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.

Analysis for the use of cumulative plots for travel time estimation on signalized network

This paper provides fundamental understanding for the use of cumulative plots for travel time estimation on signalized urban networks. Analytical modeling is performed to generate cumulative plots based on the availability of data: a) Case-D, for detector data only; b) Case-DS, for detector data and signal timings; and c) Case-DSS, for detector data, signal timings and saturation flow rate. The empirical study and sensitivity analysis based on simulation experiments have observed the consistency in performance for Case-DS and Case-DSS, whereas, for Case-D the performance is inconsistent. Case-D is sensitive to detection interval and signal timings within the interval. When detection interval is integral multiple of signal cycle then it has low accuracy and low reliability. Whereas, for detection interval around 1.5 times signal cycle both accuracy and reliability are high.

The effect of various pH, ionic strength and temperature on papain hydrolysis of salivary film

Stimulated human whole saliva (WS) was used to study the dynamics of papain hydrolysis at defined pH, ionic strength and temperature with the view of reducing an acquired pellicle. A quartz crystal microbalance with dissipation (QCM-D) was used to monitor the changes in frequency due to enzyme hydrolysis of WS films and the hydrolytic parameters were calculated using an empirical model. The morphological and conformational changes of the salivary films before and after enzymatic hydrolysis were characterized by atomic force microscopy (AFM) imaging and grazing angle infrared spectroscopy (GA-FTIR) spectra, respectively. The characteristics of papain hydrolysis of WS films were pH-, ionic strength- and temperature-dependent. The WS films were partially removed by the action of enzyme, resulting thinner and smoother surfaces. The IR data suggested that hydrolysis-induced deformation did not occur onto the remnants salivary films. The processes of papain hydrolysis of WS films can be controlled by properly regulating pH, ionic strength and temperature.

Mixed convection laminar flow along a horizontal plate subject to streamwise sinusoidal surface temperature

Mixed convection of a two-dimensional laminar incompressible flow along a horizontal flat plate with streamwise sinusoidal surface temperature has been numerically investigated for different values of Rayleigh number and Reynolds number for constant values of Prandtl number, amplitude and frequency of periodic temperature. The numerical scheme is based on the finite element method adapted to rectangular non-uniform mesh elements by a non-linear parametric solution algorithm. The fluid considered in this study is air. The results are obtained for the Rayleigh number and Reynolds number ranging from 102 to 104 and 1 to 100, respectively, with constant physical properties for the fluid medium considered. Velocity and temperature profiles, streamlines, isotherms, and average Nusselt numbers are presented to observe the effect of the investigating parameters on fluid flow and heat transfer characteristics. The present results show that the convective phenomena are greatly influenced by the variation of Rayleigh numbers and Reynolds number.

Low temperature CO sensitive nanostructured WO3 thin films doped with Fe

Nanostructured tungsten oxide thin film based gas sensors have been developed by thermal evaporation method to detect CO at low operating temperatures. The influence of Fe-doping and annealing heat treatment on microstructural and gas sensing properties of these films have been investigated. Fe was incorporated in WO3 film by co-evaporation and annealing was performed at 400oC for 2 hours in air. AFM analysis revealed a grain size of about 10-15 nm in all the films. GIXRD analysis showed that as-deposited films are amorphous and annealing at 400oC improved the crystallinity. Raman and XRD analysis indicated that Fe is incorporated in the WO3 matrix as a substitutional impurity, resulting in shorter O-W-O bonds and lattice cell parameters. Doping with Fe contributed significantly towards CO sensing performance of WO3 thin films. A good response to various concentrations (10-1000 ppm) of CO has been achieved with 400oC annealed Fe-doped WO3 film at a low operating temperature of 150oC.

Representational change and strategy use in children's number line estimation during the first years of primary school

Background: The objective of this study was to scrutinize number line estimation behaviors displayed by children in mathematics classrooms during the first three years of schooling. We extend existing research by not only mapping potential logarithmic-linear shifts but also provide a new perspective by studying in detail the estimation strategies of individual target digits within a number range familiar to children. Methods: Typically developing children (n = 67) from Years 1 – 3 completed a number-to-position numerical estimation task (0-20 number line). Estimation behaviors were first analyzed via logarithmic and linear regression modeling. Subsequently, using an analysis of variance we compared the estimation accuracy of each digit, thus identifying target digits that were estimated with the assistance of arithmetic strategy. Results: Our results further confirm a developmental logarithmic-linear shift when utilizing regression modeling; however, uniquely we have identified that children employ variable strategies when completing numerical estimation, with levels of strategy advancing with development. Conclusion: In terms of the existing cognitive research, this strategy factor highlights the limitations of any regression modeling approach, or alternatively, it could underpin the developmental time course of the logarithmic-linear shift. Future studies need to systematically investigate this relationship and also consider the implications for educational practice.

The identification and quantification of temperature-related mortality

The relationship between weather and mortality has been observed for centuries. Recently, studies on temperature-related mortality have become a popular topic as climate change continues. Most of the previous studies found that exposure to hot or cold temperature affects mortality. This study aims to address three research questions: 1. What is the overall effect of daily mean temperature variation on the elderly mortality in the published literature using a meta-analysis approach? 2. Does the association between temperature and mortality differ with age, sex, or socio-economic status in Brisbane? 3. How is the magnitude of the lag effects of the daily mean temperature on mortality varied by age and cause-of-death groups in Brisbane? In the meta-analysis, there was a 1-2 % increase in all-cause mortality for a 1ºC decrease during cold temperature intervals and a 2-5% increase for a 1ºC increment during hot temperature intervals among the elderly. Lags of up to 9 days in exposure to cold temperature intervals were statistically significantly associated with all-cause mortality, but no significant lag effects were observed for hot temperature intervals. In Brisbane, the harmful effect of high temperature (over 24ºC) on mortality appeared to be greater among the elderly than other age groups. The effect estimate among women was greater than among men. However, No evidence was found that socio-economic status modified the temperature-mortality relationship. The results of this research also show longer lag effects in cold days and shorter lag effects in hot days. For 3-day hot effects associated with 1°C increase above the threshold, the highest percent increases in mortality occurred among people aged 85 years or over (5.4% (95% CI: 1.4%, 9.5%)) compared with all age group (3.2% (95% CI: 0.9%, 5.6%)). The effect estimate among cardiovascular deaths was slightly higher than those among all-cause mortality. For overall 21-day cold effects associated with a 1°C decrease below the threshold, the percent estimates in mortality for people aged 85 years or over, and from cardiovascular diseases were 3.9% (95% CI: 1.9%, 6.0%) and 3.4% (95% CI: 0.9%, 6.0%), respectively compared with all age group (2.0% (95% CI: 0.7%, 3.3%)). Little research of this kind has been conducted in the Southern Hemisphere. This PhD research may contribute to the quantitative assessment of the overall impact, effect modification and lag effects of temperature variation on mortality in Australia and The findings may provide useful information for the development and implementation of public health policies to reduce and prevent temperature-related health problems.

MHD natural convection flow from an isothermal horizontal circular cylinder under consideration of temperature dependent viscosity

Magnetohydrodynamic (MHD) natural convection laminar flow from an iso-thermal horizontal circular cylinder immersed in a fluid with viscosity proportional to a linear function of temperature will be discussed with numerical simulations. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equa-tions are reduced to convenient form, which are solved numerically by two very efficient methods, namely, (i) Implicit finite difference method together with Keller box scheme and (ii) Direct numerical scheme. Numerical results are presented by velocity and temperature distributions of the fluid as well as heat transfer characteristics, namely the shearing stress and the local heat transfer rate in terms of the local skin-friction coefficient and the local Nusselt number for a wide range of magnetohydrodynamic parameter, viscosity-variation parameter and viscous dissipation parameter. MHD flow in this geometry with temperature dependent viscosity is absent in the literature. The results obtained from the numerical simulations have been veri-fied by two methodologies.

Estimation on disease burden related to hepatitis B virus infection in Shandong province of China [山东省乙型肝炎病毒感染所致相关疾病的疾病负担研究]

Objective: To comprehensively measure the burden of hepatitis B, liver cirrhosis and liver cancer in Shandong province, using disability-adjusted life years (DALYs) to estimate the disease burden attribute to hepatitis B virus (HBV)infection. Methods: Based on the mortality data of hepatitis B, liver cirrhosis and liver cancer derived from the third National Sampling Retrospective Survey for Causes of Death during 2004 and 2005, the incidence data of hepatitis B and the prevalence and the disability weights of liver cancer gained from the Shandong Cancer Prevalence Sampling Survey in 2007, we calculated the years of life lost (YLLs), years lived with disability (YLDs) and DALYs of three diseases following the procedures developed for the global burden of disease (GBD) study to ensure the comparability. Results: The total burden for hepatitis B, liver cirrhosis and liver cancer were 211 616 (39 377 YLLs and 172 239 YLDs), 16 783 (13 497 YLLs and 3286 YLDs) and 247 795 (240 236 YLLs and 7559 YLDs) DALYs in 2005 respectively, and men were 2.19, 2.36 and 3.16 times as that for women, respectively in Shandong province. The burden for hepatitis B was mainly because of disability (81.39%). However, most burden on liver cirrhosis and liver cancer were due to premature death (80.42% and 96.95%). The burden of each patient related to hepatitis B, liver cirrhosis and liver cancer were 4.8, 13.73 and 11.11 respectively. Conclusion: Hepatitis B, liver cirrhosis and liver cancer caused considerable burden to the people living in Shandong province, indicating that the control of hepatitis B virus infection would bring huge potential benefits.

Estimation on the mortality and disease burden attributed to selected risk factors in Shandong province [山东省主要危险因素的归因死亡和疾病负担分析]

Objective: To determine the major health related risk factors and provide evidence for policy-making,using health burden analysis on selected factors among general population from Shandong province. Methods: Based on data derived from the Third Death of Cause Sampling Survey in Shandong. Years of life lcrat(YLLs),yearS Iived with disability(YLDs)and disability-adjusted life years(DALYs) were calculated according to the GBD ethodology.Deaths and DALYs attributed to the selected risk factors were than estimated together with the PAF data from GBD 2001 study.The indirect method was employed to estimate the YLDs. Results: 51.09%of the total dearlls and 31.83%of the total DALYs from the Shandong population were resulted from the 19 selected risk factors.High blood pre.ure,smoking,low fruit and vegetable intake,aleohol consumption,indoor smoke from solid fuels,high cholesterol,urban air pollution, physical inactivity,overweight and obesity and unsafe injections in health care settings were identified as the top 10 risk faetors for mortality which together caused 50.21%of the total deaths.Alcohol use,smoking,high blood pressure,Low fruit and vegetable intake, indoor smoke from solid fuels, overweight and obesity,high cholesterol, physical inactivity,urban air pollution and iron-deficiency anemia were proved as the top 10 risk factors related to disease burden and were responsible for 29.04%of the total DALYs. Conclusion: Alcohol use.smoking and high blood pressure were determined as the major risk factors which influencing the health of residents in Shandong. The mortality and burden of disease could be reduced significantly if these major factors were effectively under control.

Temperature dependent electrical resistivity in expoxy : multiwall carbon nanotube nanocomposites

Thin films of expoxy nanocomposites modified by multiwall carbon nanotubes (MWCNTs) were prepared by shear mixing and spin casting. The electrical behaviour and its dependence with temperature between 243 and 353 degrees Kelvin were characterized by measuring the direct current (DC) conductivity. Depending on the fabrication process, both linear and non-linear relationships between conductivity and temperature were observed. In addition, the thermal history also played a role in dictating the conductivity. The implications of these observations for potential application of these files as strain sensors are discussed.

Integrated approach for HP-LNG pump diagnosis and prognostics based on health state probability estimation

This paper presents an innovative prognostics model based on health state probability estimation embedded in the closed loop diagnostic and prognostic system. To employ an appropriate classifier for health state probability estimation in the proposed prognostic model, the comparative intelligent diagnostic tests were conducted using five different classifiers applied to the progressive fault levels of three faults in HP-LNG pump. Two sets of impeller-rubbing data were employed for the prediction of pump remnant life based on estimation of discrete health state probability using an outstanding capability of SVM and a feature selection technique. The results obtained were very encouraging and showed that the proposed prognosis system has the potential to be used as an estimation tool for machine remnant life prediction in real life industrial applications.

Noninvasive in vivo assessment of soft contact lens type on tear film surface quality

To evaluate the effect of soft contact lens type on the in vivo tear film surface quality (TFSQ) on daily disposable lenses and to establish whether two recently developed techniques for noninvasive measurement of TFSQ can distinguish between different contact lens types.

Energy use, indoor temperature and possible adaptation strategies for air-conditioned office buildings in face of global warming

This paper discusses and summarises a recent systematic study on the implication of global warming on air conditioned office buildings in Australia. Four areas are covered, including analysis of historical weather data, generation of future weather data for the impact study of global warming, projection of building performance under various global warming scenarios, and evaluation of various adaptation strategies under 2070 high global warming conditions. Overall, it is found that depending on the assumed future climate scenarios and the location considered, the increase of total building energy use for the sample Australian office building may range from 0.4 to 15.1%. When the increase of annual average outdoor temperature exceeds 2 °C, the risk of overheating will increase significantly. However, the potential overheating problem could be completely eliminated if internal load density is significantly reduced.