Segmentation of cone-beam CT using a hidden Markov random field with informative priors

Purpose: Flat-detector, cone-beam computed tomography (CBCT) has enormous potential to improve the accuracy of treatment delivery in image-guided radiotherapy (IGRT). To assist radiotherapists in interpreting these images, we use a Bayesian statistical model to label each voxel according to its tissue type. Methods: The rich sources of prior information in IGRT are incorporated into a hidden Markov random field (MRF) model of the 3D image lattice. Tissue densities in the reference CT scan are estimated using inverse regression and then rescaled to approximate the corresponding CBCT intensity values. The treatment planning contours are combined with published studies of physiological variability to produce a spatial prior distribution for changes in the size, shape and position of the tumour volume and organs at risk (OAR). The voxel labels are estimated using the iterated conditional modes (ICM) algorithm. Results: The accuracy of the method has been evaluated using 27 CBCT scans of an electron density phantom (CIRS, Inc. model 062). The mean voxel-wise misclassification rate was 6.2%, with Dice similarity coefficient of 0.73 for liver, muscle, breast and adipose tissue. Conclusions: By incorporating prior information, we are able to successfully segment CBCT images. This could be a viable approach for automated, online image analysis in radiotherapy.

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.

Segmentation of cone-beam CT using a hidden Markov random field with informative priors

Cone-beam computed tomography (CBCT) has enormous potential to improve the accuracy of treatment delivery in image-guided radiotherapy (IGRT). To assist radiotherapists in interpreting these images, we use a Bayesian statistical model to label each voxel according to its tissue type. The rich sources of prior information in IGRT are incorporated into a hidden Markov random field model of the 3D image lattice. Tissue densities in the reference CT scan are estimated using inverse regression and then rescaled to approximate the corresponding CBCT intensity values. The treatment planning contours are combined with published studies of physiological variability to produce a spatial prior distribution for changes in the size, shape and position of the tumour volume and organs at risk. The voxel labels are estimated using iterated conditional modes. The accuracy of the method has been evaluated using 27 CBCT scans of an electron density phantom. The mean voxel-wise misclassification rate was 6.2\%, with Dice similarity coefficient of 0.73 for liver, muscle, breast and adipose tissue. By incorporating prior information, we are able to successfully segment CBCT images. This could be a viable approach for automated, online image analysis in radiotherapy.

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.

Modeling the viability of the free-ranging cheetah population in Namibia : an object-oriented Bayesian network approach

Conservation of free-ranging cheetah (Acinonyx jubatus) populations is multi faceted and needs to be addressed from an ecological, biological and management perspective. There is a wealth of published research, each focusing on a particular aspect of cheetah conservation. Identifying the most important factors, making sense of various (and sometimes contrasting) findings, and taking decisions when little or no empirical data is available, are everyday challenges facing conservationists. Bayesian networks (BN) provide a statistical modeling framework that enables analysis and integration of information addressing different aspects of conservation. There has been an increased interest in the use of BNs to model conservation issues, however the development of more sophisticated BNs, utilizing object-oriented (OO) features, is still at the frontier of ecological research. We describe an integrated, parallel modeling process followed during a BN modeling workshop held in Namibia to combine expert knowledge and data about free-ranging cheetahs. The aim of the workshop was to obtain a more comprehensive view of the current viability of the free-ranging cheetah population in Namibia, and to predict the effect different scenarios may have on the future viability of this free-ranging cheetah population. Furthermore, a complementary aim was to identify influential parameters of the model to more effectively target those parameters having the greatest impact on population viability. The BN was developed by aggregating diverse perspectives from local and independent scientists, agents from the national ministry, conservation agency members and local fieldworkers. This integrated BN approach facilitates OO modeling in a multi-expert context which lends itself to a series of integrated, yet independent, subnetworks describing different scientific and management components. We created three subnetworks in parallel: a biological, ecological and human factors network, which were then combined to create a complete representation of free-ranging cheetah population viability. Such OOBNs have widespread relevance to the effective and targeted conservation management of vulnerable and endangered species.

A Bayesian network approach to modelling temporal behaviour of Lyngbya majuscula bloom initiation

Lyngbya majuscula is a cyanobacterium (blue-green algae) occurring naturally in tropical and subtropical coastal areas worldwide. Deception Bay, in Northern Moreton Bay, Queensland, has a history of Lyngbya blooms, and forms a case study for this investigation. The South East Queensland (SEQ) Healthy Waterways Partnership, collaboration between government, industry, research and the community, was formed to address issues affecting the health of the river catchments and waterways of South East Queensland. The Partnership coordinated the Lyngbya Research and Management Program (2005-2007) which culminated in a Coastal Algal Blooms (CAB) Action Plan for harmful and nuisance algal blooms, such as Lyngbya majuscula. This first phase of the project was predominantly of a scientific nature and also facilitated the collection of additional data to better understand Lyngbya blooms. The second phase of this project, SEQ Healthy Waterways Strategy 2007-2012, is now underway to implement the CAB Action Plan and as such is more management focussed. As part of the first phase of the project, a Science model for the initiation of a Lyngbya bloom was built using Bayesian Networks (BN). The structure of the Science Bayesian Network was built by the Lyngbya Science Working Group (LSWG) which was drawn from diverse disciplines. The BN was then quantified with annual data and expert knowledge. Scenario testing confirmed the expected temporal nature of bloom initiation and it was recommended that the next version of the BN be extended to take this into account. Elicitation for this BN thus occurred at three levels: design, quantification and verification. The first level involved construction of the conceptual model itself, definition of the nodes within the model and identification of sources of information to quantify the nodes. The second level included elicitation of expert opinion and representation of this information in a form suitable for inclusion in the BN. The third and final level concerned the specification of scenarios used to verify the model. The second phase of the project provides the opportunity to update the network with the newly collected detailed data obtained during the previous phase of the project. Specifically the temporal nature of Lyngbya blooms is of interest. Management efforts need to be directed to the most vulnerable periods to bloom initiation in the Bay. To model the temporal aspects of Lyngbya we are using Object Oriented Bayesian networks (OOBN) to create ‘time slices’ for each of the periods of interest during the summer. OOBNs provide a framework to simplify knowledge representation and facilitate reuse of nodes and network fragments. An OOBN is more hierarchical than a traditional BN with any sub-network able to contain other sub-networks. Connectivity between OOBNs is an important feature and allows information flow between the time slices. This study demonstrates more sophisticated use of expert information within Bayesian networks, which combine expert knowledge with data (categorized using expert-defined thresholds) within an expert-defined model structure. Based on the results from the verification process the experts are able to target areas requiring greater precision and those exhibiting temporal behaviour. The time slices incorporate the data for that time period for each of the temporal nodes (instead of using the annual data from the previous static Science BN) and include lag effects to allow the effect from one time slice to flow to the next time slice. We demonstrate a concurrent steady increase in the probability of initiation of a Lyngbya bloom and conclude that the inclusion of temporal aspects in the BN model is consistent with the perceptions of Lyngbya behaviour held by the stakeholders. This extended model provides a more accurate representation of the increased risk of algal blooms in the summer months and show that the opinions elicited to inform a static BN can be readily extended to a dynamic OOBN, providing more comprehensive information for decision makers.

The impact of spatial scales and spatial smoothing on the outcome of Bayesian spatial model

Discretization of a geographical region is quite common in spatial analysis. There have been few studies into the impact of different geographical scales on the outcome of spatial models for different spatial patterns. This study aims to investigate the impact of spatial scales and spatial smoothing on the outcomes of modelling spatial point-based data. Given a spatial point-based dataset (such as occurrence of a disease), we study the geographical variation of residual disease risk using regular grid cells. The individual disease risk is modelled using a logistic model with the inclusion of spatially unstructured and/or spatially structured random effects. Three spatial smoothness priors for the spatially structured component are employed in modelling, namely an intrinsic Gaussian Markov random field, a second-order random walk on a lattice, and a Gaussian field with Matern correlation function. We investigate how changes in grid cell size affect model outcomes under different spatial structures and different smoothness priors for the spatial component. A realistic example (the Humberside data) is analyzed and a simulation study is described. Bayesian computation is carried out using an integrated nested Laplace approximation. The results suggest that the performance and predictive capacity of the spatial models improve as the grid cell size decreases for certain spatial structures. It also appears that different spatial smoothness priors should be applied for different patterns of point data.

Bayesian inference of traffic volumes based on Bluetooth data

The study of the relationship between macroscopic traffic parameters, such as flow, speed and travel time, is essential to the understanding of the behaviour of freeway and arterial roads. However, the temporal dynamics of these parameters are difficult to model, especially for arterial roads, where the process of traffic change is driven by a variety of variables. The introduction of the Bluetooth technology into the transportation area has proven exceptionally useful for monitoring vehicular traffic, as it allows reliable estimation of travel times and traffic demands. In this work, we propose an approach based on Bayesian networks for analyzing and predicting the complex dynamics of flow or volume, based on travel time observations from Bluetooth sensors. The spatio-temporal relationship between volume and travel time is captured through a first-order transition model, and a univariate Gaussian sensor model. The two models are trained and tested on travel time and volume data, from an arterial link, collected over a period of six days. To reduce the computational costs of the inference tasks, volume is converted into a discrete variable. The discretization process is carried out through a Self-Organizing Map. Preliminary results show that a simple Bayesian network can effectively estimate and predict the complex temporal dynamics of arterial volumes from the travel time data. Not only is the model well suited to produce posterior distributions over single past, current and future states; but it also allows computing the estimations of joint distributions, over sequences of states. Furthermore, the Bayesian network can achieve excellent prediction, even when the stream of travel time observation is partially incomplete.

Constructing a clinical decision-making framework for image-guided radiotherapy using a Bayesian Network

A decision-making framework for image-guided radiotherapy (IGRT) is being developed using a Bayesian Network (BN) to graphically describe, and probabilistically quantify, the many interacting factors that are involved in this complex clinical process. Outputs of the BN will provide decision-support for radiation therapists to assist them to make correct inferences relating to the likelihood of treatment delivery accuracy for a given image-guided set-up correction. The framework is being developed as a dynamic object-oriented BN, allowing for complex modelling with specific sub-regions, as well as representation of the sequential decision-making and belief updating associated with IGRT. A prototype graphic structure for the BN was developed by analysing IGRT practices at a local radiotherapy department and incorporating results obtained from a literature review. Clinical stakeholders reviewed the BN to validate its structure. The BN consists of a sub-network for evaluating the accuracy of IGRT practices and technology. The directed acyclic graph (DAG) contains nodes and directional arcs representing the causal relationship between the many interacting factors such as tumour site and its associated critical organs, technology and technique, and inter-user variability. The BN was extended to support on-line and off-line decision-making with respect to treatment plan compliance. Following conceptualisation of the framework, the BN will be quantified. It is anticipated that the finalised decision-making framework will provide a foundation to develop better decision-support strategies and automated correction algorithms for IGRT.

A Bayesian regression approach to assess uncertainty in pollutant wash-off modelling

Due to knowledge gaps in relation to urban stormwater quality processes, an in-depth understanding of model uncertainty can enhance decision making. Uncertainty in stormwater quality models can originate from a range of sources such as the complexity of urban rainfall-runoff-stormwater pollutant processes and the paucity of observed data. Unfortunately, studies relating to epistemic uncertainty, which arises from the simplification of reality are limited and often deemed mostly unquantifiable. This paper presents a statistical modelling framework for ascertaining epistemic uncertainty associated with pollutant wash-off under a regression modelling paradigm using Ordinary Least Squares Regression (OLSR) and Weighted Least Squares Regression (WLSR) methods with a Bayesian/Gibbs sampling statistical approach. The study results confirmed that WLSR assuming probability distributed data provides more realistic uncertainty estimates of the observed and predicted wash-off values compared to OLSR modelling. It was also noted that the Bayesian/Gibbs sampling approach is superior compared to the most commonly adopted classical statistical and deterministic approaches commonly used in water quality modelling. The study outcomes confirmed that the predication error associated with wash-off replication is relatively higher due to limited data availability. The uncertainty analysis also highlighted the variability of the wash-off modelling coefficient k as a function of complex physical processes, which is primarily influenced by surface characteristics and rainfall intensity.

GPU accelerated MCMC for modelling terrorist activity

The use of graphical processing unit (GPU) parallel processing is becoming a part of mainstream statistical practice. The reliance of Bayesian statistics on Markov Chain Monte Carlo (MCMC) methods makes the applicability of parallel processing not immediately obvious. It is illustrated that there are substantial gains in improved computational time for MCMC and other methods of evaluation by computing the likelihood using GPU parallel processing. Examples use data from the Global Terrorism Database to model terrorist activity in Colombia from 2000 through 2010 and a likelihood based on the explicit convolution of two negative-binomial processes. Results show decreases in computational time by a factor of over 200. Factors influencing these improvements and guidelines for programming parallel implementations of the likelihood are discussed.

Bayesian P-splines with a multiplicative term in EMG trace data

A method is proposed to describe force or compound muscle action potential (CMAP) trace data collected in an electromyography study for motor unit number estimation (MUNE). Experimental data was collected using incre- mental stimulation at multiple durations. However, stimulus information, vital for alternate MUNE methods, is not comparable for multiple duration data and therefore previous methods of MUNE (Ridall et al., 2006, 2007) cannot be used with any reliability. Hypothesised ring combinations of motor units are mod- elled using a multiplicative factor and Bayesian P-spline formulation. The model describes the process for force and CMAP in a meaningful way.

Degradation modeling and monitoring of machines using operation-specific hidden Markov models

In this paper, a novel data-driven approach to monitoring of systems operating under variable operating conditions is described. The method is based on characterizing the degradation process via a set of operation-specific hidden Markov models (HMMs), whose hidden states represent the unobservable degradation states of the monitored system while its observable symbols represent the sensor readings. Using the HMM framework, modeling, identification and monitoring methods are detailed that allow one to identify a HMM of degradation for each operation from mixed-operation data and perform operation-specific monitoring of the system. Using a large data set provided by a major manufacturer, the new methods are applied to a semiconductor manufacturing process running multiple operations in a production environment.

A review of modern computational algorithms for Bayesian optimal design

Bayesian experimental design is a fast growing area of research with many real-world applications. As computational power has increased over the years, so has the development of simulation-based design methods, which involve a number of algorithms, such as Markov chain Monte Carlo, sequential Monte Carlo and approximate Bayes methods, facilitating more complex design problems to be solved. The Bayesian framework provides a unified approach for incorporating prior information and/or uncertainties regarding the statistical model with a utility function which describes the experimental aims. In this paper, we provide a general overview on the concepts involved in Bayesian experimental design, and focus on describing some of the more commonly used Bayesian utility functions and methods for their estimation, as well as a number of algorithms that are used to search over the design space to find the Bayesian optimal design. We also discuss other computational strategies for further research in Bayesian optimal design.

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.