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.

Model selection with misspecified spatial covariance structure

Spatial data analysis has become more and more important in the studies of ecology and economics during the last decade. One focus of spatial data analysis is how to select predictors, variance functions and correlation functions. However, in general, the true covariance function is unknown and the working covariance structure is often misspecified. In this paper, our target is to find a good strategy to identify the best model from the candidate set using model selection criteria. This paper is to evaluate the ability of some information criteria (corrected Akaike information criterion, Bayesian information criterion (BIC) and residual information criterion (RIC)) for choosing the optimal model when the working correlation function, the working variance function and the working mean function are correct or misspecified. Simulations are carried out for small to moderate sample sizes. Four candidate covariance functions (exponential, Gaussian, Matern and rational quadratic) are used in simulation studies. With the summary in simulation results, we find that the misspecified working correlation structure can still capture some spatial correlation information in model fitting. When the sample size is large enough, BIC and RIC perform well even if the the working covariance is misspecified. Moreover, the performance of these information criteria is related to the average level of model fitting which can be indicated by the average adjusted R square ( [GRAPHICS] ), and overall RIC performs well.

Statistical modelling and power analysis for detecting trends in total suspended sediment loads

The export of sediments from coastal catchments can have detrimental impacts on estuaries and near shore reef ecosystems such as the Great Barrier Reef. Catchment management approaches aimed at reducing sediment loads require monitoring to evaluate their effectiveness in reducing loads over time. However, load estimation is not a trivial task due to the complex behaviour of constituents in natural streams, the variability of water flows and often a limited amount of data. Regression is commonly used for load estimation and provides a fundamental tool for trend estimation by standardising the other time specific covariates such as flow. This study investigates whether load estimates and resultant power to detect trends can be enhanced by (i) modelling the error structure so that temporal correlation can be better quantified, (ii) making use of predictive variables, and (iii) by identifying an efficient and feasible sampling strategy that may be used to reduce sampling error. To achieve this, we propose a new regression model that includes an innovative compounding errors model structure and uses two additional predictive variables (average discounted flow and turbidity). By combining this modelling approach with a new, regularly optimised, sampling strategy, which adds uniformity to the event sampling strategy, the predictive power was increased to 90%. Using the enhanced regression model proposed here, it was possible to detect a trend of 20% over 20 years. This result is in stark contrast to previous conclusions presented in the literature. (C) 2014 Elsevier B.V. All rights reserved.

A generalized estimating equations approach for analysis of the impact of new technology on a trawl fishery

The article describes a generalized estimating equations approach that was used to investigate the impact of technology on vessel performance in a trawl fishery during 1988-96, while accounting for spatial and temporal correlations in the catch-effort data. Robust estimation of parameters in the presence of several levels of clustering depended more on the choice of cluster definition than on the choice of correlation structure within the cluster. Models with smaller cluster sizes produced stable results, while models with larger cluster sizes, that may have had complex within-cluster correlation structures and that had within-cluster covariates, produced estimates sensitive to the correlation structure. The preferred model arising from this dataset assumed that catches from a vessel were correlated in the same years and the same areas, but independent in different years and areas. The model that assumed catches from a vessel were correlated in all years and areas, equivalent to a random effects term for vessel, produced spurious results. This was an unexpected finding that highlighted the need to adopt a systematic strategy for modelling. The article proposes a modelling strategy of selecting the best cluster definition first, and the working correlation structure (within clusters) second. The article discusses the selection and interpretation of the model in the light of background knowledge of the data and utility of the model, and the potential for this modelling approach to apply in similar statistical situations.

Statistical analysis of spectral data: A methodology for designing an intelligent monitoring system for the diabetic foot

Early detection of (pre-)signs of ulceration on a diabetic foot is valuable for clinical practice. Hyperspectral imaging is a promising technique for detection and classification of such (pre-)signs. However, the number of the spectral bands should be limited to avoid overfitting, which is critical for pixel classification with hyperspectral image data. The goal was to design a detector/classifier based on spectral imaging (SI) with a small number of optical bandpass filters. The performance and stability of the design were also investigated. The selection of the bandpass filters boils down to a feature selection problem. A dataset was built, containing reflectance spectra of 227 skin spots from 64 patients, measured with a spectrometer. Each skin spot was annotated manually by clinicians as "healthy" or a specific (pre-)sign of ulceration. Statistical analysis on the data set showed the number of required filters is between 3 and 7, depending on additional constraints on the filter set. The stability analysis revealed that shot noise was the most critical factor affecting the classification performance. It indicated that this impact could be avoided in future SI systems with a camera sensor whose saturation level is higher than 106, or by postimage processing.