Bayesian algorithms with applications

Advances in algorithms for approximate sampling from a multivariable target function have led to solutions to challenging statistical inference problems that would otherwise not be considered by the applied scientist. Such sampling algorithms are particularly relevant to Bayesian statistics, since the target function is the posterior distribution of the unobservables given the observables. In this thesis we develop, adapt and apply Bayesian algorithms, whilst addressing substantive applied problems in biology and medicine as well as other applications. For an increasing number of high-impact research problems, the primary models of interest are often sufficiently complex that the likelihood function is computationally intractable. Rather than discard these models in favour of inferior alternatives, a class of Bayesian "likelihoodfree" techniques (often termed approximate Bayesian computation (ABC)) has emerged in the last few years, which avoids direct likelihood computation through repeated sampling of data from the model and comparing observed and simulated summary statistics. In Part I of this thesis we utilise sequential Monte Carlo (SMC) methodology to develop new algorithms for ABC that are more efficient in terms of the number of model simulations required and are almost black-box since very little algorithmic tuning is required. In addition, we address the issue of deriving appropriate summary statistics to use within ABC via a goodness-of-fit statistic and indirect inference. Another important problem in statistics is the design of experiments. That is, how one should select the values of the controllable variables in order to achieve some design goal. The presences of parameter and/or model uncertainty are computational obstacles when designing experiments but can lead to inefficient designs if not accounted for correctly. The Bayesian framework accommodates such uncertainties in a coherent way. If the amount of uncertainty is substantial, it can be of interest to perform adaptive designs in order to accrue information to make better decisions about future design points. This is of particular interest if the data can be collected sequentially. In a sense, the current posterior distribution becomes the new prior distribution for the next design decision. Part II of this thesis creates new algorithms for Bayesian sequential design to accommodate parameter and model uncertainty using SMC. The algorithms are substantially faster than previous approaches allowing the simulation properties of various design utilities to be investigated in a more timely manner. Furthermore the approach offers convenient estimation of Bayesian utilities and other quantities that are particularly relevant in the presence of model uncertainty. Finally, Part III of this thesis tackles a substantive medical problem. A neurological disorder known as motor neuron disease (MND) progressively causes motor neurons to no longer have the ability to innervate the muscle fibres, causing the muscles to eventually waste away. When this occurs the motor unit effectively ‘dies’. There is no cure for MND, and fatality often results from a lack of muscle strength to breathe. The prognosis for many forms of MND (particularly amyotrophic lateral sclerosis (ALS)) is particularly poor, with patients usually only surviving a small number of years after the initial onset of disease. Measuring the progress of diseases of the motor units, such as ALS, is a challenge for clinical neurologists. Motor unit number estimation (MUNE) is an attempt to directly assess underlying motor unit loss rather than indirect techniques such as muscle strength assessment, which generally is unable to detect progressions due to the body’s natural attempts at compensation. Part III of this thesis builds upon a previous Bayesian technique, which develops a sophisticated statistical model that takes into account physiological information about motor unit activation and various sources of uncertainties. More specifically, we develop a more reliable MUNE method by applying marginalisation over latent variables in order to improve the performance of a previously developed reversible jump Markov chain Monte Carlo sampler. We make other subtle changes to the model and algorithm to improve the robustness of the approach.

Calcite precipitation induced by clay-bleach cation exchange in andesitic reservoir rocks

Experiments were carried out on the sodium hypochlorite bleach sensitivity of a deep subsurface andesitic reservoir in order to predict possible deleterious mineral transformations during a downhole clean-up job. Experiments involved examination of core samples from the reservoir using an Environmental Scanning Electron Microscope (ESEM) with an attached Energy Dispersive Spectrometer (EDS) before and after the samples were immersed in bleach. Bleach immersion of whole-rock samples resulted in rapid (less than 1 min) precipitation of abundant 3.0-10.0-μm-wide calcite rhombs within clay-associated micropores and on clay and feldspar grain surfaces. Abundant microporefilling calcite rhombs also formed in pure separates of constituent chlorite/corrensite, whereas no calcite formed in a pure separate of constituent zeolite. These experiments indicate that corrensite is the likely calcium source in this experimental fluid-rock system. Formation of calcite occurs via a cation exchange reaction in which calcium in the smectitic interlayers of corrensite exchanges for sodium in the bleach. Serious formation damage due to calcite precipitation would have occurred in the andesite reservoir had it been exposed to bleach. This finding gives credence to earlier suggestions that cation exchange reactions have the potential to cause calcite precipitation in some sandstone reservoirs when exposed to drilling, completion or stimulation fluids. © 1993.

Effect of aging time and Al substitution on the morphology of aluminous goethite

Goethite and Al-substituted goethite were synthesized from the reaction between ferric nitrate and/or aluminum nitrate and potassium hydroxide. XRF, XRD, TEM with EDS were used to characterize the chemical composition, phase and lattice parameters, and morphology of the synthesized products. The results show that d(020) decreases from 4.953 to 4.949 Å and the b dimension decreases from 9.951 Å to 9.906 Å when the aging time increases from 6 days to 42 days for 9.09 mol% Al-substituted goethite. A sample with 9.09 mol% Al substitution in Al-substituted goethite was prepared by a rapid co-precipitation method. In the sample, 13.45 mol%, 12.31 mol% and 5.85 mol% Al substitution with a crystal size of 163, 131, and 45 nm are observed as shown in the TEM images and EDS. The crystal size of goethite is positively related to the degree of Al substitution according to the TEM images and EDS results. Thus, this methodology is proved to be effective to distinguish the morphology of goethite and Al substituted goethite.

Effect of preparation method of palygorskite-supported Fe and Ni catalysts on catalytic cracking of biomass tar

In this study, the effect of catalyst preparation and additive precursors on the catalytic decomposition of biomass using palygorskite-supported Fe and Ni catalysts was investigated. The catalysts were characterized by X-ray diffraction (XRD) and transmission electron microscopy (TEM). It is concluded that the most active additive precursor was Fe(NO3)3·9H2O. As for the catalyst preparation method, co-precipitation had superiority over incipient wetness impregnation at low Fe loadings.

Likelihood‐free inference for transmission rates of nosocomial pathogens

This chapter contains sections titled: Introduction Case study: Estimating transmission rates of nosocomial pathogens Models and methods Data analysis and results Discussion References

Studies on self-assembly hydrothermal fabrication and thermal stability of Chromium oxyhydroxide nanomaterials synthesised from Chromium oxide colloids

Chromium oxyhydroxide nanomaterials with narrow size-distribution were synthesised through a simple hydrothermal method. Experimental conditions, such as reaction duration and pH values of the precipitation process and hydrothermal treatment played important roles in determining the nature of the final product chromium oxyhydroxide nanomaterials. The effect of these synthesis parameters were studied with the assistance of X-ray diffraction, scanning electron microscopy, X-ray photoelectron spectroscopy and thermogravimetric analyses. This research has developed a controllable synthesis of Chromium oxyhydroxide nanomaterials from Chromium oxide colloids.

Investigating effective wayfinding in airports : a Bayesian network approach

Effective Wayfinding is the successful interplay of human and environmental factors resulting in a person successfully moving from their current position to a desired location in a timely manner. To date this process has not been modelled to reflect this interplay. This paper proposes a complex modelling system approach of wayfinding by using Bayesian Networks to model this process, and applies the model to airports. The model suggests that human factors have a greater impact on effective wayfinding in airports than environmental factors. The greatest influences on human factors are found to be the level of spatial anxiety experienced by travellers and their cognitive and spatial skills. The model also predicted that the navigation pathway that a traveller must traverse has a larger impact on the effectiveness of an airport’s environment in promoting effective wayfinding than the terminal design.

Using a Bayesian network to model colonisation with Vancomycin Resistant Enterococcus (VRE)

Objective: Effective management of multi-resistant organisms is an important issue for hospitals both in Australia and overseas. This study investigates the utility of using Bayesian Network (BN) analysis to examine relationships between risk factors and colonization with Vancomycin Resistant Enterococcus (VRE). Design: Bayesian Network Analysis was performed using infection control data collected over a period of 36 months (2008-2010). Setting: Princess Alexandra Hospital (PAH), Brisbane. Outcome of interest: Number of new VRE Isolates Methods: A BN is a probabilistic graphical model that represents a set of random variables and their conditional dependencies via a directed acyclic graph (DAG). BN enables multiple interacting agents to be studied simultaneously. The initial BN model was constructed based on the infectious disease physician‟s expert knowledge and current literature. Continuous variables were dichotomised by using third quartile values of year 2008 data. BN was used to examine the probabilistic relationships between VRE isolates and risk factors; and to establish which factors were associated with an increased probability of a high number of VRE isolates. Software: Netica (version 4.16). Results: Preliminary analysis revealed that VRE transmission and VRE prevalence were the most influential factors in predicting a high number of VRE isolates. Interestingly, several factors (hand hygiene and cleaning) known through literature to be associated with VRE prevalence, did not appear to be as influential as expected in this BN model. Conclusions: This preliminary work has shown that Bayesian Network Analysis is a useful tool in examining clinical infection prevention issues, where there is often a web of factors that influence outcomes. This BN model can be restructured easily enabling various combinations of agents to be studied.

A Bayesian approach to the determination of ignition delay

A novel in-cylinder pressure method for determining ignition delay has been proposed and demonstrated. This method proposes a new Bayesian statistical model to resolve the start of combustion, defined as being the point at which the band-pass in-cylinder pressure deviates from background noise and the combustion resonance begins. Further, it is demonstrated that this method is still accurate in situations where there is noise present. The start of combustion can be resolved for each cycle without the need for ad hoc methods such as cycle averaging. Therefore, this method allows for analysis of consecutive cycles and inter-cycle variability studies. Ignition delay obtained by this method and by the net rate of heat release have been shown to give good agreement. However, the use of combustion resonance to determine the start of combustion is preferable over the net rate of heat release method because it does not rely on knowledge of heat losses and will still function accurately in the presence of noise. Results for a six-cylinder turbo-charged common-rail diesel engine run with neat diesel fuel at full, three quarters and half load have been presented. Under these conditions the ignition delay was shown to increase as the load was decreased with a significant increase in ignition delay at half load, when compared with three quarter and full loads.

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.

Influence of synthesis route on the catalytic properties of La1−xSrxMnO3

Lanthanum Strontium Manganate (LSM) powders were synthesized by six different routes, namely solid state reaction, drip pyrolysis, citrate, sol-gel, carbonate and oxalate co-precipitation. The LSM samples, produced by firing to 1000 °C for 5 h were then characterized by way of XRD, TPD's of oxygen, TPR and catalytic activity for a simple oxidation reaction, that of carbon monoxide to carbon dioxide. It was found that although the six samples had similar compositions and surface areas they performed quite differently during catalytic characterization. These observed differences correlated more closely to the mode of synthesis, than to the physical properties of the powders, or their impurity levels, indicating that the surface structures created by the different syntheses perform very differently under catalysis conditions. Co-precipitation and drip pyrolysis produced structures that were most efficient at facilitating oxidation type reactions.

In-cylinder pressure and inter-cycle variability analysis for a compression ignition engine : Bayesian approaches

This thesis introduced Bayesian statistics as an analysis technique to isolate resonant frequency information in in-cylinder pressure signals taken from internal combustion engines. Applications of these techniques are relevant to engine design (performance and noise), energy conservation (fuel consumption) and alternative fuel evaluation. The use of Bayesian statistics, over traditional techniques, allowed for a more in-depth investigation into previously difficult to isolate engine parameters on a cycle-by-cycle basis. Specifically, these techniques facilitated the determination of the start of pre-mixed and diffusion combustion and for the in-cylinder temperature profile to be resolved on individual consecutive engine cycles. Dr Bodisco further showed the utility of the Bayesian analysis techniques by applying them to in-cylinder pressure signals taken from a compression ignition engine run with fumigated ethanol.

Utility of COI, CAD and morphological data for resolving relationships within the genus Sarcophaga (sensu lato) (Diptera: Sarcophagidae) : a preliminary study

Currently there are ~3000 known species of Sarcophagidae (Diptera), which are classified into 173 genera in three subfamilies. Almost 25% of sarcophagids belong to the genus Sarcophaga (sensu lato) however little is known about the validity of, and relationships between the ~150 (or more) subgenera of Sarcophaga s.l. In this preliminary study, we evaluated the usefulness of three sources of data for resolving relationships between 35 species from 14 Sarcophaga s.l. subgenera: the mitochondrial COI barcode region, ~800. bp of the nuclear gene CAD, and 110 morphological characters. Bayesian, maximum likelihood (ML) and maximum parsimony (MP) analyses were performed on the combined dataset. Much of the tree was only supported by the Bayesian and ML analyses, with the MP tree poorly resolved. The genus Sarcophaga s.l. was resolved as monophyletic in both the Bayesian and ML analyses and strong support was obtained at the species-level. Notably, the only subgenus consistently resolved as monophyletic was Liopygia. The monophyly of and relationships between the remaining Sarcophaga s.l. subgenera sampled remain questionable. We suggest that future phylogenetic studies on the genus Sarcophaga s.l. use combined datasets for analyses. We also advocate the use of additional data and a range of inference strategies to assist with resolving relationships within Sarcophaga s.l.

Homeostatic epistemology : reliability, coherence and coordination in a Bayesian virtue epistemology

How do agents with limited cognitive capacities flourish in informationally impoverished or unexpected circumstances? Aristotle argued that human flourishing emerged from knowing about the world and our place within it. If he is right, then the virtuous processes that produce knowledge, best explain flourishing. Influenced by Aristotle, virtue epistemology defends an analysis of knowledge where beliefs are evaluated for their truth and the intellectual virtue or competences relied on in their creation. However, human flourishing may emerge from how degrees of ignorance are managed in an uncertain world. Perhaps decision-making in the shadow of knowledge best explains human wellbeing—a Bayesian approach? In this dissertation I argue that a hybrid of virtue and Bayesian epistemologies explains human flourishing—what I term homeostatic epistemology. Homeostatic epistemology supposes that an agent has a rational credence p when p is the product of reliable processes aligned with the norms of probability theory; whereas an agent knows that p when a rational credence p is the product of reliable processes such that: 1) p meets some relevant threshold for belief (such that the agent acts as though p were true and indeed p is true), 2) p coheres with a satisficing set of relevant beliefs and, 3) the relevant set of beliefs is coordinated appropriately to meet the integrated aims of the agent. Homeostatic epistemology recognizes that justificatory relationships between beliefs are constantly changing to combat uncertainties and to take advantage of predictable circumstances. Contrary to holism, justification is built up and broken down across limited sets like the anabolic and catabolic processes that maintain homeostasis in the cells, organs and systems of the body. It is the coordination of choristic sets of reliably produced beliefs that create the greatest flourishing given the limitations inherent in the situated agent.

Bayesian modelling of surveillance and proof of freedom : the mathematical, logical & psychological challenges

Keeping exotic plant pests out of our country relies on good border control or quarantine. However with increasing globalization and mobilization some things slip through. Then the back up systems become important. This can include an expensive form of surveillance that purposively targets particular pests. A much wider net is provided by general surveillance, which is assimilated into everyday activities, like farmers checking the health of their crops. In fact farmers and even home gardeners have provided a front line warning system for some pests (eg European wasp) that could otherwise have wreaked havoc. Mathematics is used to model how surveillance works in various situations. Within this virtual world we can play with various surveillance and management strategies to "see" how they would work, or how to make them work better. One of our greatest challenges is estimating some of the input parameters : because the pest hasn't been here before, it's hard to predict how well it might behave: establishing, spreading, and what types of symptoms it might express. So we rely on experts to help us with this. This talk will look at the mathematical, psychological and logical challenges of helping experts to quantify what they think. We show how the subjective Bayesian approach is useful for capturing expert uncertainty, ultimately providing a more complete picture of what they think... And what they don't!