Integrating science through Bayesian Belief Networks : case study of Lyngbya in Moreton Bay

Bayesian Belief Networks (BBNs) are emerging as valuable tools for investigating complex ecological problems. In a BBN, the important variables in a problem are identified and causal relationships are represented graphically. Underpinning this is the probabilistic framework in which variables can take on a finite range of mutually exclusive states. Associated with each variable is a conditional probability table (CPT), showing the probability of a variable attaining each of its possible states conditioned on all possible combinations of it parents. Whilst the variables (nodes) are connected, the CPT attached to each node can be quantified independently. This allows each variable to be populated with the best data available, including expert opinion, simulation results or observed data. It also allows the information to be easily updated as better data become available ----- ----- This paper reports on the process of developing a BBN to better understand the initial rapid growth phase (initiation) of a marine cyanobacterium, Lyngbya majuscula, in Moreton Bay, Queensland. Anecdotal evidence suggests that Lyngbya blooms in this region have increased in severity and extent over the past decade. Lyngbya has been associated with acute dermatitis and a range of other health problems in humans. Blooms have been linked to ecosystem degradation and have also damaged commercial and recreational fisheries. However, the causes of blooms are as yet poorly understood.

Bayesian versus frequentist statistical inference for investi gating a one-off cancer cluster reported to a health department

Background The problem of silent multiple comparisons is one of the most difficult statistical problems faced by scientists. It is a particular problem for investigating a one-off cancer cluster reported to a health department because any one of hundreds, or possibly thousands, of neighbourhoods, schools, or workplaces could have reported a cluster, which could have been for any one of several types of cancer or any one of several time periods. Methods This paper contrasts the frequentist approach with a Bayesian approach for dealing with silent multiple comparisons in the context of a one-off cluster reported to a health department. Two published cluster investigations were re-analysed using the Dunn-Sidak method to adjust frequentist p-values and confidence intervals for silent multiple comparisons. Bayesian methods were based on the Gamma distribution. Results Bayesian analysis with non-informative priors produced results similar to the frequentist analysis, and suggested that both clusters represented a statistical excess. In the frequentist framework, the statistical significance of both clusters was extremely sensitive to the number of silent multiple comparisons, which can only ever be a subjective "guesstimate". The Bayesian approach is also subjective: whether there is an apparent statistical excess depends on the specified prior. Conclusion In cluster investigations, the frequentist approach is just as subjective as the Bayesian approach, but the Bayesian approach is less ambitious in that it treats the analysis as a synthesis of data and personal judgements (possibly poor ones), rather than objective reality. Bayesian analysis is (arguably) a useful tool to support complicated decision-making, because it makes the uncertainty associated with silent multiple comparisons explicit.

Bayesian model averaging for harmful algal bloom prediction

Harmful Algal Blooms (HABs) are a worldwide problem that have been increasing in frequency and extent over the past several decades. HABs severely damage aquatic ecosystems by destroying benthic habitat, reducing invertebrate and fish populations and affecting larger species such as dugong that rely on seagrasses for food. Few statistical models for predicting HAB occurrences have been developed, and in common with most predictive models in ecology, those that have been developed do not fully account for uncertainties in parameters and model structure. This makes management decisions based on these predictions more risky than might be supposed. We used a probit time series model and Bayesian Model Averaging (BMA) to predict occurrences of blooms of Lyngbya majuscula, a toxic cyanophyte, in Deception Bay, Queensland, Australia. We found a suite of useful predictors for HAB occurrence, with Temperature figuring prominently in models with the majority of posterior support, and a model consisting of the single covariate average monthly minimum temperature showed by far the greatest posterior support. A comparison of alternative model averaging strategies was made with one strategy using the full posterior distribution and a simpler approach that utilised the majority of the posterior distribution for predictions but with vastly fewer models. Both BMA approaches showed excellent predictive performance with little difference in their predictive capacity. Applications of BMA are still rare in ecology, particularly in management settings. This study demonstrates the power of BMA as an important management tool that is capable of high predictive performance while fully accounting for both parameter and model uncertainty.

A fully Bayesian approach to inference for Coxian phase-type distributions with covariate dependent mean

Phase-type distributions represent the time to absorption for a finite state Markov chain in continuous time, generalising the exponential distribution and providing a flexible and useful modelling tool. We present a new reversible jump Markov chain Monte Carlo scheme for performing a fully Bayesian analysis of the popular Coxian subclass of phase-type models; the convenient Coxian representation involves fewer parameters than a more general phase-type model. The key novelty of our approach is that we model covariate dependence in the mean whilst using the Coxian phase-type model as a very general residual distribution. Such incorporation of covariates into the model has not previously been attempted in the Bayesian literature. A further novelty is that we also propose a reversible jump scheme for investigating structural changes to the model brought about by the introduction of Erlang phases. Our approach addresses more questions of inference than previous Bayesian treatments of this model and is automatic in nature. We analyse an example dataset comprising lengths of hospital stays of a sample of patients collected from two Australian hospitals to produce a model for a patient's expected length of stay which incorporates the effects of several covariates. This leads to interesting conclusions about what contributes to length of hospital stay with implications for hospital planning. We compare our results with an alternative classical analysis of these data.

Use of Bayesian geostatistical prediction to estimate local variations in Schistosoma haematobium infection in western Africa

Objective We aimed to predict sub-national spatial variation in numbers of people infected with Schistosoma haematobium, and associated uncertainties, in Burkina Faso, Mali and Niger, prior to implementation of national control programmes. Methods We used national field survey datasets covering a contiguous area 2,750 × 850 km, from 26,790 school-aged children (5–14 years) in 418 schools. Bayesian geostatistical models were used to predict prevalence of high and low intensity infections and associated 95% credible intervals (CrI). Numbers infected were determined by multiplying predicted prevalence by numbers of school-aged children in 1 km2 pixels covering the study area. Findings Numbers of school-aged children with low-intensity infections were: 433,268 in Burkina Faso, 872,328 in Mali and 580,286 in Niger. Numbers with high-intensity infections were: 416,009 in Burkina Faso, 511,845 in Mali and 254,150 in Niger. 95% CrIs (indicative of uncertainty) were wide; e.g. the mean number of boys aged 10–14 years infected in Mali was 140,200 (95% CrI 6200, 512,100). Conclusion National aggregate estimates for numbers infected mask important local variation, e.g. most S. haematobium infections in Niger occur in the Niger River valley. Prevalence of high-intensity infections was strongly clustered in foci in western and central Mali, north-eastern and northwestern Burkina Faso and the Niger River valley in Niger. Populations in these foci are likely to carry the bulk of the urinary schistosomiasis burden and should receive priority for schistosomiasis control. Uncertainties in predicted prevalence and numbers infected should be acknowledged and taken into consideration by control programme planners.