Statistical methods for electromyography data and associated problems

This thesis proposes three novel models which extend the statistical methodology for motor unit number estimation, a clinical neurology technique. Motor unit number estimation is important in the treatment of degenerative muscular diseases and, potentially, spinal injury. Additionally, a recent and untested statistic to enable statistical model choice is found to be a practical alternative for larger datasets. The existing methods for dose finding in dual-agent clinical trials are found to be suitable only for designs of modest dimensions. The model choice case-study is the first of its kind containing interesting results using so-called unit information prior distributions.

Interventions to control nosocomial infections : study designs and statistical issues

There is a wide range of potential study designs for intervention studies to decrease nosocomial infections in hospitals. The analysis is complex due to competing events, clustering, multiple timescales and time-dependent period and intervention variables. This review considers the popular pre-post quasi-experimental design and compares it with randomized designs. Randomization can be done in several ways: randomization of the cluster [intensive care unit (ICU) or hospital] in a parallel design; randomization of the sequence in a cross-over design; and randomization of the time of intervention in a stepped-wedge design. We introduce each design in the context of nosocomial infections and discuss the designs with respect to the following key points: bias, control for nonintervention factors, and generalizability. Statistical issues are discussed. A pre-post-intervention design is often the only choice that will be informative for a retrospective analysis of an outbreak setting. It can be seen as a pilot study with further, more rigorous designs needed to establish causality. To yield internally valid results, randomization is needed. Generally, the first choice in terms of the internal validity should be a parallel cluster randomized trial. However, generalizability might be stronger in a stepped-wedge design because a wider range of ICU clinicians may be convinced to participate, especially if there are pilot studies with promising results. For analysis, the use of extended competing risk models is recommended.

Establishing statistical foundations early : data modeling with young learners

This paper addresses research from a three-year longitudinal study that engaged children in data modeling experiences from the beginning school year through to third year (6-8 years). A data modeling approach to statistical development differs in several ways from what is typically done in early classroom experiences with data. In particular, data modeling immerses children in problems that evolve from their own questions and reasoning, with core statistical foundations established early. These foundations include a focus on posing and refining statistical questions within and across contexts, structuring and representing data, making informal inferences, and developing conceptual, representational, and metarepresentational competence. Examples are presented of how young learners developed and sustained informal inferential reasoning and metarepresentational competence across the study to become “sophisticated statisticians”.

Exploring variation in measurement as a foundation for statistical thinking in the elementary school

This study was based on the premise that variation is the foundation of statistics and statistical investigations. The study followed the development of fourth-grade students' understanding of variation through participation in a sequence of two lessons based on measurement. In the first lesson all students measured the arm span of one student, revealing pathways students follow in developing understanding of variation and linear measurement (related to research question 1). In the second lesson each student's arm span was measured once, introducing a different aspect of variation for students to observe and contrast. From this second lesson, students' development of the ability to compare their representations for the two scenarios and explain differences in terms of variation was explored (research question 2). Students' documentation, in both workbook and software formats, enabled us to monitor their engagement and identify their increasing appreciation of the need to observe, represent, and contrast the variation in the data. Following the lessons, a written student assessment was used for judging retention of understanding of variation developed through the lessons and the degree of transfer of understanding to a different scenario (research question 3).

An external field prior for the hidden Potts model with application to cone-beam computed tomography

In images with low contrast-to-noise ratio (CNR), the information gain from the observed pixel values can be insufficient to distinguish foreground objects. A Bayesian approach to this problem is to incorporate prior information about the objects into a statistical model. A method for representing spatial prior information as an external field in a hidden Potts model is introduced. This prior distribution over the latent pixel labels is a mixture of Gaussian fields, centred on the positions of the objects at a previous point in time. It is particularly applicable in longitudinal imaging studies, where the manual segmentation of one image can be used as a prior for automatic segmentation of subsequent images. The method is demonstrated by application to cone-beam computed tomography (CT), an imaging modality that exhibits distortions in pixel values due to X-ray scatter. The external field prior results in a substantial improvement in segmentation accuracy, reducing the mean pixel misclassification rate for an electron density phantom from 87% to 6%. The method is also applied to radiotherapy patient data, demonstrating how to derive the external field prior in a clinical context.

A statistical model for combustion resonance from a DI diesel engine with applications

Introduced in this paper is a Bayesian model for isolating the resonant frequency from combustion chamber resonance. The model shown in this paper focused on characterising the initial rise in the resonant frequency to investigate the rise of in-cylinder bulk temperature associated with combustion. By resolving the model parameters, it is possible to determine: the start of pre-mixed combustion, the start of diffusion combustion, the initial resonant frequency, the resonant frequency as a function of crank angle, the in-cylinder bulk temperature as a function of crank angle and the trapped mass as a function of crank angle. The Bayesian method allows for individual cycles to be examined without cycle-averaging|allowing inter-cycle variability studies. Results are shown for a turbo-charged, common-rail compression ignition engine run at 2000 rpm and full load.

Numeracy and statistical reasoning on entering university

The relationship between mathematics and statistical reasoning frequently receives comment (Vere-Jones 1995, Moore 1997); however most of the research into the area tends to focus on mathematics anxiety. Gnaldi (2003) showed that in a statistics course for psychologists, the statistical understanding of students at the end of the course depended on students’ basic numeracy, rather than the number or level of previous mathematics courses the student had undertaken. As part of a study into the development of statistical thinking at the interface between secondary and tertiary education, students enrolled in an introductory data analysis subject were assessed regarding their statistical reasoning, basic numeracy skills, mathematics background and attitudes towards statistics. This work reports on some key relationships between these factors and in particular the importance of numeracy to statistical reasoning.

Numeracy counts in the statistical reasoning equation

The relationship between mathematics and statistical reasoning frequently receives comment (Vere-Jones 1995, Moore 1997); however most of the research into the area tends to focus on maths anxiety. Gnaldi (Gnaldi 2003) showed that in a statistics course for psychologists, the statistical understanding of students at the end of the course depended on students’ basic numeracy, rather than the number or level of previous mathematics courses the student had undertaken. As part of a study into the development of statistical thinking at the interface between secondary and tertiary education, students enrolled in an introductory data analysis subject were assessed regarding their statistical reasoning ability, basic numeracy skills and attitudes towards statistics. This work reports on the relationships between these factors and in particular the importance of numeracy to statistical reasoning.

Experimental and statistical investigation of Australian native plants for second-generation biodiesel production

This work explores the potential of Australian native plants as a source of second-generation biodiesel for internal combustion engines application. Biodiesels were evaluated from a number of non-edible oil seeds which are grow naturally in Queensland, Australia. The quality of the produced biodiesels has been investigated by several experimental and numerical methods. The research methodology and numerical model developed in this study can be used for a broad range of biodiesel feedstocks and for the future development of renewable native biodiesel in Australia.

Pattern-based topic modelling and its application for information filtering and information retrieval

This thesis targets on a challenging issue that is to enhance users' experience over massive and overloaded web information. The novel pattern-based topic model proposed in this thesis can generate high-quality multi-topic user interest models technically by incorporating statistical topic modelling and pattern mining. We have successfully applied the pattern-based topic model to both fields of information filtering and information retrieval. The success of the proposed model in finding the most relevant information to users mainly comes from its precisely semantic representations to represent documents and also accurate classification of the topics at both document level and collection level.

Case Studies in Bayesian Statistical Modelling and Analysis

Provides an accessible foundation to Bayesian analysis using real world models This book aims to present an introduction to Bayesian modelling and computation, by considering real case studies drawn from diverse fields spanning ecology, health, genetics and finance. Each chapter comprises a description of the problem, the corresponding model, the computational method, results and inferences as well as the issues that arise in the implementation of these approaches. Case Studies in Bayesian Statistical Modelling and Analysis: •Illustrates how to do Bayesian analysis in a clear and concise manner using real-world problems. •Each chapter focuses on a real-world problem and describes the way in which the problem may be analysed using Bayesian methods. •Features approaches that can be used in a wide area of application, such as, health, the environment, genetics, information science, medicine, biology, industry and remote sensing. Case Studies in Bayesian Statistical Modelling and Analysis is aimed at statisticians, researchers and practitioners who have some expertise in statistical modelling and analysis, and some understanding of the basics of Bayesian statistics, but little experience in its application. Graduate students of statistics and biostatistics will also find this book beneficial.

Statistical, electrical and mathematical analysis of water treed cross-linked polyethylene cable insulation

This work examined a new method of detecting small water filled cracks in underground insulation ('water trees') using data from commecially available non-destructive testing equipment. A testing facility was constructed and a computer simulation of the insulation designed in order to test the proposed ageing factor - the degree of non-linearity. This was a large industry-backed project involving an ARC linkage grant, Ergon Energy and the University of Queensland, as well as the Queensland University of Technology.

A new registration method based on Log-Euclidean tensor metrics and its application to genetic studies

In structural brain MRI, group differences or changes in brain structures can be detected using Tensor-Based Morphometry (TBM). This method consists of two steps: (1) a non-linear registration step, that aligns all of the images to a common template, and (2) a subsequent statistical analysis. The numerous registration methods that have recently been developed differ in their detection sensitivity when used for TBM, and detection power is paramount in epidemological studies or drug trials. We therefore developed a new fluid registration method that computes the mappings and performs statistics on them in a consistent way, providing a bridge between TBM registration and statistics. We used the Log-Euclidean framework to define a new regularizer that is a fluid extension of the Riemannian elasticity, which assures diffeomorphic transformations. This regularizer constrains the symmetrized Jacobian matrix, also called the deformation tensor. We applied our method to an MRI dataset from 40 fraternal and identical twins, to revealed voxelwise measures of average volumetric differences in brain structure for subjects with different degrees of genetic resemblance.

Statistical literacy in the elementary school: Opportunities for problem posing

This chapter addresses opportunities for problem posing in developing young children’s statistical literacy, with a focus on student-directed investigations. Although the notion of problem posing has broadened in recent years, there nevertheless remains limited research on how problem posing can be integrated within the regular mathematics curriculum, especially in the areas of statistics and probability. The chapter first reviews briefly aspects of problem posing that have featured in the literature over the years. Consideration is next given to the importance of developing children’s statistical literacy in which problem posing is an inherent feature. Some findings from a school playground investigation conducted in four, fourth-grade classes illustrate the different ways in which children posed investigative questions, how they made predictions about their outcomes and compared these with their findings, and the ways in which they chose to represent their findings.

Assessing a statistical inquiry

As statistical education becomes more firmly embedded in the school curriculum and its value across the curriculum is recognised, attention moves from knowing procedures, such as calculating a mean or drawing a graph, to understanding the purpose of a statistical investigation in decision making in many disciplines. As students learn to complete the stages of an investigation, the question of meaningful assessment of the process arises. This paper considers models for carrying out a statistical inquiry and, based on a four-phase model, creates a developmental squence that can be used for the assessment of outcomes from each of the four phases as well as for the complete inquiry. The developmental sequence is based on the SOLO model, focussing on the "observed" outcomes during the inquiry process.