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.

Estimation of energy saving of commercial building by living wall and green facade in sub-tropical climate of Australia

This paper investigates energy saving potential of commercial building by living wall and green façade system using Envelope Thermal Transfer Value (ETTV) equation in Sub-tropical climate of Australia. Energy saving of four commercial buildings was quantified by applying living wall and green façade system to the west facing wall. A field experimental facility, from which temperature data of living wall system was collected, was used to quantify wall temperatures and heat gain under controlled conditions. The experimental parameters were accumulated with extensive data of existing commercial building to quantify energy saving. Based on temperature data of living wall system comprised of Australian native plants, equivalent temperature of living wall system has been computed. Then, shading coefficient of plants in green façade system has been included in mathematical equation and in graphical analysis. To minimize the air-conditioned load of commercial building, therefore to minimize the heat gain of commercial building, an analysis of building heat gain reduction by living wall and green façade system has been performed. Overall, cooling energy performance of commercial building before and after living wall and green façade system application has been examined. The quantified energy saving showed that only living wall system on opaque part of west facing wall can save 8-13 % of cooling energy consumption where as only green façade system on opaque part of west facing wall can save 9.5-18% cooling energy consumption of commercial building. Again, green façade system on fenestration system on west facing wall can save 28-35 % of cooling energy consumption where as combination of both living wall on opaque part of west facing wall and green façade on fenestration system on west facing wall can save 35-40% cooling energy consumption of commercial building in sub-tropical climate of Australia.

In vitro estimation of foetal liver volume using ultrasound, x-ray computed tomography and magnetic resonance imaging

Sixteen formalin-fixed foetal livers were scanned in vitro using a new system for estimating volume from a sequence of multiplanar 2D ultrasound images. Three different scan techniques were used (radial, parallel and slanted) and four volume estimation algorithms (ellipsoid, planimetry, tetrahedral and ray tracing). Actual liver volumes were measured by water displacement. Twelve of the sixteen livers also received x-ray computed tomography (CT) and magnetic resonance (MR) scans and the volumes were calculated using voxel counting and planimetry. The percentage accuracy (mean ± SD) was 5.3 ± 4.7%, −3.1 ± 9.6% and −0.03 ± 9.7% for ultrasound (radial scans, ray volumes), MR and CT (voxel counting) respectively. The new system may be useful for accurately estimating foetal liver volume in utero.

An estimation of crash risks using a log-linear model and the induced exposure technique

Prevention and safety promotion programmes. Traditionally, in-depth investigations of crash risks are conducted using exposure controlled study or case-control methodology. However, these studies need either observational data for control cases or exogenous exposure data like vehicle-kilometres travel, entry flow or product of conflicting flow for a particular traffic location, or a traffic site. These data are not readily available and often require extensive data collection effort on a system-wide basis. Aim: The objective of this research is to propose an alternative methodology to investigate crash risks of a road user group in different circumstances using readily available traffic police crash data. Methods: This study employs a combination of a log-linear model and the quasi-induced exposure technique to estimate crash risks of a road user group. While the log-linear model reveals the significant interactions and thus the prevalence of crashes of a road user group under various sets of traffic, environmental and roadway factors, the quasi-induced exposure technique estimates relative exposure of that road user in the same set of explanatory variables. Therefore, the combination of these two techniques provides relative measures of crash risks under various influences of roadway, environmental and traffic conditions. The proposed methodology has been illustrated using Brisbane motorcycle crash data of five years. Results: Interpretations of results on different combination of interactive factors show that the poor conspicuity of motorcycles is a predominant cause of motorcycle crashes. Inability of other drivers to correctly judge the speed and distance of an oncoming motorcyclist is also evident in right-of-way violation motorcycle crashes at intersections. Discussion and Conclusions: The combination of a log-linear model and the induced exposure technique is a promising methodology and can be applied to better estimate crash risks of other road users. This study also highlights the importance of considering interaction effects to better understand hazardous situations. A further study on the comparison between the proposed methodology and case-control method would be useful.

Accounting for calibration uncertainty in phylogenetic estimation of evolutionary divergence times

The estimation of phylogenetic divergence times from sequence data is an important component of many molecular evolutionary studies. There is now a general appreciation that the procedure of divergence dating is considerably more complex than that initially described in the 1960s by Zuckerkandl and Pauling (1962, 1965). In particular, there has been much critical attention toward the assumption of a global molecular clock, resulting in the development of increasingly sophisticated techniques for inferring divergence times from sequence data. In response to the documentation of widespread departures from clocklike behavior, a variety of local- and relaxed-clock methods have been proposed and implemented. Local-clock methods permit different molecular clocks in different parts of the phylogenetic tree, thereby retaining the advantages of the classical molecular clock while casting off the restrictive assumption of a single, global rate of substitution (Rambaut and Bromham 1998; Yoder and Yang 2000).

A framework for life cycle cost estimation of a product family at the early stage of product development

A cost estimation method is required to estimate the life cycle cost of a product family at the early stage of product development in order to evaluate the product family design. There are difficulties with existing cost estimation techniques in estimating the life cycle cost for a product family at the early stage of product development. This paper proposes a framework that combines a knowledge based system and an activity based costing techniques in estimating the life cycle cost of a product family at the early stage of product development. The inputs of the framework are the product family structure and its sub function. The output of the framework is the life cycle cost of a product family that consists of all costs at each product family level and the costs of each product life cycle stage. The proposed framework provides a life cycle cost estimation tool for a product family at the early stage of product development using high level information as its input. The framework makes it possible to estimate the life cycle cost of various product family that use any types of product structure. It provides detailed information related to the activity and resource costs of both parts and products that can assist the designer in analyzing the cost of the product family design. In addition, it can reduce the required amount of information and time to construct the cost estimation system.

Informational constraints on the emergence of passing direction in the team sport of futsal

This study investigated compound spatial and temporal measures of interpersonal interactions purported to constrain the emergence of affordances for passing direction in the team sport of futsal. For this purpose, attacker–defender interactions in 37 sequences of play from a futsal competition in which 24 male professional players participated (M=30.04 years, SD=4.10) were filmed and analysed using TACTO software. Relative angle data were used as measures to study coordination tendencies that emerged between players during performance. Results showed that the direction for a pass emerged from relative angles between: (1) the vector from a ball carrier to ball receiver and the vector from the ball carrier to the nearest defender (70°) (p<0.01) and (2) the vector from a ball carrier to ball receiver and the vector from the ball carrier to a ball receiver's nearest defender (31°) (p < 0.01). Furthermore, passing direction was also constrained by temporal information from the emergence of both angles, since the pass was performed to attacker–defender dyads with the highest velocities of these angles (p < 0.05). Results suggested that decisions on selecting the direction of a pass in the team sport of futsal emerged at critical values of these key compound motion measures.