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.

Characterisation and source identification of selected pollutants in house dust

House dust is a heterogeneous matrix, which contains a number of biological materials and particulate matter gathered from several sources. It is the accumulation of a number of semi-volatile and non-volatile contaminants. The contaminants are trapped and preserved. Therefore, house dust can be viewed as an archive of both the indoor and outdoor air pollution. There is evidence to show that on average, people tend to stay indoors most of the time and this increases exposure to house dust. The aims of this investigation were to: " assess the levels of Polycyclic Aromatic Hydrocarbons (PAHs), elements and pesticides in the indoor environment of the Brisbane area; " identify and characterise the possible sources of elemental constituents (inorganic elements), PAHs and pesticides by means of Positive Matrix Factorisation (PMF); and " establish the correlations between the levels of indoor air pollutants (PAHs, elements and pesticides) with the external and internal characteristics or attributes of the buildings and indoor activities by means of multivariate data analysis techniques. The dust samples were collected during the period of 2005-2007 from homes located in different suburbs of Brisbane, Ipswich and Toowoomba, in South East Queensland, Australia. A vacuum cleaner fitted with a paper bag was used as a sampler for collecting the house dust. A survey questionnaire was filled by the house residents which contained information about the indoor and outdoor characteristics of their residences. House dust samples were analysed for three different pollutants: Pesticides, Elements and PAHs. The analyses were carried-out for samples of particle size less than 250 µm. The chemical analyses for both pesticides and PAHs were performed using a Gas Chromatography Mass Spectrometry (GC-MS), while elemental analysis was carried-out by using Inductively-Coupled Plasma-Mass Spectroscopy (ICP-MS). The data was subjected to multivariate data analysis techniques such as multi-criteria decision-making procedures, Preference Ranking Organisation Method for Enrichment Evaluations (PROMETHEE), coupled with Geometrical Analysis for Interactive Aid (GAIA) in order to rank the samples and to examine data display. This study showed that compared to the results from previous works, which were carried-out in Australia and overseas, the concentrations of pollutants in house dusts in Brisbane and the surrounding areas were relatively very high. The results of this work also showed significant correlations between some of the physical parameters (types of building material, floor level, distance from industrial areas and major road, and smoking) and the concentrations of pollutants. Types of building materials and the age of houses were found to be two of the primary factors that affect the concentrations of pesticides and elements in house dust. The concentrations of these two types of pollutant appear to be higher in old houses (timber houses) than in the brick ones. In contrast, the concentrations of PAHs were noticed to be higher in brick houses than in the timber ones. Other factors such as floor level, and distance from the main street and industrial area, also affected the concentrations of pollutants in the house dust samples. To apportion the sources and to understand mechanisms of pollutants, Positive Matrix Factorisation (PMF) receptor model was applied. The results showed that there were significant correlations between the degree of concentration of contaminants in house dust and the physical characteristics of houses, such as the age and the type of the house, the distance from the main road and industrial areas, and smoking. Sources of pollutants were identified. For PAHs, the sources were cooking activities, vehicle emissions, smoking, oil fumes, natural gas combustion and traces of diesel exhaust emissions; for pesticides the sources were application of pesticides for controlling termites in buildings and fences, treating indoor furniture and in gardens for controlling pests attacking horticultural and ornamental plants; for elements the sources were soil, cooking, smoking, paints, pesticides, combustion of motor fuels, residual fuel oil, motor vehicle emissions, wearing down of brake linings and industrial activities.

Extreme architecture : can architects future proof us against fire and flood.

In the face of Australia’s disaster-prone environment, architects Ian Weir and James Davidson are reconceptualising how our residential buildings might become more resilient to fire, flood and cyclone. With their first-hand experience of natural disasters, James, director of Emergency Architects Australia (EAA), and Ian, one of Australia’s few ‘bushfire architects’, discuss the ways we can design with disaster in mind. Dr Ian Weir is one of Australia’s few ‘bushfire architects’. Exploring a holistic ‘ground up’ approach to bushfire where landscape, building design and habitation patterns are orchestrated to respond to site-specific fire characteristics. Ian’s research is developed through design studio teaching at QUT and through built works in Western Australia’s fire prone forests and heathlands.

Bayesian algorithms with applications

Advances in algorithms for approximate sampling from a multivariable target function have led to solutions to challenging statistical inference problems that would otherwise not be considered by the applied scientist. Such sampling algorithms are particularly relevant to Bayesian statistics, since the target function is the posterior distribution of the unobservables given the observables. In this thesis we develop, adapt and apply Bayesian algorithms, whilst addressing substantive applied problems in biology and medicine as well as other applications. For an increasing number of high-impact research problems, the primary models of interest are often sufficiently complex that the likelihood function is computationally intractable. Rather than discard these models in favour of inferior alternatives, a class of Bayesian "likelihoodfree" techniques (often termed approximate Bayesian computation (ABC)) has emerged in the last few years, which avoids direct likelihood computation through repeated sampling of data from the model and comparing observed and simulated summary statistics. In Part I of this thesis we utilise sequential Monte Carlo (SMC) methodology to develop new algorithms for ABC that are more efficient in terms of the number of model simulations required and are almost black-box since very little algorithmic tuning is required. In addition, we address the issue of deriving appropriate summary statistics to use within ABC via a goodness-of-fit statistic and indirect inference. Another important problem in statistics is the design of experiments. That is, how one should select the values of the controllable variables in order to achieve some design goal. The presences of parameter and/or model uncertainty are computational obstacles when designing experiments but can lead to inefficient designs if not accounted for correctly. The Bayesian framework accommodates such uncertainties in a coherent way. If the amount of uncertainty is substantial, it can be of interest to perform adaptive designs in order to accrue information to make better decisions about future design points. This is of particular interest if the data can be collected sequentially. In a sense, the current posterior distribution becomes the new prior distribution for the next design decision. Part II of this thesis creates new algorithms for Bayesian sequential design to accommodate parameter and model uncertainty using SMC. The algorithms are substantially faster than previous approaches allowing the simulation properties of various design utilities to be investigated in a more timely manner. Furthermore the approach offers convenient estimation of Bayesian utilities and other quantities that are particularly relevant in the presence of model uncertainty. Finally, Part III of this thesis tackles a substantive medical problem. A neurological disorder known as motor neuron disease (MND) progressively causes motor neurons to no longer have the ability to innervate the muscle fibres, causing the muscles to eventually waste away. When this occurs the motor unit effectively ‘dies’. There is no cure for MND, and fatality often results from a lack of muscle strength to breathe. The prognosis for many forms of MND (particularly amyotrophic lateral sclerosis (ALS)) is particularly poor, with patients usually only surviving a small number of years after the initial onset of disease. Measuring the progress of diseases of the motor units, such as ALS, is a challenge for clinical neurologists. Motor unit number estimation (MUNE) is an attempt to directly assess underlying motor unit loss rather than indirect techniques such as muscle strength assessment, which generally is unable to detect progressions due to the body’s natural attempts at compensation. Part III of this thesis builds upon a previous Bayesian technique, which develops a sophisticated statistical model that takes into account physiological information about motor unit activation and various sources of uncertainties. More specifically, we develop a more reliable MUNE method by applying marginalisation over latent variables in order to improve the performance of a previously developed reversible jump Markov chain Monte Carlo sampler. We make other subtle changes to the model and algorithm to improve the robustness of the approach.

Disaster strikes, then what? Using evaluation in narrative driven (oral history & digital storytelling) community-based projects

In 2011 Queensland suffered both floods and cyclones, leaving residents without homes and their communities in ruins (2011). This paper presents how researchers from QUT, who are also members of the Oral History Association of Australia (OHAA) Queensland’s chapter, are using oral history, photographs, videography and digital storytelling to help heal and empower rural communities around the state and how evaluation has become a key element of our research. QUT researchers ran storytelling workshops in the capital city of Brisbane i early 2011, after the city suffered sever flooding. Cyclone Yasi then struck the town of Cardwell (in February 2011) destroying their historical museum and recording equipment. We delivered an 'emergency workshop', offering participants hands on use of the equipment, ethical and interviewing theory, so that the community could start to build a new collection. We included oral history workshops as well as sessions on how best to use a video camera, digital camera and creative writing sessions, so the community would also know how to make 'products' or exhibition pieces out of the interviews they were recording. We returned six months later to conduct follow-up workshops and the material produced by and with the community had been amazing. More funding has now been secured to replicate audio/visual/writing workshops in other remote rural Queensland communities including Townsville, Mackay and Cunnamulla and Toowoomba in 2012, highlighting the need for a multi media approach, to leverage the most out of OH interviews as a mechanism to restore and promote community resilience and pride.

Framing local stories for community consumption facilitation and evaluation in narrative driven arts-based projects

Cyclone Yasi struck the Cassowary Coast of Queensland in the early hours of Feb 3, 2011, destroying many homes sand property, including the destruction of the Cardwell and district historical society’s premises. With their own homes flattened, many were forced to live in mobile accommodation, with extended family, or leave altogether. The historical society members however were more devastated by their flattened foreshore museum and loss of their collection material. A call for assistance was made through the OHAA Qld branch, who along with QUT sponsored a trip to somehow plan how they could start to pick up the pieces to start again. This presentation highlights the need for communities to gather, preserve and present their own stories, in a way that is sustainable and meaningful to them, but that good advice and support along the way is important. Two 2 day workshops were held in March and then September, augmented by plenty of email correspondence and phone calls in between. Participants learnt that if they could conduct quality oral history interviews, they could later use these in many exhibitable ways including: documentary pieces; digital stories; photographic collections; creative short stories; audio segments –while also drawing closely together a suffering community. This story is not only about the people who were interviewed about the night Yasi struck, but the amazing women (all over 50) of the historical society who were willing to try and leap the digital divide that faces older Australians, especially those in rural Australia, so that their older local stories would not be lost and so that new stories could also be remembered.

Yasi : Digital stories and oral histories collection

"The second of the Oral History Workshops conducted by Associate Professor Helen Klaebe and the Oral History team from the Queensland University of Technology in Brisbane, was conducted in El Arish on the last weekend in September 2011. The first workshop was held in Cardwell in March 2011. Historical Society members and other researchers from both the Cardwell and El Arish areas combined to organise and fund the workshops, which have produced a growing collection of recordings of personal stories from people with a wide variety of experiences during and after cyclone Yasi. Aside from being productive in documenting history, the workshops have offered a greatly appreciated educational opportunity for many people, most of whom have never before had access to such benefits. Not only were they able to learn history gathering methodologies and the relevant technical skills, but they also gained new experience in the use of computers to apply these skills. These far northern oral history workshops took the form of a shortened version of the 5 series workshops being presented at QUT in Brisbane this year. The agenda was aligned to the wishes and requirements of the participants who attended from the Cassowary Coast and Tableland regions."

Sustainability in post disaster road infrastructure recovery projects in Queensland, Australia

between mid 2010 and early 2011, Queensland road related infrastructures were devastated by flood and cyclone related natural disasters. Responding to these recent events and in preparing for more regular and intense climate-change induced events in future, the Queensland Government is now reviewing how post-disaster road infrastructure recovery projects are planned and delivered. In particular, there is awareness that rebuilding such infrastructure need sustainable strategies across economic, environmental and social dimensions. A comprehensive sustainability assessment framework for pre and post disaster situations can minimize negative impact on our communities, economy and environment. This research is underway to develop a comprehensive sustainability element frame work for post disaster management in road infrastructures in Queensland, Australia. Analyzing the implications of disruption to transport network and associated services is an important part of preparing local and regional responses to the impacts of natural disasters. This research can contribute to strategic planning, management leading to safe, efficient and integrated transport system that supports sustainable economic, social and environmental outcomes in Queensland. Within this context, this paper provides an overview of the qualitative mixed-method research approach involving literature reviews and case studies to explore and evaluate a number of sustainability elements with a view to develop operational strategies for disaster recovery road projects.

Sustainability in post disaster road infrastructure recovery projects in Queensland, Australia

Between mid 2010 and early 2013, Queensland road related infrastructures were devastated by flood and cyclone related natural disasters. Responding to these recent events and in preparing for more regular and intense climate-change induced events in future, the Queensland Government is now reviewing how post-disaster road infrastructure recovery projects are planned and delivered. In particular, there is awareness that rebuilding such infrastructure need sustainable strategies across economic, environmental and social dimensions. A comprehensive sustainability assessment framework for pre and post disaster situations can minimize negative impact on our communities, economy and environment. This research is underway to develop a comprehensive sustainability element frame work for post disaster management in road infrastructures in Queensland, Australia. Analyzing the implications of disruption to transport network and associated services is an important part of preparing local and regional responses to the impacts of natural disasters. This research can contribute to strategic planning, management leading to safe, efficient and integrated transport system that supports sustainable economic, social and environmental outcomes in Queensland. Within this context, this paper provides an overview of the qualitative mixed-method research approach involving literature reviews and case studies to explore and evaluate a number of sustainability elements with a view to develop operational strategies for disaster recovery road projects.

Facilitating local stories in post-disaster regional communities : evaluation in narrative-driven oral history projects

Cyclone Yasi struck the Cassowary Coast of Northern Queensland, Australia, in the early hours of February 3, 2011, destroying many homes and property, including the destruction of the Cardwell and district historical society’s premises. With their own homes flattened, many residents were forced to live in mobile accommodation, with extended family, or leave the area altogether. The historical society members seemed, however, particularly devastated by their flattened foreshore museum and loss of their precious collection of material. A call for assistance was made through the Oral History Association of Australia’s Queensland branch (OHAA Qld), which along with a Queensland University of Technology (QUT) research team sponsored a trip to best plan how they could start to pick up the pieces to rebuild the museum. This chapter highlights the need for communities to gather, preserve and present their own stories, in a way that is sustainable and meaningful to them – whether that be because of a disaster, or as they go about life in their contemporary communities – the key being that good advice, professional support and embedded evaluation practices at crucial moments along the way can be critically important.

Estimating present day extreme water level exceedance probabilities around the coastline of Australia : tides, extra-tropical storm surges and mean sea level

The occurrence of extreme water levels along low-lying, highly populated and/or developed coastlines can lead to considerable loss of life and billions of dollars of damage to coastal infrastructure. Therefore it is vitally important that the exceedance probabilities of extreme water levels are accurately evaluated to inform risk-based flood management, engineering and future land-use planning. This ensures the risk of catastrophic structural failures due to under-design or expensive wastes due to over-design are minimised. This paper estimates for the first time present day extreme water level exceedence probabilities around the whole coastline of Australia. A high-resolution depth averaged hydrodynamic model has been configured for the Australian continental shelf region and has been forced with tidal levels from a global tidal model and meteorological fields from a global reanalysis to generate a 61-year hindcast of water levels. Output from this model has been successfully validated against measurements from 30 tide gauge sites. At each numeric coastal grid point, extreme value distributions have been fitted to the derived time series of annual maxima and the several largest water levels each year to estimate exceedence probabilities. This provides a reliable estimate of water level probabilities around southern Australia; a region mainly impacted by extra-tropical cyclones. However, as the meteorological forcing used only weakly includes the effects of tropical cyclones, extreme water level probabilities are underestimated around the western, northern and north-eastern Australian coastline. In a companion paper we build on the work presented here and more accurately include tropical cyclone-induced surges in the estimation of extreme water level. The multi-decadal hindcast generated here has been used primarily to estimate extreme water level exceedance probabilities but could be used more widely in the future for a variety of other research and practical applications.

Sustainability in post disaster road infrastructure recovery projects and asset management

Civil infrastructure and especially roads are being impacted with increasing frequency by flood, Tsunami, cyclone related natural and manmade disasters in the world. Responding to such events and in preparing for more regular and intense climate-change induced events in future, the road governing agencies are reviewing how postdisaster road infrastructure recovery projects are best planned and delivered. In particular, there is awareness that rebuilding such infrastructure require sustainable asset management strategies across economic, environmental and social dimensions. A comprehensive asset management framework for pre and post disaster situations can minimize negative impacts on our communities, economy and environment. This research paper is focused on post disaster management in road infrastructures and road infrastructure asset management strategies used by road authorities. Analyzing the implications of disruption to transport network and associated services is an important part of preparing local and regional responses to the impacts of disasters. This research paper will contribute to strategic infrastructure asset planning, management leading to safe, efficient and integrated transport system that supports sustainable economic, social and environmental outcomes. This paper also focuses on proper asset management, governance and engineering principles which should be followed and adopted in post disaster recovery projects to maximize sustainability in environmental, social and economic dimensions.

Design of light gauge steel roofing systems subject to high wind forces

Light gauge steel roofing systems made of thin profiled roof sheeting and battens are used commonly in residential, industrial and commercial buildings. Their critical design load combination is that due to wind uplift forces that occur during high wind events such as tropical cyclones and thunderstorms. However, premature local failures at their screw connections have been a concern for many decades since cyclone Tracy that devastated Darwin in 1974. Extensive research that followed cyclone Tracy on the pull-through and pull-out failures of roof sheeting to batten connections has significantly improved the safety of roof sheeting. However, this has made the batten to rafter/truss connection the weakest, and recent wind damage investigations have shown the failures of these connections and the resulting loss of entire roof structures. Therefore an experimental research program using both small scale and full scale air-box tests is currently under way to investigate the pull-through failures of thin-walled steel battens under high wind uplift forces. Tests have demonstrated that occurrence of pull-through failures in the bottom flanges of steel batttens and the need to develop simple test and design methods as a function of many critical parameters such as steel batten geometry, thickness and grade, screw fastener sizes and other fastening details. This paper presents the details of local failures that occur in light fauge roofing systems, a review of the current design and test methods for steel battens and associated short comings, and the test results obtained to date on pull-through failures of battens from small scale and full scale tests. Finally, it proposes the use of suitable small scale test methods that can be used by both researchers and manufacturers of such screw-fastened light gauge steel batten systems.

Estimating present day extreme total water level exceedance probabilities around the Australian coastline

The occurrence of extreme water level events along low-lying, highly populated and/or developed coastlines can lead to devastating impacts on coastal infrastructure. Therefore it is very important that the probabilities of extreme water levels are accurately evaluated to inform flood and coastal management and for future planning. The aim of this study was to provide estimates of present day extreme total water level exceedance probabilities around the whole coastline of Australia, arising from combinations of mean sea level, astronomical tide and storm surges generated by both extra-tropical and tropical storms, but exclusive of surface gravity waves. The study has been undertaken in two main stages. In the first stage, a high-resolution (~10 km along the coast) hydrodynamic depth averaged model has been configured for the whole coastline of Australia using the Danish Hydraulics Institute’s Mike21 modelling suite of tools. The model has been forced with astronomical tidal levels, derived from the TPX07.2 global tidal model, and meteorological fields, from the US National Center for Environmental Prediction’s global reanalysis, to generate a 61-year (1949 to 2009) hindcast of water levels. This model output has been validated against measurements from 30 tide gauge sites around Australia with long records. At each of the model grid points located around the coast, time series of annual maxima and the several highest water levels for each year were derived from the multi-decadal water level hindcast and have been fitted to extreme value distributions to estimate exceedance probabilities. Stage 1 provided a reliable estimate of the present day total water level exceedance probabilities around southern Australia, which is mainly impacted by extra-tropical storms. However, as the meteorological fields used to force the hydrodynamic model only weakly include the effects of tropical cyclones the resultant water levels exceedance probabilities were underestimated around western, northern and north-eastern Australia at higher return periods. Even if the resolution of the meteorological forcing was adequate to represent tropical cyclone-induced surges, multi-decadal periods yielded insufficient instances of tropical cyclones to enable the use of traditional extreme value extrapolation techniques. Therefore, in the second stage of the study, a statistical model of tropical cyclone tracks and central pressures was developed using histroic observations. This model was then used to generate synthetic events that represented 10,000 years of cyclone activity for the Australia region, with characteristics based on the observed tropical cyclones over the last ~40 years. Wind and pressure fields, derived from these synthetic events using analytical profile models, were used to drive the hydrodynamic model to predict the associated storm surge response. A random time period was chosen, during the tropical cyclone season, and astronomical tidal forcing for this period was included to account for non-linear interactions between the tidal and surge components. For each model grid point around the coast, annual maximum total levels for these synthetic events were calculated and these were used to estimate exceedance probabilities. The exceedance probabilities from stages 1 and 2 were then combined to provide a single estimate of present day extreme water level probabilities around the whole coastline of Australia.