A fully Bayesian approach to inference for Coxian phase-type distributions with covariate dependent mean

Phase-type distributions represent the time to absorption for a finite state Markov chain in continuous time, generalising the exponential distribution and providing a flexible and useful modelling tool. We present a new reversible jump Markov chain Monte Carlo scheme for performing a fully Bayesian analysis of the popular Coxian subclass of phase-type models; the convenient Coxian representation involves fewer parameters than a more general phase-type model. The key novelty of our approach is that we model covariate dependence in the mean whilst using the Coxian phase-type model as a very general residual distribution. Such incorporation of covariates into the model has not previously been attempted in the Bayesian literature. A further novelty is that we also propose a reversible jump scheme for investigating structural changes to the model brought about by the introduction of Erlang phases. Our approach addresses more questions of inference than previous Bayesian treatments of this model and is automatic in nature. We analyse an example dataset comprising lengths of hospital stays of a sample of patients collected from two Australian hospitals to produce a model for a patient's expected length of stay which incorporates the effects of several covariates. This leads to interesting conclusions about what contributes to length of hospital stay with implications for hospital planning. We compare our results with an alternative classical analysis of these data.

A model to predict hypovigilance during a monotonous task

The driving task requires sustained attention during prolonged periods, and can be performed in highly predictable or repetitive environments. Such conditions could create drowsiness or hypovigilance and impair the ability to react to critical events. Identifying vigilance decrement in monotonous conditions has been a major subject of research, but no research to date has attempted to predict this vigilance decrement. This pilot study aims to show that vigilance decrements due to monotonous tasks can be predicted through mathematical modelling. A short vigilance task sensitive to short periods of lapses of vigilance called Sustained Attention to Response Task is used to assess participants’ performance. This task models the driver’s ability to cope with unpredicted events by performing the expected action. A Hidden Markov Model (HMM) is proposed to predict participants’ hypovigilance. Driver’s vigilance evolution is modelled as a hidden state and is correlated to an observable variable: the participant’s reactions time. This experiment shows that the monotony of the task can lead to an important vigilance decline in less than five minutes. This impairment can be predicted four minutes in advance with an 86% accuracy using HMMs. This experiment showed that mathematical models such as HMM can efficiently predict hypovigilance through surrogate measures. The presented model could result in the development of an in-vehicle device that detects driver hypovigilance in advance and warn the driver accordingly, thus offering the potential to enhance road safety and prevent road crashes.

An effective approach to verbose queries using a limited dependencies language model

Intuitively, any `bag of words' approach in IR should benefit from taking term dependencies into account. Unfortunately, for years the results of exploiting such dependencies have been mixed or inconclusive. To improve the situation, this paper shows how the natural language properties of the target documents can be used to transform and enrich the term dependencies to more useful statistics. This is done in three steps. The term co-occurrence statistics of queries and documents are each represented by a Markov chain. The paper proves that such a chain is ergodic, and therefore its asymptotic behavior is unique, stationary, and independent of the initial state. Next, the stationary distribution is taken to model queries and documents, rather than their initial distri- butions. Finally, ranking is achieved following the customary language modeling paradigm. The main contribution of this paper is to argue why the asymptotic behavior of the document model is a better representation then just the document's initial distribution. A secondary contribution is to investigate the practical application of this representation in case the queries become increasingly verbose. In the experiments (based on Lemur's search engine substrate) the default query model was replaced by the stable distribution of the query. Just modeling the query this way already resulted in significant improvements over a standard language model baseline. The results were on a par or better than more sophisticated algorithms that use fine-tuned parameters or extensive training. Moreover, the more verbose the query, the more effective the approach seems to become.

Population Monte Carlo Algorithm in High Dimensions

The population Monte Carlo algorithm is an iterative importance sampling scheme for solving static problems. We examine the population Monte Carlo algorithm in a simplified setting, a single step of the general algorithm, and study a fundamental problem that occurs in applying importance sampling to high-dimensional problem. The precision of the computed estimate from the simplified setting is measured by the asymptotic variance of estimate under conditions on the importance function. We demonstrate the exponential growth of the asymptotic variance with the dimension and show that the optimal covariance matrix for the importance function can be estimated in special cases.

HABITAT : a longitudinal multilevel study of physical acitvity change in mid-aged adults

Purpose. To explore the role of the neighborhood environment in supporting walking Design. Cross sectional study of 10,286 residents of 200 neighborhoods. Participants were selected using a stratified two-stage cluster design. Data were collected by mail survey (68.5% response rate). Setting. The Brisbane City Local Government Area, Australia, 2007. Subjects. Brisbane residents aged 40 to 65 years. Measures. Environmental: street connectivity, residential density, hilliness, tree coverage, bikeways, and street lights within a one kilometer circular buffer from each resident’s home; and network distance to nearest river or coast, public transport, shop, and park. Walking: minutes in the previous week categorized as < 30 minutes, ≥ 30 < 90 minutes, ≥ 90 < 150 minutes, ≥ 150 < 300 minutes, and ≥ 300 minutes. Analysis. The association between each neighborhood characteristic and walking was examined using multilevel multinomial logistic regression and the model parameters were estimated using Markov chain Monte Carlo simulation. Results. After adjustment for individual factors, the likelihood of walking for more than 300 minutes (relative to <30 minutes) was highest in areas with the most connectivity (OR=1.93, 99% CI 1.32-2.80), the greatest residential density (OR=1.47, 99% CI 1.02-2.12), the least tree coverage (OR=1.69, 99% CI 1.13-2.51), the most bikeways (OR=1.60, 99% CI 1.16-2.21), and the most street lights (OR=1.50, 99% CI 1.07-2.11). The likelihood of walking for more than 300 minutes was also higher among those who lived closest to a river or the coast (OR=2.06, 99% CI 1.41-3.02). Conclusion. The likelihood of meeting (and exceeding) physical activity recommendations on the basis of walking was higher in neighborhoods with greater street connectivity and residential density, more street lights and bikeways, closer proximity to waterways, and less tree coverage. Interventions targeting these neighborhood characteristics may lead to improved environmental quality as well as lower rates of overweight and obesity and associated chromic disease.

Neighborhood disadvantage and physical activity : baseline results from the HABITAT multilevel longitudinal study

PURPOSE: To examine the association between neighborhood disadvantage and physical activity (PA). ---------- METHODS: We use data from the HABITAT multilevel longitudinal study of PA among mid-aged (40-65 years) men and women (n=11, 037, 68.5% response rate) living in 200 neighborhoods in Brisbane, Australia. PA was measured using three questions from the Active Australia Survey (general walking, moderate, and vigorous activity), one indicator of total activity, and two questions about walking and cycling for transport. The PA measures were operationalized using multiple categories based on time and estimated energy expenditure that were interpretable with reference to the latest PA recommendations. The association between neighborhood disadvantage and PA was examined using multilevel multinomial logistic regression and Markov Chain Monte Carlo simulation. The contribution of neighborhood disadvantage to between-neighborhood variation in PA was assessed using the 80% interval odds ratio. ---------- RESULTS: After adjustment for sex, age, living arrangement, education, occupation, and household income, reported participation in all measures and levels of PA varied significantly across Brisbane’s neighborhoods, and neighborhood disadvantage accounted for some of this variation. Residents of advantaged neighborhoods reported significantly higher levels of total activity, general walking, moderate, and vigorous activity; however, they were less likely to walk for transport. There was no statistically significant association between neighborhood disadvantage and cycling for transport. In terms of total PA, residents of advantaged neighborhoods were more likely to exceed PA recommendations. ---------- CONCLUSIONS: Neighborhoods may exert a contextual effect on residents’ likelihood of participating in PA. The greater propensity of residents in advantaged neighborhoods to do high levels of total PA may contribute to lower rates of cardiovascular disease and obesity in these areas

Vision-based detection and tracking of aerial targets for UAV collision avoidance

Machine vision represents a particularly attractive solution for sensing and detecting potential collision-course targets due to the relatively low cost, size, weight, and power requirements of the sensors involved (as opposed to radar). This paper describes the development and evaluation of a vision-based collision detection algorithm suitable for fixed-wing aerial robotics. The system was evaluated using highly realistic vision data of the moments leading up to a collision. Based on the collected data, our detection approaches were able to detect targets at distances ranging from 400m to about 900m. These distances (with some assumptions about closing speeds and aircraft trajectories) translate to an advanced warning of between 8-10 seconds ahead of impact, which approaches the 12.5 second response time recommended for human pilots. We make use of the enormous potential of graphic processing units to achieve processing rates of 30Hz (for images of size 1024-by- 768). Currently, integration in the final platform is under way.

Bayesian hybrid algorithms and models : implementation and associated issues

This thesis addresses computational challenges arising from Bayesian analysis of complex real-world problems. Many of the models and algorithms designed for such analysis are ‘hybrid’ in nature, in that they are a composition of components for which their individual properties may be easily described but the performance of the model or algorithm as a whole is less well understood. The aim of this research project is to after a better understanding of the performance of hybrid models and algorithms. The goal of this thesis is to analyse the computational aspects of hybrid models and hybrid algorithms in the Bayesian context. The first objective of the research focuses on computational aspects of hybrid models, notably a continuous finite mixture of t-distributions. In the mixture model, an inference of interest is the number of components, as this may relate to both the quality of model fit to data and the computational workload. The analysis of t-mixtures using Markov chain Monte Carlo (MCMC) is described and the model is compared to the Normal case based on the goodness of fit. Through simulation studies, it is demonstrated that the t-mixture model can be more flexible and more parsimonious in terms of number of components, particularly for skewed and heavytailed data. The study also reveals important computational issues associated with the use of t-mixtures, which have not been adequately considered in the literature. The second objective of the research focuses on computational aspects of hybrid algorithms for Bayesian analysis. Two approaches will be considered: a formal comparison of the performance of a range of hybrid algorithms and a theoretical investigation of the performance of one of these algorithms in high dimensions. For the first approach, the delayed rejection algorithm, the pinball sampler, the Metropolis adjusted Langevin algorithm, and the hybrid version of the population Monte Carlo (PMC) algorithm are selected as a set of examples of hybrid algorithms. Statistical literature shows how statistical efficiency is often the only criteria for an efficient algorithm. In this thesis the algorithms are also considered and compared from a more practical perspective. This extends to the study of how individual algorithms contribute to the overall efficiency of hybrid algorithms, and highlights weaknesses that may be introduced by the combination process of these components in a single algorithm. The second approach to considering computational aspects of hybrid algorithms involves an investigation of the performance of the PMC in high dimensions. It is well known that as a model becomes more complex, computation may become increasingly difficult in real time. In particular the importance sampling based algorithms, including the PMC, are known to be unstable in high dimensions. This thesis examines the PMC algorithm in a simplified setting, a single step of the general sampling, and explores a fundamental problem that occurs in applying importance sampling to a high-dimensional problem. The precision of the computed estimate from the simplified setting is measured by the asymptotic variance of the estimate under conditions on the importance function. Additionally, the exponential growth of the asymptotic variance with the dimension is demonstrated and we illustrates that the optimal covariance matrix for the importance function can be estimated in a special case.

Incorporating uncertainty in environmental models informed by imagery

In this thesis, the issue of incorporating uncertainty for environmental modelling informed by imagery is explored by considering uncertainty in deterministic modelling, measurement uncertainty and uncertainty in image composition. Incorporating uncertainty in deterministic modelling is extended for use with imagery using the Bayesian melding approach. In the application presented, slope steepness is shown to be the main contributor to total uncertainty in the Revised Universal Soil Loss Equation. A spatial sampling procedure is also proposed to assist in implementing Bayesian melding given the increased data size with models informed by imagery. Measurement error models are another approach to incorporating uncertainty when data is informed by imagery. These models for measurement uncertainty, considered in a Bayesian conditional independence framework, are applied to ecological data generated from imagery. The models are shown to be appropriate and useful in certain situations. Measurement uncertainty is also considered in the context of change detection when two images are not co-registered. An approach for detecting change in two successive images is proposed that is not affected by registration. The procedure uses the Kolmogorov-Smirnov test on homogeneous segments of an image to detect change, with the homogeneous segments determined using a Bayesian mixture model of pixel values. Using the mixture model to segment an image also allows for uncertainty in the composition of an image. This thesis concludes by comparing several different Bayesian image segmentation approaches that allow for uncertainty regarding the allocation of pixels to different ground components. Each segmentation approach is applied to a data set of chlorophyll values and shown to have different benefits and drawbacks depending on the aims of the analysis.