Approximate Bayesian Computation for astronomical model analysis : a case study in galaxy demographics and morphological transformation at high redshift

Approximate Bayesian Computation’ (ABC) represents a powerful methodology for the analysis of complex stochastic systems for which the likelihood of the observed data under an arbitrary set of input parameters may be entirely intractable – the latter condition rendering useless the standard machinery of tractable likelihood-based, Bayesian statistical inference [e.g. conventional Markov chain Monte Carlo (MCMC) simulation]. In this paper, we demonstrate the potential of ABC for astronomical model analysis by application to a case study in the morphological transformation of high-redshift galaxies. To this end, we develop, first, a stochastic model for the competing processes of merging and secular evolution in the early Universe, and secondly, through an ABC-based comparison against the observed demographics of massive (Mgal > 1011 M⊙) galaxies (at 1.5 < z < 3) in the Cosmic Assembly Near-IR Deep Extragalatic Legacy Survey (CANDELS)/Extended Groth Strip (EGS) data set we derive posterior probability densities for the key parameters of this model. The ‘Sequential Monte Carlo’ implementation of ABC exhibited herein, featuring both a self-generating target sequence and self-refining MCMC kernel, is amongst the most efficient of contemporary approaches to this important statistical algorithm. We highlight as well through our chosen case study the value of careful summary statistic selection, and demonstrate two modern strategies for assessment and optimization in this regard. Ultimately, our ABC analysis of the high-redshift morphological mix returns tight constraints on the evolving merger rate in the early Universe and favours major merging (with disc survival or rapid reformation) over secular evolution as the mechanism most responsible for building up the first generation of bulges in early-type discs.

Model choice problems using approximate Bayesian computation with applications to pathogen transmission data sets

Analytically or computationally intractable likelihood functions can arise in complex statistical inferential problems making them inaccessible to standard Bayesian inferential methods. Approximate Bayesian computation (ABC) methods address such inferential problems by replacing direct likelihood evaluations with repeated sampling from the model. ABC methods have been predominantly applied to parameter estimation problems and less to model choice problems due to the added difficulty of handling multiple model spaces. The ABC algorithm proposed here addresses model choice problems by extending Fearnhead and Prangle (2012, Journal of the Royal Statistical Society, Series B 74, 1–28) where the posterior mean of the model parameters estimated through regression formed the summary statistics used in the discrepancy measure. An additional stepwise multinomial logistic regression is performed on the model indicator variable in the regression step and the estimated model probabilities are incorporated into the set of summary statistics for model choice purposes. A reversible jump Markov chain Monte Carlo step is also included in the algorithm to increase model diversity for thorough exploration of the model space. This algorithm was applied to a validating example to demonstrate the robustness of the algorithm across a wide range of true model probabilities. Its subsequent use in three pathogen transmission examples of varying complexity illustrates the utility of the algorithm in inferring preference of particular transmission models for the pathogens.

Design and experimental testing of air slab caps which convert commercial electron diodes into dual purpose, correction-free diodes for small field dosimetry

Purpose Two diodes which do not require correction factors for small field relative output measurements are designed and validated using experimental methodology. This was achieved by adding an air layer above the active volume of the diode detectors, which canceled out the increase in response of the diodes in small fields relative to standard field sizes. Methods Due to the increased density of silicon and other components within a diode, additional electrons are created. In very small fields, a very small air gap acts as an effective filter of electrons with a high angle of incidence. The aim was to design a diode that balanced these perturbations to give a response similar to a water-only geometry. Three thicknesses of air were placed at the proximal end of a PTW 60017 electron diode (PTWe) using an adjustable “air cap”. A set of output ratios (ORfclin Det ) for square field sizes of side length down to 5 mm was measured using each air thickness and compared to ORfclin Det measured using an IBA stereotactic field diode (SFD). k fclin, f msr Qclin,Qmsr was transferred from the SFD to the PTWe diode and plotted as a function of air gap thickness for each field size. This enabled the optimal air gap thickness to be obtained by observing which thickness of air was required such that k fclin, f msr Qclin,Qmsr was equal to 1.00 at all field sizes. A similar procedure was used to find the optimal air thickness required to make a modified Sun Nuclear EDGE detector (EDGEe) which s “correction-free” in small field relative dosimetry. In addition, the feasibility of experimentally transferring k fclin, f msr Qclin,Qmsr values from the SFD to unknown diodes was tested by comparing the experimentally transferred k fclin, f msr Qclin,Qmsr values for unmodified PTWe and EDGEe diodes to Monte Carlo simulated values. Results 1.0 mm of air was required to make the PTWe diode correction-free. This modified diode (PTWeair) produced output factors equivalent to those in water at all field sizes (5–50 mm). The optimal air thickness required for the EDGEe diode was found to be 0.6 mm. The modified diode (EDGEeair) produced output factors equivalent to those in water, except at field sizes of 8 and 10 mm where it measured approximately 2% greater than the relative dose to water. The experimentally calculated k fclin, f msr Qclin,Qmsr for both the PTWe and the EDGEe diodes (without air) matched Monte Carlo simulated results, thus proving that it is feasible to transfer k fclin, f msr Qclin,Qmsr from one commercially available detector to another using experimental methods and the recommended experimental setup. Conclusions It is possible to create a diode which does not require corrections for small field output factor measurements. This has been performed and verified experimentally. The ability of a detector to be “correction-free” depends strongly on its design and composition. A nonwater-equivalent detector can only be “correction-free” if competing perturbations of the beam cancel out at all field sizes. This should not be confused with true water equivalency of a detector.

SHM through flexible vibration sensing technologies and robust safety evaluation paradigm

This research has successfully developed a novel synthetic structural health monitoring system model that is cost-effective and flexible in sensing and data acquisition; and robust in the structural safety evaluation aspect for the purpose of long-term and frequent monitoring of large-scale civil infrastructure during their service lives. Not only did it establish a real-world structural monitoring test-bed right at the heart of QUT Gardens Point Campus but it can also facilitate reliable and prompt protection for any built infrastructure system as well as the user community involved.

Contributions to Bayesian experimental design

This thesis progresses Bayesian experimental design by developing novel methodologies and extensions to existing algorithms. Through these advancements, this thesis provides solutions to several important and complex experimental design problems, many of which have applications in biology and medicine. This thesis consists of a series of published and submitted papers. In the first paper, we provide a comprehensive literature review on Bayesian design. In the second paper, we discuss methods which may be used to solve design problems in which one is interested in finding a large number of (near) optimal design points. The third paper presents methods for finding fully Bayesian experimental designs for nonlinear mixed effects models, and the fourth paper investigates methods to rapidly approximate the posterior distribution for use in Bayesian utility functions.

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.

Pre-processing for approximate Bayesian computation in image analysis

Most of the existing algorithms for approximate Bayesian computation (ABC) assume that it is feasible to simulate pseudo-data from the model at each iteration. However, the computational cost of these simulations can be prohibitive for high dimensional data. An important example is the Potts model, which is commonly used in image analysis. Images encountered in real world applications can have millions of pixels, therefore scalability is a major concern. We apply ABC with a synthetic likelihood to the hidden Potts model with additive Gaussian noise. Using a pre-processing step, we fit a binding function to model the relationship between the model parameters and the synthetic likelihood parameters. Our numerical experiments demonstrate that the precomputed binding function dramatically improves the scalability of ABC, reducing the average runtime required for model fitting from 71 hours to only 7 minutes. We also illustrate the method by estimating the smoothing parameter for remotely sensed satellite imagery. Without precomputation, Bayesian inference is impractical for datasets of that scale.

Estimating the burden of disease attributable to excess body weight in South Africa in 2000

Objective. To estimate the burden of disease attributable to excess body weight using the body mass index (BMI), by age and sex, in South Africa in 2000. Design. World Health Organization comparative risk assessment (CRA) methodology was followed. Re-analysis of the 1998 South Africa Demographic and Health Survey data provided mean BMI estimates by age and sex. Populationattributable fractions were calculated and applied to revised burden of disease estimates. Monte Carlo simulation-modelling techniques were used for the uncertainty analysis. Setting. South Africa. Subjects. Adults 30 years of age. Outcome measures. Deaths and disability-adjusted life years (DALYs) from ischaemic heart disease, ischaemic stroke, hypertensive disease, osteoarthritis, type 2 diabetes mellitus, and selected cancers. Results. Overall, 87% of type 2 diabetes, 68% of hypertensive disease, 61% of endometrial cancer, 45% of ischaemic stroke, 38% of ischaemic heart disease, 31% of kidney cancer, 24% of osteoarthritis, 17% of colon cancer, and 13% of postmenopausal breast cancer were attributable to a BMI 21 kg/m2. Excess body weight is estimated to have caused 36 504 deaths (95% uncertainty interval 31 018 - 38 637) or 7% (95% uncertainty interval 6.0 - 7.4%) of all deaths in 2000, and 462 338 DALYs (95% uncertainty interval 396 512 - 478 847) or 2.9% of all DALYs (95% uncertainty interval 2.4 - 3.0%). The burden in females was approximately double that in males. Conclusions. This study shows the importance of recognising excess body weight as a major risk to health, particularly among females, highlighting the need to develop, implement and evaluate comprehensive interventions to achieve lasting change in the determinants and impact of excess body weight.

Estimating the burden of disease attributable to physical inactivity in South Africa in 2000

Objectives. To quantify the burden of disease attributable to physical inactivity in persons 15 years or older, by age group and sex, in South Africa for 2000. Design. The global comparative risk assessment (CRA) methodology of the World Health Organization was followed to estimate the disease burden attributable to physical inactivity. Levels of physical activity for South Africa were obtained from the World Health Survey 2003. A theoretical minimum risk exposure of zero, associated outcomes, relative risks, and revised burden of disease estimates were used to calculate population-attributable fractions and the burden attributed to physical inactivity. Monte Carlo simulation-modelling techniques were used for the uncertainty analysis. Setting. South Africa. Subjects. Adults ≥ 15 years. Outcome measures. Deaths and disability-adjusted life years (DALYs) from ischaemic heart disease, ischaemic stroke, breast cancer, colon cancer, and type 2 diabetes mellitus. Results. Overall in adults ≥ 15 years in 2000, 30% of ischaemic heart disease, 27% of colon cancer, 22% of ischaemic stroke, 20% of type 2 diabetes, and 17% of breast cancer were attributable to physical inactivity. Physical inactivity was estimated to have caused 17 037 (95% uncertainty interval 11 394 - 20 407), or 3.3% (95% uncertainty interval 2.2 - 3.9%) of all deaths in 2000, and 176 252 (95% uncertainty interval 133 733 - 203 628) DALYs, or 1.1% (95% uncertainty interval 0.8 - 1.3%) of all DALYs in 2000. Conclusions. Compared with other regions and the global average, South African adults have a particularly high prevalence of physical inactivity. In terms of attributable deaths, physical inactivity ranked 9th compared with other risk factors, and 12th in terms of DALYs. There is a clear need to assess why South Africans are particularly inactive, and to ensure that physical activity/inactivity is addressed as a national health priority.

Multi-modal deformable medical image registration

Non-rigid image registration is an essential tool required for overcoming the inherent local anatomical variations that exist between images acquired from different individuals or atlases. Furthermore, certain applications require this type of registration to operate across images acquired from different imaging modalities. One popular local approach for estimating this registration is a block matching procedure utilising the mutual information criterion. However, previous block matching procedures generate a sparse deformation field containing displacement estimates at uniformly spaced locations. This neglects to make use of the evidence that block matching results are dependent on the amount of local information content. This paper presents a solution to this drawback by proposing the use of a Reversible Jump Markov Chain Monte Carlo statistical procedure to optimally select grid points of interest. Three different methods are then compared to propagate the estimated sparse deformation field to the entire image including a thin-plate spline warp, Gaussian convolution, and a hybrid fluid technique. Results show that non-rigid registration can be improved by using the proposed algorithm to optimally select grid points of interest.

Characterisation of the half-field beam penumbra for a variety of blocking set-ups

Measurements of half-field beam penumbra were taken using EBT2 film for a variety of blocking techniques. It was shown that minimizing the SSD reduces the penumbra as the effects of beam divergence are diminished. The addition of a lead block directly on the surface provides optimal results with a 10-90% penumbra of 0.53 ± 0.02 cm. To resolve the uncertainties encountered in film measurements, future Monte Carlo measurements of halffield penumbras are to be conducted.

Estimating the burden of disease attributable to four selected environmental risk factors in South Africa

INTRODUCTION: The first South African National Burden of Disease study quantified the underlying causes of premature mortality and morbidity experienced in South Africa in the year 2000. This was followed by a Comparative Risk Assessment to estimate the contributions of 17 selected risk factors to burden of disease in South Africa. This paper describes the health impact of exposure to four selected environmental risk factors: unsafe water, sanitation and hygiene; indoor air pollution from household use of solid fuels; urban outdoor air pollution and lead exposure. METHODS: The study followed World Health Organization comparative risk assessment methodology. Population-attributable fractions were calculated and applied to revised burden of disease estimates (deaths and disability adjusted life years, [DALYs]) from the South African Burden of Disease study to obtain the attributable burden for each selected risk factor. The burden attributable to the joint effect of the four environmental risk factors was also estimated taking into account competing risks and common pathways. Monte Carlo simulation-modeling techniques were used to quantify sampling, uncertainty. RESULTS: Almost 24 000 deaths were attributable to the joint effect of these four environmental risk factors, accounting for 4.6% (95% uncertainty interval 3.8-5.3%) of all deaths in South Africa in 2000. Overall the burden due to these environmental risks was equivalent to 3.7% (95% uncertainty interval 3.4-4.0%) of the total disease burden for South Africa, with unsafe water sanitation and hygiene the main contributor to joint burden. The joint attributable burden was especially high in children under 5 years of age, accounting for 10.8% of total deaths in this age group and 9.7% of burden of disease. CONCLUSION: This study highlights the public health impact of exposure to environmental risks and the significant burden of preventable disease attributable to exposure to these four major environmental risk factors in South Africa. Evidence-based policies and programs must be developed and implemented to address these risk factors at individual, household, and community levels.

Estimating the burden of disease attributable to high cholesterol in South Africa in 2000

Objectives To estimate the burden of disease attributable to high cholesterol in adults aged 30 years and older in South Africa in 2000. Design World Health Organization comparative risk assessment (CRA) methodology was followed. Small community studies were used to derive the prevalence by population group. Population-attributable fractions were calculated and applied to revised burden of disease estimates for the relevant disease categories for each population group. The total attributable burden for South Africa in 2000 was obtained by adding the burden attributed to high cholesterol for the four population groups. Monte Carlo simulation-modelling techniques were used for uncertainty analysis. Setting South Africa. Subjects Black African, coloured, white and Indian adults aged 30 years and older. Outcome measures Mortality and disability-adjusted life years (DALYs) from ischaemic heart disease (IHD) and ischaemic stroke. Results Overall, about 59% of IHD and 29% of ischaemic stroke burden in adult males and females (30+ years) were attributable to high cholesterol (≥ 3.8 mmol/l), with marked variation by population group. High cholesterol was estimated to have caused 24 144 deaths (95% uncertainty interval 22 404 - 25 286) or 4.6% (95% uncertainty interval 4.3 - 4.9%) of all deaths in South Africa in 2000. Since most cholesterol-related cardiovascular disease events occurred in middle or old age, the loss of life years comprised a smaller proportion of the total: 222 923 DALYs (95% uncertainty interval 206 712 - 233 460) or 1.4% of all DALYs (95% uncertainty interval 1.3 - 1.4%) in South Africa in 2000. Conclusions High cholesterol is an important cardiovascular risk factor in all population groups in South Africa.