A Bayesian network approach to modelling temporal behaviour of Lyngbya majuscula bloom initiation

Lyngbya majuscula is a cyanobacterium (blue-green algae) occurring naturally in tropical and subtropical coastal areas worldwide. Deception Bay, in Northern Moreton Bay, Queensland, has a history of Lyngbya blooms, and forms a case study for this investigation. The South East Queensland (SEQ) Healthy Waterways Partnership, collaboration between government, industry, research and the community, was formed to address issues affecting the health of the river catchments and waterways of South East Queensland. The Partnership coordinated the Lyngbya Research and Management Program (2005-2007) which culminated in a Coastal Algal Blooms (CAB) Action Plan for harmful and nuisance algal blooms, such as Lyngbya majuscula. This first phase of the project was predominantly of a scientific nature and also facilitated the collection of additional data to better understand Lyngbya blooms. The second phase of this project, SEQ Healthy Waterways Strategy 2007-2012, is now underway to implement the CAB Action Plan and as such is more management focussed. As part of the first phase of the project, a Science model for the initiation of a Lyngbya bloom was built using Bayesian Networks (BN). The structure of the Science Bayesian Network was built by the Lyngbya Science Working Group (LSWG) which was drawn from diverse disciplines. The BN was then quantified with annual data and expert knowledge. Scenario testing confirmed the expected temporal nature of bloom initiation and it was recommended that the next version of the BN be extended to take this into account. Elicitation for this BN thus occurred at three levels: design, quantification and verification. The first level involved construction of the conceptual model itself, definition of the nodes within the model and identification of sources of information to quantify the nodes. The second level included elicitation of expert opinion and representation of this information in a form suitable for inclusion in the BN. The third and final level concerned the specification of scenarios used to verify the model. The second phase of the project provides the opportunity to update the network with the newly collected detailed data obtained during the previous phase of the project. Specifically the temporal nature of Lyngbya blooms is of interest. Management efforts need to be directed to the most vulnerable periods to bloom initiation in the Bay. To model the temporal aspects of Lyngbya we are using Object Oriented Bayesian networks (OOBN) to create ‘time slices’ for each of the periods of interest during the summer. OOBNs provide a framework to simplify knowledge representation and facilitate reuse of nodes and network fragments. An OOBN is more hierarchical than a traditional BN with any sub-network able to contain other sub-networks. Connectivity between OOBNs is an important feature and allows information flow between the time slices. This study demonstrates more sophisticated use of expert information within Bayesian networks, which combine expert knowledge with data (categorized using expert-defined thresholds) within an expert-defined model structure. Based on the results from the verification process the experts are able to target areas requiring greater precision and those exhibiting temporal behaviour. The time slices incorporate the data for that time period for each of the temporal nodes (instead of using the annual data from the previous static Science BN) and include lag effects to allow the effect from one time slice to flow to the next time slice. We demonstrate a concurrent steady increase in the probability of initiation of a Lyngbya bloom and conclude that the inclusion of temporal aspects in the BN model is consistent with the perceptions of Lyngbya behaviour held by the stakeholders. This extended model provides a more accurate representation of the increased risk of algal blooms in the summer months and show that the opinions elicited to inform a static BN can be readily extended to a dynamic OOBN, providing more comprehensive information for decision makers.

A Bayesian regression approach to assess uncertainty in pollutant wash-off modelling

Due to knowledge gaps in relation to urban stormwater quality processes, an in-depth understanding of model uncertainty can enhance decision making. Uncertainty in stormwater quality models can originate from a range of sources such as the complexity of urban rainfall-runoff-stormwater pollutant processes and the paucity of observed data. Unfortunately, studies relating to epistemic uncertainty, which arises from the simplification of reality are limited and often deemed mostly unquantifiable. This paper presents a statistical modelling framework for ascertaining epistemic uncertainty associated with pollutant wash-off under a regression modelling paradigm using Ordinary Least Squares Regression (OLSR) and Weighted Least Squares Regression (WLSR) methods with a Bayesian/Gibbs sampling statistical approach. The study results confirmed that WLSR assuming probability distributed data provides more realistic uncertainty estimates of the observed and predicted wash-off values compared to OLSR modelling. It was also noted that the Bayesian/Gibbs sampling approach is superior compared to the most commonly adopted classical statistical and deterministic approaches commonly used in water quality modelling. The study outcomes confirmed that the predication error associated with wash-off replication is relatively higher due to limited data availability. The uncertainty analysis also highlighted the variability of the wash-off modelling coefficient k as a function of complex physical processes, which is primarily influenced by surface characteristics and rainfall intensity.

A Hybrid Queue-based Bayesian Network framework for passenger facilitation modelling

This paper presents a novel framework for the modelling of passenger facilitation in a complex environment. The research is motivated by the challenges in the airport complex system, where there are multiple stakeholders, differing operational objectives and complex interactions and interdependencies between different parts of the airport system. Traditional methods for airport terminal modelling do not explicitly address the need for understanding causal relationships in a dynamic environment. Additionally, existing Bayesian Network (BN) models, which provide a means for capturing causal relationships, only present a static snapshot of a system. A method to integrate a BN complex systems model with stochastic queuing theory is developed based on the properties of the Poisson and exponential distributions. The resultant Hybrid Queue-based Bayesian Network (HQBN) framework enables the simulation of arbitrary factors, their relationships, and their effects on passenger flow and vice versa. A case study implementation of the framework is demonstrated on the inbound passenger facilitation process at Brisbane International Airport. The predicted outputs of the model, in terms of cumulative passenger flow at intermediary and end points in the inbound process, are found to have an R2 goodness of fit of 0.9994 and 0.9982 respectively over a 10 h test period. The utility of the framework is demonstrated on a number of usage scenarios including causal analysis and ‘what-if’ analysis. This framework provides the ability to analyse and simulate a dynamic complex system, and can be applied to other socio-technical systems such as hospitals.

Spatio-temporal modelling of cancer data in Queensland using Bayesian methods

Cancer is the leading contributor to the disease burden in Australia. This thesis develops and applies Bayesian hierarchical models to facilitate an investigation of the spatial and temporal associations for cancer diagnosis and survival among Queenslanders. The key objectives are to document and quantify the importance of spatial inequalities, explore factors influencing these inequalities, and investigate how spatial inequalities change over time. Existing Bayesian hierarchical models are refined, new models and methods developed, and tangible benefits obtained for cancer patients in Queensland. The versatility of using Bayesian models in cancer control are clearly demonstrated through these detailed and comprehensive analyses.

Bayesian approach to signal modelling

In this paper, an introduction to Bayesian methods in signal processing will be given. The paper starts by considering the important issues of model selection and parameter estimation and derives analytic expressions for the model probabilities of two simple models. The idea of marginal estimation of certain model parameter is then introduced and expressions are derived for the marginal probability densities for frequencies in white Gaussian noise and a Bayesian approach to general changepoint analysis is given. Numerical integration methods are introduced based on Markov chain Monte Carlo techniques and the Gibbs sampler in particular.

The Bayesian Approach to Signal Modelling

In this paper, an introduction to Bayesian methods in signal processing will be given. The paper starts by considering the important issues of model selection and parameter estimation and derives analytic expressions for the model probabilities of two simple models. The idea of marginal estimation of certain model parameter is then introduced and expressions are derived for the marginal probabilitiy densities for frequencies in white Gaussian noise and a Bayesian approach to general changepoint analysis is given. Numerical integration methods are introduced based on Markov chain Monte Carlo techniques and the Gibbs sampler in particular.

Bayesian estimation of simultaneous musical notes based on frequency domain modelling

This paper proposes a Bayesian method for polyphonic music description. The method first divides an input audio signal into a series of sections called snapshots, and then estimates parameters such as fundamental frequencies and amplitudes of the notes contained in each snapshot. The parameter estimation process is based on a frequency domain modelling and Gibbs sampling. Experimental results obtained from audio signals of test note patterns are encouraging; the accuracy is better than 80% for the estimation of fundamental frequencies in terms of semitones and instrument names when the number of simultaneous notes is two.

Causality enabled compositional modelling of Bayesian networks

J. Keppens and Q. Shen. Causality enabled compositional modelling of Bayesian networks. Proceedings of the 18th International Workshop on Qualitative Reasoning, pages 33-40, 2004.

Adaptive Mixture Modelling Metropolis Methods for Bayesian Analysis of Non-linear State-Space Models.

We describe a strategy for Markov chain Monte Carlo analysis of non-linear, non-Gaussian state-space models involving batch analysis for inference on dynamic, latent state variables and fixed model parameters. The key innovation is a Metropolis-Hastings method for the time series of state variables based on sequential approximation of filtering and smoothing densities using normal mixtures. These mixtures are propagated through the non-linearities using an accurate, local mixture approximation method, and we use a regenerating procedure to deal with potential degeneracy of mixture components. This provides accurate, direct approximations to sequential filtering and retrospective smoothing distributions, and hence a useful construction of global Metropolis proposal distributions for simulation of posteriors for the set of states. This analysis is embedded within a Gibbs sampler to include uncertain fixed parameters. We give an example motivated by an application in systems biology. Supplemental materials provide an example based on a stochastic volatility model as well as MATLAB code.