Bayesian computation via empirical likelihood

Approximate Bayesian computation has become an essential tool for the analysis of complex stochastic models when the likelihood function is numerically unavailable. However, the well-established statistical method of empirical likelihood provides another route to such settings that bypasses simulations from the model and the choices of the approximate Bayesian computation parameters (summary statistics, distance, tolerance), while being convergent in the number of observations. Furthermore, bypassing model simulations may lead to significant time savings in complex models, for instance those found in population genetics. The Bayesian computation with empirical likelihood algorithm we develop in this paper also provides an evaluation of its own performance through an associated effective sample size. The method is illustrated using several examples, including estimation of standard distributions, time series, and population genetics models.

Exact and approximate Bayesian inference for low count time series models with intractable likelihoods

In this paper we present a new simulation methodology in order to obtain exact or approximate Bayesian inference for models for low-valued count time series data that have computationally demanding likelihood functions. The algorithm fits within the framework of particle Markov chain Monte Carlo (PMCMC) methods. The particle filter requires only model simulations and, in this regard, our approach has connections with approximate Bayesian computation (ABC). However, an advantage of using the PMCMC approach in this setting is that simulated data can be matched with data observed one-at-a-time, rather than attempting to match on the full dataset simultaneously or on a low-dimensional non-sufficient summary statistic, which is common practice in ABC. For low-valued count time series data we find that it is often computationally feasible to match simulated data with observed data exactly. Our particle filter maintains $N$ particles by repeating the simulation until $N+1$ exact matches are obtained. Our algorithm creates an unbiased estimate of the likelihood, resulting in exact posterior inferences when included in an MCMC algorithm. In cases where exact matching is computationally prohibitive, a tolerance is introduced as per ABC. A novel aspect of our approach is that we introduce auxiliary variables into our particle filter so that partially observed and/or non-Markovian models can be accommodated. We demonstrate that Bayesian model choice problems can be easily handled in this framework.

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.

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.

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!

Bayesian survival analysis using gene expression

This thesis developed and applied Bayesian models for the analysis of survival data. The gene expression was considered as explanatory variables within the Bayesian survival model which can be considered the new contribution in the analysis of such data. The censoring factor that is inherent of survival data has also been addressed in terms of its impact on the fitting of a finite mixture of Weibull distribution with and without covariates. To investigate this, simulation study were carried out under several censoring percentages. Censoring percentage as high as 80% is acceptable here as the work involved high dimensional data. Lastly the Bayesian model averaging approach was developed to incorporate model uncertainty in the prediction of survival.

A flexible Bayesian model for describing temporal variability of N2O emissions from an Australian pasture

Soil-based emissions of nitrous oxide (N2O), a well-known greenhouse gas, have been associated with changes in soil water-filled pore space (WFPS) and soil temperature in many previous studies. However, it is acknowledged that the environment-N2O relationship is complex and still relatively poorly unknown. In this article, we employed a Bayesian model selection approach (Reversible jump Markov chain Monte Carlo) to develop a data-informed model of the relationship between daily N2O emissions and daily WFPS and soil temperature measurements between March 2007 and February 2009 from a soil under pasture in Queensland, Australia, taking seasonal factors and time-lagged effects into account. The model indicates a very strong relationship between a hybrid seasonal structure and daily N2O emission, with the latter substantially increased in summer. Given the other variables in the model, daily soil WFPS, lagged by a week, had a negative influence on daily N2O; there was evidence of a nonlinear positive relationship between daily soil WFPS and daily N2O emission; and daily soil temperature tended to have a linear positive relationship with daily N2O emission when daily soil temperature was above a threshold of approximately 19°C. We suggest that this flexible Bayesian modeling approach could facilitate greater understanding of the shape of the covariate-N2O flux relation and detection of effect thresholds in the natural temporal variation of environmental variables on N2O emission.

An intuitive dashboard for Bayesian network inference

Current Bayesian network software packages provide good graphical interface for users who design and develop Bayesian networks for various applications. However, the intended end-users of these networks may not necessarily find such an interface appealing and at times it could be overwhelming, particularly when the number of nodes in the network is large. To circumvent this problem, this paper presents an intuitive dashboard, which provides an additional layer of abstraction, enabling the end-users to easily perform inferences over the Bayesian networks. Unlike most software packages, which display the nodes and arcs of the network, the developed tool organises the nodes based on the cause-and-effect relationship, making the user-interaction more intuitive and friendly. In addition to performing various types of inferences, the users can conveniently use the tool to verify the behaviour of the developed Bayesian network. The tool has been developed using QT and SMILE libraries in C++.

Bayesian indirect inference using a parametric auxiliary model

Indirect inference (II) is a methodology for estimating the parameters of an intractable (generative) model on the basis of an alternative parametric (auxiliary) model that is both analytically and computationally easier to deal with. Such an approach has been well explored in the classical literature but has received substantially less attention in the Bayesian paradigm. The purpose of this paper is to compare and contrast a collection of what we call parametric Bayesian indirect inference (pBII) methods. One class of pBII methods uses approximate Bayesian computation (referred to here as ABC II) where the summary statistic is formed on the basis of the auxiliary model, using ideas from II. Another approach proposed in the literature, referred to here as parametric Bayesian indirect likelihood (pBIL), we show to be a fundamentally different approach to ABC II. We devise new theoretical results for pBIL to give extra insights into its behaviour and also its differences with ABC II. Furthermore, we examine in more detail the assumptions required to use each pBII method. The results, insights and comparisons developed in this paper are illustrated on simple examples and two other substantive applications. The first of the substantive examples involves performing inference for complex quantile distributions based on simulated data while the second is for estimating the parameters of a trivariate stochastic process describing the evolution of macroparasites within a host based on real data. We create a novel framework called Bayesian indirect likelihood (BIL) which encompasses pBII as well as general ABC methods so that the connections between the methods can be established.

A Hybrid Queue-based Bayesian Network Framework for passenger facilitation modelling

This paper presents a novel framework for the modelling of passenger facilitation in a complex environment. The research is motivated by the challenges in the airport complex system, where there are multiple stakeholders, differing operational objectives and complex interactions and interdependencies between different parts of the airport system. Traditional methods for airport terminal modelling do not explicitly address the need for understanding causal relationships in a dynamic environment. Additionally, existing Bayesian Network (BN) models, which provide a means for capturing causal relationships, only present a static snapshot of a system. A method to integrate a BN complex systems model with stochastic queuing theory is developed based on the properties of the Poisson and Exponential distributions. The resultant Hybrid Queue-based Bayesian Network (HQBN) framework enables the simulation of arbitrary factors, their relationships, and their effects on passenger flow and vice versa. A case study implementation of the framework is demonstrated on the inbound passenger facilitation process at Brisbane International Airport. The predicted outputs of the model, in terms of cumulative passenger flow at intermediary and end points in the inbound process, are found to have an $R^2$ goodness of fit of 0.9994 and 0.9982 respectively over a 10 hour test period. The utility of the framework is demonstrated on a number of usage scenarios including real time monitoring and `what-if' analysis. This framework provides the ability to analyse and simulate a dynamic complex system, and can be applied to other socio-technical systems such as hospitals.

Fully Bayesian experimental design for pharmacokinetic studies

Utility functions in Bayesian experimental design are usually based on the posterior distribution. When the posterior is found by simulation, it must be sampled from for each future data set drawn from the prior predictive distribution. Many thousands of posterior distributions are often required. A popular technique in the Bayesian experimental design literature to rapidly obtain samples from the posterior is importance sampling, using the prior as the importance distribution. However, importance sampling will tend to break down if there is a reasonable number of experimental observations and/or the model parameter is high dimensional. In this paper we explore the use of Laplace approximations in the design setting to overcome this drawback. Furthermore, we consider using the Laplace approximation to form the importance distribution to obtain a more efficient importance distribution than the prior. The methodology is motivated by a pharmacokinetic study which investigates the effect of extracorporeal membrane oxygenation on the pharmacokinetics of antibiotics in sheep. The design problem is to find 10 near optimal plasma sampling times which produce precise estimates of pharmacokinetic model parameters/measures of interest. We consider several different utility functions of interest in these studies, which involve the posterior distribution of parameter functions.

From science to management : using Bayesian networks to learn about Lyngbya

Toxic blooms of Lyngbya majuscula occur in coastal areas worldwide and have major ecological, health and economic consequences. The exact causes and combinations of factors which lead to these blooms are not clearly understood. Lyngbya experts and stakeholders are a particularly diverse group, including ecologists, scientists, state and local government representatives, community organisations, catchment industry groups and local fishermen. An integrated Bayesian Network approach was developed to better understand and model this complex environmental problem, identify knowledge gaps, prioritise future research and evaluate management options.