One-dimensional Model for Fluids of Third-grade in Tubes with Constant Radius

Our goal in this paper is to extend previous results obtained for Newtonian and secondgrade fluids to third-grade fluids in the case of an axisymmetric, straight, rigid and impermeable tube with constant cross-section using a one-dimensional hierarchical model based on the Cosserat theory related to fluid dynamics. In this way we can reduce the full threedimensional system of equations for the axisymmetric unsteady motion of a non-Newtonian incompressible third-grade fluid to a system of equations depending on time and on a single spatial variable. Some numerical simulations for the volume flow rate and the the wall shear stress are presented.

Incorporating interdependence in risk likelihood analysis to enhance diagnostics in condition monitoring

This research is aimed at addressing problems in the field of asset management relating to risk analysis and decision making based on data from a Supervisory Control and Data Acquisition (SCADA) system. It is apparent that determining risk likelihood in risk analysis is difficult, especially when historical information is unreliable. This relates to a problem in SCADA data analysis because of nested data. A further problem is in providing beneficial information from a SCADA system to a managerial level information system (e.g. Enterprise Resource Planning/ERP). A Hierarchical Model is developed to address the problems. The model is composed of three different Analyses: Hierarchical Analysis, Failure Mode and Effect Analysis, and Interdependence Analysis. The significant contributions from the model include: (a) a new risk analysis model, namely an Interdependence Risk Analysis Model which does not rely on the existence of historical information because it utilises Interdependence Relationships to determine the risk likelihood, (b) improvement of the SCADA data analysis problem by addressing the nested data problem through the Hierarchical Analysis, and (c) presentation of a framework to provide beneficial information from SCADA systems to ERP systems. The case study of a Water Treatment Plant is utilised for model validation.

Combining expert opinions in prior elicitation

A method of eliciting prior distributions for Bayesian models using expert knowledge is proposed. Elicitation is a widely studied problem, from a psychological perspective as well as from a statistical perspective. Here, we are interested in combining opinions from more than one expert using an explicitly model-based approach so that we may account for various sources of variation affecting elicited expert opinions. We use a hierarchical model to achieve this. We apply this approach to two problems. The first problem involves a food risk assessment problem involving modelling dose-response for Listeria monocytogenes contamination of mice. The second concerns the time taken by PhD students to submit their thesis in a particular school.

Daily average temperature and mortality among the elderly : a meta-analysis and systematic review of epidemiological evidence

The impact of climate change on the health of vulnerable groups such as the elderly has been of increasing concern. However, to date there has been no meta-analysis of current literature relating to the effects of temperature fluctuations upon mortality amongst the elderly. We synthesised risk estimates of the overall impact of daily mean temperature on elderly mortality across different continents. A comprehensive literature search was conducted using MEDLINE and PubMed to identify papers published up to December 2010. Selection criteria including suitable temperature indicators, endpoints, study-designs and identification of threshold were used. A two-stage Bayesian hierarchical model was performed to summarise the percent increase in mortality with a 1°C temperature increase (or decrease) with 95% confidence intervals in hot (or cold) days, with lagged effects also measured. Fifteen studies met the eligibility criteria and almost 13 million elderly deaths were included in this meta-analysis. In total, there was a 2-5% increase for a 1°C increment during hot temperature intervals, and a 1-2 % increase in all-cause mortality for a 1°C decrease during cold temperature intervals. Lags of up to 9 days in exposure to cold temperature intervals were substantially associated with all-cause mortality, but no substantial lagged effects were observed for hot intervals. Thus, both hot and cold temperatures substantially increased mortality among the elderly, but the magnitude of heat-related effects seemed to be larger than that of cold effects within a global context.

Speckle reduction in optical coherence tomography imaging by affine-motion image registration

Signal-degrading speckle is one factor that can reduce the quality of optical coherence tomography images. We demonstrate the use of a hierarchical model-based motion estimation processing scheme based on an affine-motion model to reduce speckle in optical coherence tomography imaging, by image registration and the averaging of multiple B-scans. The proposed technique is evaluated against other methods available in the literature. The results from a set of retinal images show the benefit of the proposed technique, which provides an improvement in signal-to-noise ratio of the square root of the number of averaged images, leading to clearer visual information in the averaged image. The benefits of the proposed technique are also explored in the case of ocular anterior segment imaging.

A Bayesian approach for estimating detection times in horses : exploring the pharmacokinetics of a urinary acepromazine metabolite

We describe the population pharmacokinetics of an acepromazine (ACP) metabolite (2-(1-hydroxyethyl)promazine) (HEPS) in horses for the estimation of likely detection times in plasma and urine. Acepromazine (30 mg) was administered to 12 horses, and blood and urine samples were taken at frequent intervals for chemical analysis. A Bayesian hierarchical model was fitted to describe concentration-time data and cumulative urine amounts for HEPS. The metabolite HEPS was modelled separately from the parent ACP as the half-life of the parent was considerably less than that of the metabolite. The clearance ($Cl/F_{PM}$) and volume of distribution ($V/F_{PM}$), scaled by the fraction of parent converted to metabolite, were estimated as 769 L/h and 6874 L, respectively. For a typical horse in the study, after receiving 30 mg of ACP, the upper limit of the detection time was 35 hours in plasma and 100 hours in urine, assuming an arbitrary limit of detection of 1 $\mu$g/L, and a small ($\approx 0.01$) probability of detection. The model derived allowed the probability of detection to be estimated at the population level. This analysis was conducted on data collected from only 12 horses, but we assume that this is representative of the wider population.

Critical Factors of Promoting Market Demand of Sustainable Housing in Australia

Strong regulatory pressure on environmental issues and the improved public awareness will continue to influence the market demand for sustainable housing in the coming years. Despite this potential, the voluntary up-take rate of sustainable practices is not as high as expected within the new built housing industry. This is in contrast to the influx of emerging building technologies, new materials and innovative designs as seen in office buildings and exemplar homes built worldwide. One possible reason for this is that key stakeholders such as developers, builders and consumers do not fully understand and appreciate the tangible and mutual benefits of sustainability in their professional and business activities. This situation warrants the study of a multifaceted strategy that integrates the needs of multiple stakeholders. This research investigates multiple factors that affect key stakeholder’s benefits in sustainable housing implementation. Drawing insights from a quantitative study on a questionnaire survey and a qualitative study of in-depth interviews with key stakeholders in the Australian housing industry, 11 critical factors of driving market demand for sustainable housing were unearthed. Their inter-relationships were identified with the aid of Interpretive Structural Modelling. The study concludes with a hierarchical model that amalgamates the strategies for the decision making of key stakeholders.

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

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

Marginal reversible jump Markov chain Monte Carlo with application to motor unit number estimation

Motor unit number estimation (MUNE) is a method which aims to provide a quantitative indicator of progression of diseases that lead to loss of motor units, such as motor neurone disease. However the development of a reliable, repeatable and fast real-time MUNE method has proved elusive hitherto. Ridall et al. (2007) implement a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm to produce a posterior distribution for the number of motor units using a Bayesian hierarchical model that takes into account biological information about motor unit activation. However we find that the approach can be unreliable for some datasets since it can suffer from poor cross-dimensional mixing. Here we focus on improved inference by marginalising over latent variables to create the likelihood. In particular we explore how this can improve the RJMCMC mixing and investigate alternative approaches that utilise the likelihood (e.g. DIC (Spiegelhalter et al., 2002)). For this model the marginalisation is over latent variables which, for a larger number of motor units, is an intractable summation over all combinations of a set of latent binary variables whose joint sample space increases exponentially with the number of motor units. We provide a tractable and accurate approximation for this quantity and also investigate simulation approaches incorporated into RJMCMC using results of Andrieu and Roberts (2009).

Combining elicited expert knowledge into Bayesian priors

Information that is elicited from experts can be treated as `data', so can be analysed using a Bayesian statistical model, to formulate a prior model. Typically methods for encoding a single expert's knowledge have been parametric, constrained by the extent of an expert's knowledge and energy regarding a target parameter. Interestingly these methods have often been deterministic, in that all elicited information is treated at `face value', without error. Here we sought a parametric and statistical approach for encoding assessments from multiple experts. Our recent work proposed and demonstrated the use of a flexible hierarchical model for this purpose. In contrast to previous mathematical approaches like linear or geometric pooling, our new approach accounts for several sources of variation: elicitation error, encoding error and expert diversity. Of interest are the practical, mathematical and philosophical interpretations of this form of hierarchical pooling (which is both statistical and parametric), and how it fits within the subjective Bayesian paradigm. Case studies from a bioassay and project management (on PhDs) are used to illustrate the approach.