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Register a new userFrom Science to Management: Using Bayesian Networks to Learn about Lyngbya
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Toxic blooms of Lyngbya majuscula occur in coastal areas worldwide and have major ecological, health and economic consequences. The exact causes and combinations of factors which lead to these blooms are not clearly understood. Lyngbya experts and stakeholders are a particularly diverse group, including ecologists, scientists, state and local government representatives, community organisations, catchment industry groups and local fishermen. An integrated Bayesian network approach was developed to better understand and model this complex environmental problem, identify knowledge gaps, prioritise future research and evaluate management options.
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Epidemiological forecasts are beset by uncertainties about the underlying epidemiological processes, and the surveillance process through which data are acquired. We present a Bayesian inference methodology that quantifies these uncertainties, for epidemics that are modelled by (possibly) non-stationary, continuous-time, Markov population processes. The efficiency of the method derives from a functional central limit theorem approximation of the likelihood, valid for large populations. We demonstrate the methodology by analysing the early stages of the COVID-19 pandemic in the UK, based on age-structured data for the number of deaths. This includes maximum a posteriori estimates, MCMC sampling of the posterior, computation of the model evidence, and the determination of parameter sensitivities via the Fisher information matrix. Our methodology is implemented in PyRoss, an open-source platform for analysis of epidemiological compartment models.
Variational approaches to approximate Bayesian inference provide very efficient means of performing parameter estimation and model selection. Among these, so-called variational-Laplace or VL schemes rely on Gaussian approximations to posterior densities on model parameters. In this note, we review the main variants of VL approaches, that follow from considering nonlinear models of continuous and/or categorical data. En passant, we also derive a few novel theoretical results that complete the portfolio of existing analyses of variational Bayesian approaches, including investigations of their asymptotic convergence. We also suggest practical ways of extending existing VL approaches to hierarchical generative models that include (e.g., precision) hyperparameters.
The modeling of the spreading of communicable diseases has experienced significant advances in the last two decades or so. This has been possible due to the proliferation of data and the development of new methods to gather, mine and analyze it. A key role has also been played by the latest advances in new disciplines like network science. Nonetheless, current models still lack a faithful representation of all possible heterogeneities and features that can be extracted from data. Here, we bridge a current gap in the mathematical modeling of infectious diseases and develop a framework that allows to account simultaneously for both the connectivity of individuals and the age-structure of the population. We compare different scenarios, namely, i) the homogeneous mixing setting, ii) one in which only the social mixing is taken into account, iii) a setting that considers the connectivity of individuals alone, and finally, iv) a multilayer representation in which both the social mixing and the number of contacts are included in the model. We analytically show that the thresholds obtained for these four scenarios are different. In addition, we conduct extensive numerical simulations and conclude that heterogeneities in the contact network are important for a proper determination of the epidemic threshold, whereas the age-structure plays a bigger role beyond the onset of the outbreak. Altogether, when it comes to evaluate interventions such as vaccination, both sources of individual heterogeneity are important and should be concurrently considered. Our results also provide an indication of the errors incurred in situations in which one cannot access all needed information in terms of connectivity and age of the population.
In this short technical report we model, within the Bayesian framework, the rate of positive tests reported by the the State of Indiana, accounting also for the substantial variability (and overdispeartion) in the daily count of the tests performed. The approach we take, results with a simple procedure for prediction, a posteriori, of this rate of positivity and allows for an easy and a straightforward adaptation by any agency tracking daily results of COVID-19 tests. The numerical results provided herein were obtained via an updatable R Markdown document.
Differential networks (DN) are important tools for modeling the changes in conditional dependencies between multiple samples. A Bayesian approach for estimating DNs, from the classical viewpoint, is introduced with a computationally efficient threshold selection for graphical model determination. The algorithm separately estimates the precision matrices of the DN using the Bayesian adaptive graphical lasso procedure. Synthetic experiments illustrate that the Bayesian DN performs exceptionally well in numerical accuracy and graphical structure determination in comparison to state-of-the-art methods. The proposed method is applied to South African COVID-$19$ data to investigate the change in DN structure between various phases of the pandemic.
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