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.

Wound problems following hip arthroplasty before and after the introduction of a direct thrombin inhibitor for thromboprophylaxis

NICE guidelines have stated that patients undergoing elective hip surgery are at increased risk for venous thromboembolic events (VTE) following surgery and have recommended thromboprophylaxis for 28-35 days1, 2. However the studies looking at the new direct thrombin inhibitors have only looked at major bleeding. We prospectively looked at wound discharge in patients who underwent hip arthroplasty and were given dabigatran postoperatively between March 2010 and April 2010 (n=56). We retrospectively compared these results to a matched group of patients who underwent similar operations six months earlier when all patients were given dalteparin routinely postoperatively until discharge, and discharged home on 150mg aspirin daily for 6 weeks (n=67). Wound discharge after 5 days was significantly higher in the patients taking dabigatran (32% dabigatran n=18, 10% dalteparin n=17, p=0.003) and our rate of delayed discharges due to wound discharge significantly increased from 7% in the dalteparin group (n=5) to 27% for dabigatran (n=15, p=0.004). Patients who received dabigatran were more than five times as likely to return to theatre with a wound complication as those who received dalteparin (7% dabigatran n=4, vs. 1% dalteparin n=1), however, this was not statistically significant (p=0.18). The significantly higher wound discharge and return to theatre rates demonstrated in this study have meant that we have changed our practice to administering dalteparin until the wound is dry and then starting dabigatran. Our study demonstrates the need for further clinical studies regarding wound discharge and dabigatran.

An experimental and computational investigation of performance of Green Gully for reusing stormwater

A new stormwater quality improvement device (SQID) called ‘Green Gully’ has been designed and developed in this study with an aim to re-using stormwater for irrigating plants and trees. The main purpose of the Green Gully is to collect road runoff/stormwater, make it suitable for irrigation and provide an automated network system for watering roadside plants and irrigational areas. This paper presents the design and development of Green Gully along with experimental and computational investigations of the performance of Green Gully. Performance (in the form of efficiency, i.e. the percentage of water flow through the gully grate) was experimentally determined using a gully model in the laboratory first, then a three dimensional numerical model was developed and simulated to predict the efficiency of Green Gully as a function of flow rate. Computational Fluid Dynamics (CFD) code FLUENT was used for the simulation. GAMBIT was used for geometry creation and mesh generation. Experimental and simulation results are discussed and compared in this paper. The predicted efficiency was compared with the laboratory measured efficiency. It was found that the simulated results are in good agreement with the experimental results.

An experimental study of a reactive plume in grid turbulence

Experimental results for a reactive non-buoyant plume of nitric oxide (NO) in a turbulent grid flow doped with ozone (O3) are presented. The Damkohler number (Nd) for the experiment is of order unity indicating the turbulence and chemistry have similar timescales and both affect the chemical reaction rate. Continuous measurements of two components of velocity using hot-wire anemometry and the two reactants using chemiluminescent analysers have been made. A spatial resolution for the reactants of four Kolmogorov scales has been possible because of the novel design of the experiment. Measurements at this resolution for a reactive plume are not found in the literature. The experiment has been conducted relatively close to the grid in the region where self-similarity of the plume has not yet developed. Statistics of a conserved scalar, deduced from both reactive and non-reactive scalars by conserved scalar theory, are used to establish the mixing field of the plume, which is found to be consistent with theoretical considerations and with those found by other investigators in non-reative flows. Where appropriate the reactive species means and higher moments, probability density functions, joint statistics and spectra are compared with their respective frozen, equilibrium and reaction-dominated limits deduced from conserved scalar theory. The theoretical limits bracket reactive scalar statistics where this should be so according to conserved scalar theory. Both reactants approach their equilibrium limits with greater distance downstream. In the region of measurement, the plume reactant behaves as the reactant not in excess and the ambient reactant behaves as the reactant in excess. The reactant covariance lies outside its frozen and equilibrium limits for this value of Vd. The reaction rate closure of Toor (1969) is compared with the measured reaction rate. The gradient model is used to obtain turbulent diffusivities from turbulent fluxes. Diffusivity of a non-reactive scalar is found to be close to that measured in non-reactive flows by others.

Efficient modular exponentiation-based puzzles for denial-of-service protection

Client puzzles are moderately-hard cryptographic problems neither easy nor impossible to solve that can be used as a counter-measure against denial of service attacks on network protocols. Puzzles based on modular exponentiation are attractive as they provide important properties such as non-parallelisability, deterministic solving time, and linear granularity. We propose an efficient client puzzle based on modular exponentiation. Our puzzle requires only a few modular multiplications for puzzle generation and verification. For a server under denial of service attack, this is a significant improvement as the best known non-parallelisable puzzle proposed by Karame and Capkun (ESORICS 2010) requires at least 2k-bit modular exponentiation, where k is a security parameter. We show that our puzzle satisfies the unforgeability and difficulty properties defined by Chen et al. (Asiacrypt 2009). We present experimental results which show that, for 1024-bit moduli, our proposed puzzle can be up to 30 times faster to verify than the Karame-Capkun puzzle and 99 times faster than the Rivest et al.'s time-lock puzzle.

Raising awareness of traffic pollution: the potential benefits and problems of using a warning smell

Exposure to traffic pollution is increasing worldwide as people move to cities, and as more vehicles join the roads, creating longer journeys and more traffic jams. Most traffic pollutants are odourless and invisible, which hides exposure from the public. If traffic pollution had a distinctive smell it would enable people to avoid exposure, and increase the political will for difficult policy changes. A smell may also instigate longer-term changes, such as switching to active transport for school pick-ups. A smell could be added using a fuel additive or a temporary device attached to vehicle exhausts.

Effective shear modulus approach for two dimensional solids and plate bending problems by meshless point collocation method

For the analysis of material nonlinearity, an effective shear modulus approach based on the strain control method is proposed in this paper by using point collocation method. Hencky’s total deformation theory is used to evaluate the effective shear modulus, Young’s modulus and Poisson’s ratio, which are treated as spatial field variables. These effective properties are obtained by the strain controlled projection method in an iterative manner. To evaluate the second order derivatives of shape function at the field point, the radial basis function (RBF) in the local support domain is used. Several numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method and comparisons have been made with analytical solutions and the finite element method (ABAQUS).

Enriching XML documents clustering by using concise structure and content

With the growing number of XML documents on theWeb it becomes essential to effectively organise these XML documents in order to retrieve useful information from them. A possible solution is to apply clustering on the XML documents to discover knowledge that promotes effective data management, information retrieval and query processing. However, many issues arise in discovering knowledge from these types of semi-structured documents due to their heterogeneity and structural irregularity. Most of the existing research on clustering techniques focuses only on one feature of the XML documents, this being either their structure or their content due to scalability and complexity problems. The knowledge gained in the form of clusters based on the structure or the content is not suitable for reallife datasets. It therefore becomes essential to include both the structure and content of XML documents in order to improve the accuracy and meaning of the clustering solution. However, the inclusion of both these kinds of information in the clustering process results in a huge overhead for the underlying clustering algorithm because of the high dimensionality of the data. The overall objective of this thesis is to address these issues by: (1) proposing methods to utilise frequent pattern mining techniques to reduce the dimension; (2) developing models to effectively combine the structure and content of XML documents; and (3) utilising the proposed models in clustering. This research first determines the structural similarity in the form of frequent subtrees and then uses these frequent subtrees to represent the constrained content of the XML documents in order to determine the content similarity. A clustering framework with two types of models, implicit and explicit, is developed. The implicit model uses a Vector Space Model (VSM) to combine the structure and the content information. The explicit model uses a higher order model, namely a 3- order Tensor Space Model (TSM), to explicitly combine the structure and the content information. This thesis also proposes a novel incremental technique to decompose largesized tensor models to utilise the decomposed solution for clustering the XML documents. The proposed framework and its components were extensively evaluated on several real-life datasets exhibiting extreme characteristics to understand the usefulness of the proposed framework in real-life situations. Additionally, this research evaluates the outcome of the clustering process on the collection selection problem in the information retrieval on the Wikipedia dataset. The experimental results demonstrate that the proposed frequent pattern mining and clustering methods outperform the related state-of-the-art approaches. In particular, the proposed framework of utilising frequent structures for constraining the content shows an improvement in accuracy over content-only and structure-only clustering results. The scalability evaluation experiments conducted on large scaled datasets clearly show the strengths of the proposed methods over state-of-the-art methods. In particular, this thesis work contributes to effectively combining the structure and the content of XML documents for clustering, in order to improve the accuracy of the clustering solution. In addition, it also contributes by addressing the research gaps in frequent pattern mining to generate efficient and concise frequent subtrees with various node relationships that could be used in clustering.

M-ary trees for combinatorial asset management decision problems

A novel m-ary tree based approach is presented to solve asset management decisions which are combinatorial in nature. The approach introduces a new dynamic constraint based control mechanism which is capable of excluding infeasible solutions from the solution space. The approach also provides a solution to the challenges with ordering of assets decisions.

Impacts of experimental warming and fire on phenology of subalpine open-heath species

The present study examined experimentally the phenological responses of a range of plant species to rises in temperature. We used the climate-change field protocol of the International Tundra Experiment (ITEX), which measures plant responses to warming of 1 to 2°C inside small open-topped chambers. The field study was established on the Bogong High Plains, Australia, in subalpine open heathlands; the most common treeless plant community on the Bogong High Plains. The study included areas burnt by fire in 2003, and therefore considers the interactive effects of warming and fire, which have rarely been studied in high mountain environments. From November 2003 to March 2006, various phenological phases were monitored inside and outside chambers during the snow-free periods. Warming resulted in earlier occurrence of key phenological events in 7 of the 14 species studied. Burning altered phenology in 9 of 10 species studied, with both earlier and later phenological changes depending on the species. There were no common phenological responses to warming or burning among species of the same family, growth form or flowering type (i.e. early or late-flowering species), when all phenological events were examined. The proportion of plants that formed flower buds was influenced by fire in half of the species studied. The findings support previous findings of ITEX and other warming experiments; that is, species respond individualistically to experimental warming. The inter-year variation in phenological response, the idiosyncratic nature of the responses to experimental warming among species, and an inherent resilience to fire, may result in community resilience to short-term climate change. In the first 3 years of experimental warming, phenological responses do not appear to be driving community-level change. Our findings emphasise the value of examining multiple species in climate-change studies.

Phenological changes in six Australian subalpine plants in response to experimental warming and year-to-year variation

The likely phenological responses of plants to climate warming can be measured through experimental manipulation of field sites, but results are rarely validated against year-to-year changes in climate. Here, we describe the response of 1-5 years of experimental warming on phenology (budding, flowering and seed maturation) of six common subalpine plant species in the Australian Alps using the International Tundra Experiment (ITEX) protocol.2. Phenological changes in some species (particularly the forb Craspedia jamesii) were detected in experimental plots within a year of warming, whereas changes in most other species (the forb Erigeron bellidioides, the shrub Asterolasia trymalioides and the graminoids Carex breviculmis and Poa hiemata) did not develop until after 2-4 years; thus, there appears to be a cumulative effect of warming for some species across multiple years.3. There was evidence of changes in the length of the period between flowering and seed maturity in one species (P. hiemata) that led to a similar timing of seed maturation, suggesting compensation.4. Year-to-year variation in phenology was greater than variation between warmed and control plots and could be related to differences in thawing degree days (particularly, for E. bellidioides) due to earlier timing of budding and other events under warmer conditions. However, in Carex breviculmis, there was no association between phenology and temperature changes across years.5. These findings indicate that, although phenological changes occurred earlier in response to warming in all six species, some species showed buffered rather than immediate responses.6. Synthesis. Warming in ITEX open-top chambers in the Australian Alps produced earlier budding, flowering and seed set in several alpine species. Species also altered the timing of these events, particularly budding, in response to year-to-year temperature variation. Some species responded immediately, whereas in others the cumulative effects of warming across several years were required before a response was detected.

When individual child psychotherapy exacerbates family systems problems in child abuse cases : a clinical analysis

Children who have suffered physical or sexual abuse are as vulnerable as adult trauma victims to experience "secondary trauma", in which the reactions of the family or broader system exacerbate the child's difficulties. Three clinical cases (a 7 yr old male, an 8 yr old male, and a 7 yr old female) are presented that suggest that this secondary trauma can be made worse by either excessive or insufficient provision of individual child psychotherapy, and the way the system interprets and reacts to these clinical decisions. Types of secondary trauma and their interactions with clinical decisions are discussed. Ways of framing clinical decisions to minimize the potential secondary trauma are presented.

Ethical issues in research on adolescent depression and suicidal behaviour

Argues that the codes of ethical conduct of the Australian Psychological Society and the American Psychological Association imply that researchers of adolescent depression and suicidal behavior must plan to intervene to assess risk where a participant in a study indicates an intention to commit suicide. Participants in research of this kind need to be advised of this possibility in advance. The obligation to intervene, and to advise of the possibility of intervention, poses practical and methodological problems for research in this area but does not, it is argued, absolve the researcher of the primary responsibility to contribute to the welfare of the research participant. This obligation exists only when there is indication of harm but not, for instance, in the case of depression without suicidal intent.