Mathematical modelling of fumigant transport in stored grain

Computational fluid dynamics, analytical solutions, and mathematical modelling approaches are used to gain insights into the distribution of fumigant gas within farm-scale, grain storage silos. Both fan-forced and tablet fumigation are considered in this work, which develops new models for use by researchers, primary producers and silo manufacturers to assist in the eradication grain storage pests.

Bayesian models for spatio-temporal assessment of disease

This thesis has contributed to the advancement of knowledge in disease modelling by addressing interesting and crucial issues relevant to modelling health data over space and time. The research has led to the increased understanding of spatial scales, temporal scales, and spatial smoothing for modelling diseases, in terms of their methodology and applications. This research is of particular significance to researchers seeking to employ statistical modelling techniques over space and time in various disciplines. A broad class of statistical models are employed to assess what impact of spatial and temporal scales have on simulated and real data.

An investigation of the impact of various geographical scales for the specification of spatial dependence

Ecological studies are based on characteristics of groups of individuals, which are common in various disciplines including epidemiology. It is of great interest for epidemiologists to study the geographical variation of a disease by accounting for the positive spatial dependence between neighbouring areas. However, the choice of scale of the spatial correlation requires much attention. In view of a lack of studies in this area, this study aims to investigate the impact of differing definitions of geographical scales using a multilevel model. We propose a new approach -- the grid-based partitions and compare it with the popular census region approach. Unexplained geographical variation is accounted for via area-specific unstructured random effects and spatially structured random effects specified as an intrinsic conditional autoregressive process. Using grid-based modelling of random effects in contrast to the census region approach, we illustrate conditions where improvements are observed in the estimation of the linear predictor, random effects, parameters, and the identification of the distribution of residual risk and the aggregate risk in a study region. The study has found that grid-based modelling is a valuable approach for spatially sparse data while the SLA-based and grid-based approaches perform equally well for spatially dense data.

Bayesian hierarchical models for analysing spatial point-based data at a grid level: A comparison of approaches

Spatial data are now prevalent in a wide range of fields including environmental and health science. This has led to the development of a range of approaches for analysing patterns in these data. In this paper, we compare several Bayesian hierarchical models for analysing point-based data based on the discretization of the study region, resulting in grid-based spatial data. The approaches considered include two parametric models and a semiparametric model. We highlight the methodology and computation for each approach. Two simulation studies are undertaken to compare the performance of these models for various structures of simulated point-based data which resemble environmental data. A case study of a real dataset is also conducted to demonstrate a practical application of the modelling approaches. Goodness-of-fit statistics are computed to compare estimates of the intensity functions. The deviance information criterion is also considered as an alternative model evaluation criterion. The results suggest that the adaptive Gaussian Markov random field model performs well for highly sparse point-based data where there are large variations or clustering across the space; whereas the discretized log Gaussian Cox process produces good fit in dense and clustered point-based data. One should generally consider the nature and structure of the point-based data in order to choose the appropriate method in modelling a discretized spatial point-based data.

Shared autonomy for close-quarters navigation and control of a VTOL platform

This thesis presents an approach for a vertical infrastructure inspection using a vertical take-off and landing (VTOL) unmanned aerial vehicle and shared autonomy. Inspecting vertical structure such as light and power distribution poles is a difficult task. There are challenges involved with developing such an inspection system, such as flying in close proximity to a target while maintaining a fixed stand-off distance from it. The contributions of this thesis fall into three main areas. Firstly, an approach to vehicle dynamic modeling is evaluated in simulation and experiments. Secondly, EKF-based state estimators are demonstrated, as well as estimator-free approaches such as image based visual servoing (IBVS) validated with motion capture ground truth data. Thirdly, an integrated pole inspection system comprising a VTOL platform with human-in-the-loop control, (shared autonomy) is demonstrated. These contributions are comprehensively explained through a series of published papers.

A pseudo-marginal sequential Monte Carlo algorithm for random effects models in Bayesian sequential design

A computationally efficient sequential Monte Carlo algorithm is proposed for the sequential design of experiments for the collection of block data described by mixed effects models. The difficulty in applying a sequential Monte Carlo algorithm in such settings is the need to evaluate the observed data likelihood, which is typically intractable for all but linear Gaussian models. To overcome this difficulty, we propose to unbiasedly estimate the likelihood, and perform inference and make decisions based on an exact-approximate algorithm. Two estimates are proposed: using Quasi Monte Carlo methods and using the Laplace approximation with importance sampling. Both of these approaches can be computationally expensive, so we propose exploiting parallel computational architectures to ensure designs can be derived in a timely manner. We also extend our approach to allow for model uncertainty. This research is motivated by important pharmacological studies related to the treatment of critically ill patients.

Simulation-based density estimation for time series using covariate data

This paper proposes a simulation-based density estimation technique for time series that exploits information found in covariate data. The method can be paired with a large range of parametric models used in time series estimation. We derive asymptotic properties of the estimator and illustrate attractive finite sample properties for a range of well-known econometric and financial applications.

Short-data recursive HMM parameter estimation for rapid vision-based aircraft heading estimation

Rapid recursive estimation of hidden Markov Model (HMM) parameters is important in applications that place an emphasis on the early availability of reasonable estimates (e.g. for change detection) rather than the provision of longer-term asymptotic properties (such as convergence, convergence rate, and consistency). In the context of vision- based aircraft (image-plane) heading estimation, this paper suggests and evaluates the short-data estimation properties of 3 recursive HMM parameter estimation techniques (a recursive maximum likelihood estimator, an online EM HMM estimator, and a relative entropy based estimator). On both simulated and real data, our studies illustrate the feasibility of rapid recursive heading estimation, but also demonstrate the need for careful step-size design of HMM recursive estimation techniques when these techniques are intended for use in applications where short-data behaviour is paramount.

Adaptive finite element analysis of elliptic problems based on bubble-type local mesh generation

A new mesh adaptivity algorithm that combines a posteriori error estimation with bubble-type local mesh generation (BLMG) strategy for elliptic differential equations is proposed. The size function used in the BLMG is defined on each vertex during the adaptive process based on the obtained error estimator. In order to avoid the excessive coarsening and refining in each iterative step, two factor thresholds are introduced in the size function. The advantages of the BLMG-based adaptive finite element method, compared with other known methods, are given as follows: the refining and coarsening are obtained fluently in the same framework; the local a posteriori error estimation is easy to implement through the adjacency list of the BLMG method; at all levels of refinement, the updated triangles remain very well shaped, even if the mesh size at any particular refinement level varies by several orders of magnitude. Several numerical examples with singularities for the elliptic problems, where the explicit error estimators are used, verify the efficiency of the algorithm. The analysis for the parameters introduced in the size function shows that the algorithm has good flexibility.

‘Pop Melayu vs. Pop Indonesia: Marketeers, producers and new interpretations of a genre into the 2000s’ in Sonic Modernities in Southeast Asia Leiden: Brill pp. 187- 215

Kangen Band, as an example of reclaiming of the derisive term kampungan. In it, I argue that this reclaiming represents an interesting case of genre manipulation, and consider what this can reveal about how Indonesian pop genres are constituted, what they ‘are’ and what they ‘do’. In so doing, I seek to rework existing scholarship relating to Indonesian pop genres and modernity, as well as interrogate some broader theories of genre. In this essay, I extend the argument that Indonesian pop genres are not purely technical categories, they touch on myths of class and nation (Wallach 2008; Weintraub 2010; Yampolsky 1989. As we shall see, in the New Order period, pop music genres reached out to these myths by positioning themselves variously vis-à-vis the capital city, Jakarta. Such positioning, achieved through use of the terms gedongan (a term that strives to infer refinement by stressing the non-masses’ central position in the urban environment) and kampungan (a term that strives to enforce subalterns’ marginal position in relation to the metropolis, see also the previous contribution by Weintraub), continues to haunt the constitution of genre in the post-New Order period, but in novel ways. These novel ways, I argue, may be seen to result from industrial transformation and new systems of knowledge production.

Towards strongly consistent online HMM parameter estimation using one-step Kerridge inaccuracy

In this paper, we propose a novel online hidden Markov model (HMM) parameter estimator based on the new information-theoretic concept of one-step Kerridge inaccuracy (OKI). Under several regulatory conditions, we establish a convergence result (and some limited strong consistency results) for our proposed online OKI-based parameter estimator. In simulation studies, we illustrate the global convergence behaviour of our proposed estimator and provide a counter-example illustrating the local convergence of other popular HMM parameter estimators.

The subordinated processes controlled by a family of subordinators and corresponding Fokker-Planck type equations

In this work, we consider subordinated processes controlled by a family of subordinators which consist of a power function of a time variable and a negative power function of an α-stable random variable. The effect of parameters in the subordinators on the subordinated process is discussed. By suitable variable substitutions and the Laplace transform technique, the corresponding fractional Fokker–Planck-type equations are derived. We also compute their mean square displacements in a free force field. By choosing suitable ranges of parameters, the resulting subordinated processes may be subdiffusive, normal diffusive or superdiffusive

Methods for constructing uncertainty intervals for queries of Bayesian nets

In this paper the issue of finding uncertainty intervals for queries in a Bayesian Network is reconsidered. The investigation focuses on Bayesian Nets with discrete nodes and finite populations. An earlier asymptotic approach is compared with a simulation-based approach, together with further alternatives, one based on a single sample of the Bayesian Net of a particular finite population size, and another which uses expected population sizes together with exact probabilities. We conclude that a query of a Bayesian Net should be expressed as a probability embedded in an uncertainty interval. Based on an investigation of two Bayesian Net structures, the preferred method is the simulation method. However, both the single sample method and the expected sample size methods may be useful and are simpler to compute. Any method at all is more useful than none, when assessing a Bayesian Net under development, or when drawing conclusions from an ‘expert’ system.

Estimation of the time of a linear trend in monitoring survival time

Change point estimation is recognized as an essential tool of root cause analyses within quality control programs as it enables clinical experts to search for potential causes of change in hospital outcomes more effectively. In this paper, we consider estimation of the time when a linear trend disturbance has occurred in survival time following an in-control clinical intervention in the presence of variable patient mix. To model the process and change point, a linear trend in the survival time of patients who underwent cardiac surgery is formulated using hierarchical models in a Bayesian framework. The data are right censored since the monitoring is conducted over a limited follow-up period. We capture the effect of risk factors prior to the surgery using a Weibull accelerated failure time regression model. We use Markov Chain Monte Carlo to obtain posterior distributions of the change point parameters including the location and the slope size of the trend and also corresponding probabilistic intervals and inferences. The performance of the Bayesian estimator is investigated through simulations and the result shows that precise estimates can be obtained when they are used in conjunction with the risk-adjusted survival time cumulative sum control chart (CUSUM) control charts for different trend scenarios. In comparison with the alternatives, step change point model and built-in CUSUM estimator, more accurate and precise estimates are obtained by the proposed Bayesian estimator over linear trends. These superiorities are enhanced when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered.

A directed continuous time random walk model with jump length depending on waiting time

In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model, the Laplace-Laplace transform of the probability density function P(x,t) of finding the walker at position at time is completely determined by the Laplace transform of the probability density function φ(t) of the waiting time. In terms of the probability density function of the waiting time in the Laplace domain, the limit distribution of the random process and the corresponding evolving equations are derived.