Variational inference for heteroscedastic and longitudinal regression models

University of Technology Sydney. Faculty of Science.The focus of this thesis is on the development and assessment of mean field variational Bayes (MFVB), which is a fast, deterministic tool for inference in a Bayesian hierarchical model setting. We assess the performance of MFVB via the use of comprehensive comparisons against a Markov chain Monte Carlo (MCMC) benchmark. Each of the models considered are special cases of semiparametric regression. In particular, we focus on the development and assessment of the performance of MFVB for heteroscedastic and longitudinal semiparametric regression models. Generally, the new MFVB methodology performs well in its assessment of accuracy against MCMC for the semiparametric and nonparametric regression models considered in this thesis. It is also much faster and is shown to be applicable to real-time analyses. Several real data illustrations are provided. Altogether, MFVB proves to be a credible inference tool and a good alternative to MCMC, especially when analysis is hindered by time constraints

Optimal location of tsunami warning buoys and sea level monitoring stations in the mediterranean sea

The present study determines the optimal location of detection components of a tsunami warning system in the Mediterranean region given the existing and planned infrastructure. Specifically, we examine the locations of existing tsunameters DART buoys and coastal sea-level monitoring stations to see if additional buoys and stations will improve the proportion of the coastal population that may receive a warning ensuring a timely response. A spreadsheet model is used to examine this issue. Based on the historical record of tsunamis and assuming international cooperation in tsunami detection, it is demonstrated that the existing network of sea level stations and tsunameters enable around ninety percent of the coastal population of the Mediterranean Sea to receive a 15 minute warning. Improvement in this result can be achieved through investment in additional real-time, coastal, sea level monitoring stations. This work was undertaken as a final year undergraduate research project

Streamlined variational inference for higher level group-specific curve models

© 2020 Statistical Modeling Society. A two-level group-specific curve model is such that the mean response of each member of a group is a separate smooth function of a predictor of interest. The three-level extension is such that one grouping variable is nested within another one, and higher level extensions are analogous. Streamlined variational inference for higher level group-specific curve models is a challenging problem. We confront it by systematically working through two-level and then three-level cases and making use of the higher level sparse matrix infrastructure laid down in (Nolan and Wand (2020), ANZIAM Journal, doi: 10.1017/S1446181120000061). A motivation is analysis of data from ultrasound technology for which three-level group-specific curve models are appropriate. Whilst extension to the number of levels exceeding three is not covered explicitly, the pattern established by our systematic approach sheds light on what is required for even higher level group-specific curve models

Partial least squares structural equation modeling-based discrete choice modeling: An illustration in modeling retailer choice

Commonly used discrete choice model analyses (e.g., probit, logit and multinomial logit models) draw on the estimation of importance weights that apply to different attribute levels. But directly estimating the importance weights of the attribute as a whole, rather than of distinct attribute levels, is challenging. This article substantiates the usefulness of partial least squares structural equation modeling (PLS-SEM) for the analysis of stated preference data generated through choice experiments in discrete choice modeling. This ability of PLS-SEM to directly estimate the importance weights for attributes as a whole, rather than for the attribute’s levels, and to compute determinant respondent-specific latent variable scores applicable to attributes, can more effectively model and distinguish between rational (i.e., optimizing) decisions and pragmatic (i.e., heuristic) ones, when parameter estimations for attributes as a whole are crucial to understanding choice decisions

Identifying weak signals to prepare for uncertainty in the energy sector

This study aims to prepare the energy sector for uncertainty using a foresight tool known as weak signals. Weak signals (subtle signs of emerging issues with significant impact potential) are often overlooked during strategic planning due to their inherent predictive uncertainty. However, the value does not lie in precise forecasting but in broadening the consideration of future possibilities. By proactively monitoring and addressing these otherwise neglected developments, stakeholders can gain early awareness of threats and opportunities and enhance their resilience, adaptability, and innovation. A panel of technology experts identified eight weak signals in this study: 1) growing mistrust and local grid security measures, 2) consumer reactions to overly prescriptive policies, 3) long-term forecasting errors for thin-margin projects, 4) emergence of variable power industries, and 5) establishment of intercontinental transmission precedence; including three potential ‘wild cards’ requiring proactive mitigation: 6) escalating electrical generation dependence on continued imports, 7) a new threat surpassing climate change, and 8) mass deployment of low-emissions technology triggering a runaway loss of social license. Political factors were the predominant source of uncertainty, as decisions can suddenly transform the energy landscape. Economic, technological, and social factors followed closely behind, generally through the emergence of new industries and behavioural responses. While environmental and legal factors were less frequent, stakeholders should still adopt a holistic approach, as the signals were found to be highly interconnected. Organisations should also assess their local context when applying these findings and continuously update and respond to their own list of weak signals

Variational inference for marginal longitudinal semiparametric regression

© 2013 John Wiley & Sons Ltd. We derive a variational inference procedure for approximate Bayesian inference in marginal longitudinal semiparametric regression. Fitting and inference is much faster than existing Markov chain Monte Carlo approaches. Numerical studies indicate that the new methodology is very accurate for the class of models under consideration

Streamlined Computing for Variational Inference with Higher Level Random Effects

We derive and present explicit algorithms to facilitate streamlined computing for variational inference for models containing higher level random effects. Existing literature, such as Lee and Wand (2016), is such that streamlined variational inference is restricted to mean field variational Bayes algorithms for two-level random effects models. Here we provide the following extensions: (1) explicit Gaussian response mean field variational Bayes algorithms for three-level models, (2) explicit algorithms for the alternative variational message passing approach in the case of two-level and three-level models, and (3) an explanation of how arbitrarily high levels of nesting can be handled based on the recently published matrix algebraic results of the authors. A pay-off from (2) is simple extension to non-Gaussian response models. In summary, we remove barriers for streamlining variational inference algorithms based on either the mean field variational Bayes approach or the variational message passing approach when higher level random effects are present