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.

Attitudes of employees and employers towards older workers in a climate of anti-discrimination

Attitudes and practices towards older workers were surveyed in Brisbane with 525 employees randomly sampled from the electoral roll and executives of 104 companies obtained by stratified random sampling from the Register of Workplaces (response rates, 60% and 80% respectively). The results indicated that “older workers” are young in terms of contemporary life expectancy, and younger for employers than employees; they have some desirable personal qualities (eg. loyalty), but are not perceived as adaptable; workers aged 25–39 were preferred on qualities held to be important in the workplace and there was minimal interest in recruiting anyone over 45 years.

Free surface flow past topography : a beyond-all-orders approach

The problem of steady subcritical free surface flow past a submerged inclined step is considered. The asymptotic limit of small Froude number is treated, with particular emphasis on the effect that changing the angle of the step face has on the surface waves. As demonstrated by Chapman & Vanden-Broeck (2006), the divergence of a power series expansion in powers of the square of the Froude number is caused by singularities in the analytic continuation of the free surface; for an inclined step, these singularities may correspond to either the corners or stagnation points of the step, or both, depending on the angle of incline. Stokes lines emanate from these singularities, and exponentially small waves are switched on at the point the Stokes lines intersect with the free surface. Our results suggest that for a certain range of step angles, two wavetrains are switched on, but the exponentially subdominant one is switched on first, leading to an intermediate wavetrain not previously noted. We extend these ideas to the problem of flow over a submerged bump or trench, again with inclined sides. This time there may be two, three or four active Stokes lines, depending on the inclination angles. We demonstrate how to construct a base topography such that wave contributions from separate Stokes lines are of equal magnitude but opposite phase, thus cancelling out. Our asymptotic results are complemented by numerical solutions to the fully nonlinear equations.

Keeping friends safe : a prospective study examining early adolescent's confidence and support networks

There is a continued need to consider ways to prevent early adolescent engagement in a variety of harmful risk-taking behaviours for example, violence, road-related risks and alcohol use. The current prospective study examined adolescents’ reports of intervening to try and stop friends’ engagement in such behaviours among 207 early adolescents (mean age = 13.51 years, 50.1% females). Findings showed that intervening behaviour after three months was predicted by the confidence to intervene which in turn was predicted by student and teacher support although not parental support. The findings suggest that the benefits of positive relationship experiences might extend to the safety of early adolescent friendship groups particularly through the development of confidence to try and stop friends’ risky and dangerous behaviours. Findings from the study support the important role of the school in creating a culture of positive adolescent behaviour whereby young people take social responsibility.

How quantum theory is developing the field of information retrieval

This position paper provides an overview of work conducted and an outlook of future directions within the field of Information Retrieval (IR) that aims to develop novel models, methods and frameworks inspired by Quantum Theory (QT).

Automata modeling for cognitive interference in users' relevance judgement

Quantum theory has recently been employed to further advance the theory of information retrieval (IR). A challenging research topic is to investigate the so called quantum-like interference in users’ relevance judgement process, where users are involved to judge the relevance degree of each document with respect to a given query. In this process, users’ relevance judgement for the current document is often interfered by the judgement for previous documents, due to the interference on users’ cognitive status. Research from cognitive science has demonstrated some initial evidence of quantum-like cognitive interference in human decision making, which underpins the user’s relevance judgement process. This motivates us to model such cognitive interference in the relevance judgement process, which in our belief will lead to a better modeling and explanation of user behaviors in relevance judgement process for IR and eventually lead to more user-centric IR models. In this paper, we propose to use probabilistic automaton(PA) and quantum finite automaton (QFA), which are suitable to represent the transition of user judgement states, to dynamically model the cognitive interference when the user is judging a list of documents.

CgDN24 : a gene involved in hyphal development in the fungal phytopathogen Colletotrichum gloeosporioides

A cDNA corresponding to a transcript induced in culture by N starvation, was identified in Colletotrichum gloeosporioides by a differential hybridisation strategy. The cDNA comprised 905 bp and predicted a 215 aa protein; the gene encoding the cDNA was termed CgDN24. No function for CgDN24 could be predicted by database homology searches using the cDNA sequence and no homologues were found in the sequenced fungal genomes. Transcripts of CgDN24 were detected in infected leaves of Stylosanthes guianensis at stages of infection that corresponded with symptom development. The CgDN24 gene was disrupted by homologous recombination and this led to reduced radial growth rates and the production of hyphae with a hyperbranching phenotype. Normal sporulation was observed, and following conidial inoculation of S. guianensis, normal disease development was obtained. These results demonstrate that CgDN24 is necessary for normal hyphal development in axenic culture but dispensable for phytopathogenicity. © 2005 Elsevier GmbH. All rights reserved.

Comparison of three-dimensional profiles over time

In this paper, we describe an analysis for data collected on a three-dimensional spatial lattice with treatments applied at the horizontal lattice points. Spatial correlation is accounted for using a conditional autoregressive model. Observations are defined as neighbours only if they are at the same depth. This allows the corresponding variance components to vary by depth. We use the Markov chain Monte Carlo method with block updating, together with Krylov subspace methods, for efficient estimation of the model. The method is applicable to both regular and irregular horizontal lattices and hence to data collected at any set of horizontal sites for a set of depths or heights, for example, water column or soil profile data. The model for the three-dimensional data is applied to agricultural trial data for five separate days taken roughly six months apart in order to determine possible relationships over time. The purpose of the trial is to determine a form of cropping that leads to less moist soils in the root zone and beyond.We estimate moisture for each date, depth and treatment accounting for spatial correlation and determine relationships of these and other parameters over time.

A Bayesian analysis of an agricultural field trial with three spatial dimensions

Modern technology now has the ability to generate large datasets over space and time. Such data typically exhibit high autocorrelations over all dimensions. The field trial data motivating the methods of this paper were collected to examine the behaviour of traditional cropping and to determine a cropping system which could maximise water use for grain production while minimising leakage below the crop root zone. They consist of moisture measurements made at 15 depths across 3 rows and 18 columns, in the lattice framework of an agricultural field. Bayesian conditional autoregressive (CAR) models are used to account for local site correlations. Conditional autoregressive models have not been widely used in analyses of agricultural data. This paper serves to illustrate the usefulness of these models in this field, along with the ease of implementation in WinBUGS, a freely available software package. The innovation is the fitting of separate conditional autoregressive models for each depth layer, the ‘layered CAR model’, while simultaneously estimating depth profile functions for each site treatment. Modelling interest also lay in how best to model the treatment effect depth profiles, and in the choice of neighbourhood structure for the spatial autocorrelation model. The favoured model fitted the treatment effects as splines over depth, and treated depth, the basis for the regression model, as measured with error, while fitting CAR neighbourhood models by depth layer. It is hierarchical, with separate onditional autoregressive spatial variance components at each depth, and the fixed terms which involve an errors-in-measurement model treat depth errors as interval-censored measurement error. The Bayesian framework permits transparent specification and easy comparison of the various complex models compared.

A process evaluation of a comprehensive school based injury prevention program

A process evaluation enables understanding of critical issues that can inform the improved, ongoing implementation of an intervention program. This study describes the process evaluation of a comprehensive, multi-level injury prevention program for adolescents. The program targets change in injury associated with violence, transport and alcohol risks and incorporates two primary elements: an 8-week, teacher delivered attitude and behaviour change curriculum for Grade 8 students; and a professional development program for teachers on school level methods of protection, focusing on strategies to increase students’ connectedness to school.

"My friend was over the alcohol limit, so I asked him not to drive" : Young females intervening in alcohol-impaired driving

Potential to strengthen a commitment to intervene within a friendship group: – all knew the other passengers, – 3 in 4 discussed intervening with other passengers, – expectations of friends was a key predictive factor. - young women have potential and willingness to intervene in their friends’ drink driving behaviour - majority of campaigns and strategies to reduce alcohol related crashes target the driver however it is arguable that some strategies should target the young female passenger.

Hydrothermal syntheses of zeolite N from kaolin

Zeolite N, an EDI type framework structure with ideal chemical formula K12Al10Si10O40Cl2•5H2O, was produced from kaolin between 100oC and 200oC in a continuously stirred reactor using potassic and potassic+sodic liquors containing a range of anions. Reactions using liquors such as KOH, KOH + KX (where X = F, Cl, Br, I, NO3, NO2), K2X (where X=CO3), KOH + NaCl or NaOH + KCl were complete (>95% product) in less than two hours depending on the batch composition and temperature of reaction. With KOH and KCl in the reaction mixture and H2O/Al2O3~49, zeolite N was formed over a range of concentrations (1M < [KOH] < 18M) and reaction times (0.5h < t < 60h). At higher temperatures or higher KOH molarity, other potassic phases such as kalsilite or kaliophyllite formed. In general, temperature and KOH molarity defined the extent of zeolite N formation under these conditions. The introduction of sodic reagents to the starting mixture or use of one potassic reagent in the starting mixture reduced the stability field for zeolite N formation. Zeolite N was also formed using zeolite 4A as a source of Al and Si albeit for longer reaction times at a particular temperature when compared with kaolin as the source material.

Evolution of life drama program

Life Drama is a program of drama-based experiential learning activities involving groups of community leaders and members. The three-year project evolved from a theatre-in-education approach to an intercultural theatre approach incorporating Papua New Guinean performance traditions. It involved Australian, English and Papua New Guinean researchers at four key sites: Tari, Southern Highlands Province; Port Moresby, National Capital District; Madang, Madang Province; and Karkar Island, Madang Province. The project was innovative in a number of ways, including: a Participatory Action Research approach, involving community leaders at various levels as co-researchers; a participatory theatre approach as opposed to a performance approach; emphasis on sexual health promotion and HIV prevention through an experiential learning paradigm; addressing the norms and realities of the community rather than targeting only individual behaviour; an International Theatre Research Laboratory to explore the fusion of traditional cultural elements with contemporary health promotion aims; and an innovative method-assemblage approach to collecting and triangulating quantitative, qualitative, and performative data. The project attracted over $350,000 in funding and support from the Australian Research Council, National AIDS Secretariat in PNG, and private sector and non-government partners. Findings were presented at various conferences and symposia including the annual Medical Symposium in Wewak (2010), the triennial Research in Drama Education conference in Exeter (2011), and the International Research in Drama Education conference (Sydney 2009 and Limerick 2012). A number of peer-reviewed journal articles have been published. Elements of the program have been incorporated into the University of Goroka's compulsory HIV awareness program for undergraduate students. A national dissemination strategy for Life Drama in Papua New Guinea is now underway, with seed funding of AUD$74,000 from the National AIDS Council Secretariat, PNG.