data

Collecting information on multiple longitudinal outcomes is increasingly common in many clinical settings. In many cases, it is desirable to model these outcomes jointly. However, in large data sets, with many outcomes, computational burden often prevents the simultaneous modeling of multiple outcomes within a single model. We develop a mean field variational Bayes algorithm, to jointly model multiple Gaussian, Poisson, or binary longitudinal markers within a multivariate generalized linear mixed model. Through simulation studies and clinical applications (in the fields of sight threatening diabetic retinopathy and primary biliary cirrhosis), we demonstrate substantial computational savings of our approximate approach when compared to a standard Markov Chain Monte Carlo, while maintaining good levels of accuracy of model parameters