Hierarchical models for 2D presence/absence data having ambiguous zeroes: With a biogeographical case study on dingo behaviour

This dissertation is primarily an applied statistical modelling investigation, motivated by a case study comprising real data and real questions. Theoretical questions on modelling and computation of normalization constants arose from pursuit of these data analytic questions. The essence of the thesis can be described as follows. Consider binary data observed on a two-dimensional lattice. A common problem with such data is the ambiguity of zeroes recorded. These may represent zero response given some threshold (presence) or that the threshold has not been triggered (absence). Suppose that the researcher wishes to estimate the effects of covariates on the binary responses, whilst taking into account underlying spatial variation, which is itself of some interest. This situation arises in many contexts and the dingo, cypress and toad case studies described in the motivation chapter are examples of this. Two main approaches to modelling and inference are investigated in this thesis. The first is frequentist and based on generalized linear models, with spatial variation modelled by using a block structure or by smoothing the residuals spatially. The EM algorithm can be used to obtain point estimates, coupled with bootstrapping or asymptotic MLE estimates for standard errors. The second approach is Bayesian and based on a three- or four-tier hierarchical model, comprising a logistic regression with covariates for the data layer, a binary Markov Random field (MRF) for the underlying spatial process, and suitable priors for parameters in these main models. The three-parameter autologistic model is a particular MRF of interest. Markov chain Monte Carlo (MCMC) methods comprising hybrid Metropolis/Gibbs samplers is suitable for computation in this situation. Model performance can be gauged by MCMC diagnostics. Model choice can be assessed by incorporating another tier in the modelling hierarchy. This requires evaluation of a normalization constant, a notoriously difficult problem. Difficulty with estimating the normalization constant for the MRF can be overcome by using a path integral approach, although this is a highly computationally intensive method. Different methods of estimating ratios of normalization constants (N Cs) are investigated, including importance sampling Monte Carlo (ISMC), dependent Monte Carlo based on MCMC simulations (MCMC), and reverse logistic regression (RLR). I develop an idea present though not fully developed in the literature, and propose the Integrated mean canonical statistic (IMCS) method for estimating log NC ratios for binary MRFs. The IMCS method falls within the framework of the newly identified path sampling methods of Gelman & Meng (1998) and outperforms ISMC, MCMC and RLR. It also does not rely on simplifying assumptions, such as ignoring spatio-temporal dependence in the process. A thorough investigation is made of the application of IMCS to the three-parameter Autologistic model. This work introduces background computations required for the full implementation of the four-tier model in Chapter 7. Two different extensions of the three-tier model to a four-tier version are investigated. The first extension incorporates temporal dependence in the underlying spatio-temporal process. The second extensions allows the successes and failures in the data layer to depend on time. The MCMC computational method is extended to incorporate the extra layer. A major contribution of the thesis is the development of a fully Bayesian approach to inference for these hierarchical models for the first time. Note: The author of this thesis has agreed to make it open access but invites people downloading the thesis to send her an email via the 'Contact Author' function.

Spatial analysis of notified dengue fever infections

This study aimed to investigate the spatial clustering and dynamic dispersion of dengue incidence in Queensland, Australia. We used Moran’s I statistic to assess the spatial autocorrelation of reported dengue cases. Spatial empirical Bayes smoothing estimates were used to display the spatial distribution of dengue in postal areas throughout Queensland. Local indicators of spatial association (LISA) maps and logistic regression models were used to identify spatial clusters and examine the spatio-temporal patterns of the spread of dengue. The results indicate that the spatial distribution of dengue was clustered during each of the three periods of 1993–1996, 1997–2000 and 2001–2004. The high-incidence clusters of dengue were primarily concentrated in the north of Queensland and low-incidence clusters occurred in the south-east of Queensland. The study concludes that the geographical range of notified dengue cases has significantly expanded in Queensland over recent years.

Hierarchical Bayesian models for estimating the extent of plant pest invasions

Plant biosecurity requires statistical tools to interpret field surveillance data in order to manage pest incursions that threaten crop production and trade. Ultimately, management decisions need to be based on the probability that an area is infested or free of a pest. Current informal approaches to delimiting pest extent rely upon expert ecological interpretation of presence / absence data over space and time. Hierarchical Bayesian models provide a cohesive statistical framework that can formally integrate the available information on both pest ecology and data. The overarching method involves constructing an observation model for the surveillance data, conditional on the hidden extent of the pest and uncertain detection sensitivity. The extent of the pest is then modelled as a dynamic invasion process that includes uncertainty in ecological parameters. Modelling approaches to assimilate this information are explored through case studies on spiralling whitefly, Aleurodicus dispersus and red banded mango caterpillar, Deanolis sublimbalis. Markov chain Monte Carlo simulation is used to estimate the probable extent of pests, given the observation and process model conditioned by surveillance data. Statistical methods, based on time-to-event models, are developed to apply hierarchical Bayesian models to early detection programs and to demonstrate area freedom from pests. The value of early detection surveillance programs is demonstrated through an application to interpret surveillance data for exotic plant pests with uncertain spread rates. The model suggests that typical early detection programs provide a moderate reduction in the probability of an area being infested but a dramatic reduction in the expected area of incursions at a given time. Estimates of spiralling whitefly extent are examined at local, district and state-wide scales. The local model estimates the rate of natural spread and the influence of host architecture, host suitability and inspector efficiency. These parameter estimates can support the development of robust surveillance programs. Hierarchical Bayesian models for the human-mediated spread of spiralling whitefly are developed for the colonisation of discrete cells connected by a modified gravity model. By estimating dispersal parameters, the model can be used to predict the extent of the pest over time. An extended model predicts the climate restricted distribution of the pest in Queensland. These novel human-mediated movement models are well suited to demonstrating area freedom at coarse spatio-temporal scales. At finer scales, and in the presence of ecological complexity, exploratory models are developed to investigate the capacity for surveillance information to estimate the extent of red banded mango caterpillar. It is apparent that excessive uncertainty about observation and ecological parameters can impose limits on inference at the scales required for effective management of response programs. The thesis contributes novel statistical approaches to estimating the extent of pests and develops applications to assist decision-making across a range of plant biosecurity surveillance activities. Hierarchical Bayesian modelling is demonstrated as both a useful analytical tool for estimating pest extent and a natural investigative paradigm for developing and focussing biosecurity programs.

Hierarchical Bayesian modelling of early detection surveillance for plant pest invasions

Early detection surveillance programs aim to find invasions of exotic plant pests and diseases before they are too widespread to eradicate. However, the value of these programs can be difficult to justify when no positive detections are made. To demonstrate the value of pest absence information provided by these programs, we use a hierarchical Bayesian framework to model estimates of incursion extent with and without surveillance. A model for the latent invasion process provides the baseline against which surveillance data are assessed. Ecological knowledge and pest management criteria are introduced into the model using informative priors for invasion parameters. Observation models assimilate information from spatio-temporal presence/absence data to accommodate imperfect detection and generate posterior estimates of pest extent. When applied to an early detection program operating in Queensland, Australia, the framework demonstrates that this typical surveillance regime provides a modest reduction in the estimate that a surveyed district is infested. More importantly, the model suggests that early detection surveillance programs can provide a dramatic reduction in the putative area of incursion and therefore offer a substantial benefit to incursion management. By mapping spatial estimates of the point probability of infestation, the model identifies where future surveillance resources can be most effectively deployed.

Stochastic simulation of chemical reactions in spatially complex media

Discrete stochastic simulations, via techniques such as the Stochastic Simulation Algorithm (SSA) are a powerful tool for understanding the dynamics of chemical kinetics when there are low numbers of certain molecular species. However, an important constraint is the assumption of well-mixedness and homogeneity. In this paper, we show how to use Monte Carlo simulations to estimate an anomalous diffusion parameter that encapsulates the crowdedness of the spatial environment. We then use this parameter to replace the rate constants of bimolecular reactions by a time-dependent power law to produce an SSA valid in cases where anomalous diffusion occurs or the system is not well-mixed (ASSA). Simulations then show that ASSA can successfully predict the temporal dynamics of chemical kinetics in a spatially constrained environment.

Using Bayesian methods for the estimation of uncertainty in complex statistical models

The research objectives of this thesis were to contribute to Bayesian statistical methodology by contributing to risk assessment statistical methodology, and to spatial and spatio-temporal methodology, by modelling error structures using complex hierarchical models. Specifically, I hoped to consider two applied areas, and use these applications as a springboard for developing new statistical methods as well as undertaking analyses which might give answers to particular applied questions. Thus, this thesis considers a series of models, firstly in the context of risk assessments for recycled water, and secondly in the context of water usage by crops. The research objective was to model error structures using hierarchical models in two problems, namely risk assessment analyses for wastewater, and secondly, in a four dimensional dataset, assessing differences between cropping systems over time and over three spatial dimensions. The aim was to use the simplicity and insight afforded by Bayesian networks to develop appropriate models for risk scenarios, and again to use Bayesian hierarchical models to explore the necessarily complex modelling of four dimensional agricultural data. The specific objectives of the research were to develop a method for the calculation of credible intervals for the point estimates of Bayesian networks; to develop a model structure to incorporate all the experimental uncertainty associated with various constants thereby allowing the calculation of more credible credible intervals for a risk assessment; to model a single day’s data from the agricultural dataset which satisfactorily captured the complexities of the data; to build a model for several days’ data, in order to consider how the full data might be modelled; and finally to build a model for the full four dimensional dataset and to consider the timevarying nature of the contrast of interest, having satisfactorily accounted for possible spatial and temporal autocorrelations. This work forms five papers, two of which have been published, with two submitted, and the final paper still in draft. The first two objectives were met by recasting the risk assessments as directed, acyclic graphs (DAGs). In the first case, we elicited uncertainty for the conditional probabilities needed by the Bayesian net, incorporated these into a corresponding DAG, and used Markov chain Monte Carlo (MCMC) to find credible intervals, for all the scenarios and outcomes of interest. In the second case, we incorporated the experimental data underlying the risk assessment constants into the DAG, and also treated some of that data as needing to be modelled as an ‘errors-invariables’ problem [Fuller, 1987]. This illustrated a simple method for the incorporation of experimental error into risk assessments. In considering one day of the three-dimensional agricultural data, it became clear that geostatistical models or conditional autoregressive (CAR) models over the three dimensions were not the best way to approach the data. Instead CAR models are used with neighbours only in the same depth layer. This gave flexibility to the model, allowing both the spatially structured and non-structured variances to differ at all depths. We call this model the CAR layered model. Given the experimental design, the fixed part of the model could have been modelled as a set of means by treatment and by depth, but doing so allows little insight into how the treatment effects vary with depth. Hence, a number of essentially non-parametric approaches were taken to see the effects of depth on treatment, with the model of choice incorporating an errors-in-variables approach for depth in addition to a non-parametric smooth. The statistical contribution here was the introduction of the CAR layered model, the applied contribution the analysis of moisture over depth and estimation of the contrast of interest together with its credible intervals. These models were fitted using WinBUGS [Lunn et al., 2000]. The work in the fifth paper deals with the fact that with large datasets, the use of WinBUGS becomes more problematic because of its highly correlated term by term updating. In this work, we introduce a Gibbs sampler with block updating for the CAR layered model. The Gibbs sampler was implemented by Chris Strickland using pyMCMC [Strickland, 2010]. This framework is then used to consider five days data, and we show that moisture in the soil for all the various treatments reaches levels particular to each treatment at a depth of 200 cm and thereafter stays constant, albeit with increasing variances with depth. In an analysis across three spatial dimensions and across time, there are many interactions of time and the spatial dimensions to be considered. Hence, we chose to use a daily model and to repeat the analysis at all time points, effectively creating an interaction model of time by the daily model. Such an approach allows great flexibility. However, this approach does not allow insight into the way in which the parameter of interest varies over time. Hence, a two-stage approach was also used, with estimates from the first-stage being analysed as a set of time series. We see this spatio-temporal interaction model as being a useful approach to data measured across three spatial dimensions and time, since it does not assume additivity of the random spatial or temporal effects.

Controlled drift: an investigation into the controllability of underwater vehicles with minimal actuation

This paper is directed towards providing an answer to the question, ”Can you control the trajectory of a Lagrangian float?” Being a float that has minimal actuation (only buoyancy control), their horizontal trajectory is dictated through drifting with ocean currents. However, with the appropriate vertical actuation and utilising spatio-temporal variations in water speed and direction, we show here that broad controllabilty results can be met such as waypoint following to keep a float inside of a bay or out of a designated region. This paper extends theory experimen- tally evaluted on horizontally actuated Autonomous Underwater Vehicles (AUVs) for trajectory control utilising ocean forecast models and presents an initial investi- gation into the controllability of these minimally actuated drifting AUVs. Simulated results for offshore coastal and within highly dynamic tidal bays illustrate two tech- niques with the promise for an affirmative answer to the posed question above.

When There's Love

This work is an installation featuring three video projections, music and mirror balls. The three projections fill the walls with scrolling text borrowed from love song lyrics. Headphones in the gallery space allow you to hear a male voice sing the same words to an impromptu tune. Mirror balls send fragments of light spinning around the room while The Righteous Brothers’ Unchained Melody plays on repeat. This work emphasizes fragmentary, repetitious and spatio-temporal experiences of language in order to question the symbolic conventions of romance. By exaggerating and mixing hackneyed symbolic elements, this work extends on some of Nicolas Bourriaud’s theoretical insights into the creative and critical strategies of ‘postproduction’. In particular, it toys with the intersections between popular culture and inter-subjective experiences.

Estimating the effects of environmental exposures using a weighted mean of monitoring stations

The health effects of environmental hazards are often examined using time series of the association between a daily response variable (e.g., death) and a daily level of exposure (e.g., temperature). Exposures are usually the average from a network of stations. This gives each station equal importance, and negates the opportunity for some stations to be better measures of exposure. We used a Bayesian hierarchical model that weighted stations using random variables between zero and one. We compared the weighted estimates to the standard model using data on health outcomes (deaths and hospital admissions) and exposures (air pollution and temperature) in Brisbane, Australia. The improvements in model fit were relatively small, and the estimated health effects of pollution were similar using either the standard or weighted estimates. Spatial weighted exposures would be probably more worthwhile when there is either greater spatial detail in the health outcome, or a greater spatial variation in exposure.

Solution methods for advection-diffusion-reaction equations on growing domains and subdomains, with application to modelling skin substitutes

Problems involving the solution of advection-diffusion-reaction equations on domains and subdomains whose growth affects and is affected by these equations, commonly arise in developmental biology. Here, a mathematical framework for these situations, together with methods for obtaining spatio-temporal solutions and steady states of models built from this framework, is presented. The framework and methods are applied to a recently published model of epidermal skin substitutes. Despite the use of Eulerian schemes, excellent agreement is obtained between the numerical spatio-temporal, numerical steady state, and analytical solutions of the model.

Semi-parametric modelling of ultrafine particle number concentration

Quantifying spatial and/or temporal trends in environmental modelling data requires that measurements be taken at multiple sites. The number of sites and duration of measurement at each site must be balanced against costs of equipment and availability of trained staff. The split panel design comprises short measurement campaigns at multiple locations and continuous monitoring at reference sites [2]. Here we present a modelling approach for a spatio-temporal model of ultrafine particle number concentration (PNC) recorded according to a split panel design. The model describes the temporal trends and background levels at each site. The data were measured as part of the “Ultrafine Particles from Transport Emissions and Child Health” (UPTECH) project which aims to link air quality measurements, child health outcomes and a questionnaire on the child’s history and demographics. The UPTECH project involves measuring aerosol and particle counts and local meteorology at each of 25 primary schools for two weeks and at three long term monitoring stations, and health outcomes for a cohort of students at each school [3].

Digital technologies and musical participation for people with intellectual disabilities

Research on the aspirations of people with intellectual disabilities documents the importance of alternative zones of inclusion where they can assert their own definitions of ability and normality. This stands in contrast to assumptions concerning technology and disability that position technology as ‘normalising’ the disabled body. This paper reports on the role of a digital music jamming tool in providing access to creative practice by people with intellectual disabilities. The tool contributed to the development of a spatio-temporal zone to enable aesthetic agency within and beyond the contexts of deinstitutionalised care. The research identifies the interactions among tools, individuals and groups that facilitated participants’ agency in shaping the form of musical practice. Further, we document the properties of emergent interaction - supported by a tool oriented to enabling music improvisation - as potentially resisting assumptions regarding normalisation.

Surveillance of dengue fever virus: a review of epidemiological models and early warning systems

Dengue fever is one of the world’s most important vector-borne diseases. The transmission area of this disease continues to expand due to many factors including urban sprawl, increased travel and global warming. Current preventative techniques are primarily based on controlling mosquito vectors as other prophylactic measures, such as a tetravalent vaccine are unlikely to be available in the foreseeable future. However, the continually increasing dengue incidence suggests that this strategy alone is not sufficient. Epidemiological models attempt to predict future outbreaks using information on the risk factors of the disease. Through a systematic literature review, this paper aims at analyzing the different modeling methods and their outputs in terms of accurately predicting disease outbreaks. We found that many previous studies have not sufficiently accounted for the spatio-temporal features of the disease in the modeling process. Yet with advances in technology, the ability to incorporate such information as well as the socio-environmental aspect allowed for its use as an early warning system, albeit limited geographically to a local scale.

Review of statistical methods for disease mapping

Cancer poses an undeniable burden to the health and wellbeing of the Australian community. In a recent report commissioned by the Australian Institute for Health and Welfare(AIHW, 2010), one in every two Australians on average will be diagnosed with cancer by the age of 85, making cancer the second leading cause of death in 2007, preceded only by cardiovascular disease. Despite modest decreases in standardised combined cancer mortality over the past few decades, in part due to increased funding and access to screening programs, cancer remains a significant economic burden. In 2010, all cancers accounted for an estimated 19% of the country's total burden of disease, equating to approximately $3:8 billion in direct health system costs (Cancer Council Australia, 2011). Furthermore, there remains established socio-economic and other demographic inequalities in cancer incidence and survival, for example, by indigenous status and rurality. Therefore, in the interests of the nation's health and economic management, there is an immediate need to devise data-driven strategies to not only understand the socio-economic drivers of cancer but also facilitate the implementation of cost-effective resource allocation for cancer management...