Bayesian models for the determination of resonant frequencies in a DI diesel engine

A time series method for the determination of combustion chamber resonant frequencies is outlined. This technique employs the use of Markov-chain Monte Carlo (MCMC) to infer parameters in a chosen model of the data. The development of the model is included and the resonant frequency is characterised as a function of time. Potential applications for cycle-by-cycle analysis are discussed and the bulk temperature of the gas and the trapped mass in the combustion chamber are evaluated as a function of time from resonant frequency information.

A geographical analysis of the role of water supply and sanitation in the risk of helminth infections of children in West Africa

Background We investigated the geographical variation of water supply and sanitation indicators (WS&S) and their role to the risk of schistosomiasis and hookworm infection in school age children in West Africa. The aim was to predict large-scale geographical variation in WS&S, quantify the attributable risk of S. haematobium, S. mansoni and hookworm infections due to WS&S and identify communities where sustainable transmission control could be targeted across the region. Methods National cross-sectional household-based demographic health surveys were conducted in 24,542 households in Burkina Faso, Ghana and Mali, in 2003–2006. We generated spatially-explicit predictions of areas without piped water, toilet facilities and finished floors in West Africa, adjusting for household covariates. Using recently published helminth prevalence data we developed Bayesian geostatistical models (MGB) of S. haematobium, S. mansoni and hookworm infection in West Africa including environmental and the mapped outputs for WS&S. Using these models we estimated the effect of WS&S on parasite risk, quantified their attributable fraction of infection, and mapped the risk of infection in West Africa. Findings Our maps show that most areas in West Africa are very poorly served by water supply except in major urban centers. There is a better geographical coverage for toilet availability and improved household flooring. We estimated smaller attributable risks for water supply in S. mansoni (47%) compared to S. haematobium (71%), and 5% of hookworm cases could be averted by improving sanitation. Greater levels of inadequate sanitation increased the risk of schistosomiasis, and increased levels of unsafe water supply increased the risk of hookworm. The role of floor type for S. haematobium infection (21%) was comparable to that of S. mansoni (16%), but was significantly higher for hookworm infection (86%). S. haematobium and hookworm maps accounting for WS&S show small clusters of maximal prevalence areas in areas bordering Burkina Faso and Mali smaller. The map of S. mansoni shows that this parasite is much more wide spread across the north of the Niger River basin than previously predicted. Interpretation Our maps identify areas where the Millennium Development Goal for water and sanitation is lagging behind. Our results show that WS&S are important contributors to the burden of major helminth infections of children in West Africa. Including information about WS&S as well as the “traditional” environmental risk factors in spatial models of helminth risk yielded a substantial gain both in model fit and at explaining the proportion of spatial variance in helminth risk. Mapping the distribution of infection risk adjusted for WS&S allowed the identification of communities in West Africa where integrative preventive chemotherapy and engineering interventions will yield the greatest public health benefits.

PySSM : a Python module for Bayesian inference of linear Gaussian state space models

PySSM is a Python package that has been developed for the analysis of time series using linear Gaussian state space models (SSM). PySSM is easy to use; models can be set up quickly and efficiently and a variety of different settings are available to the user. It also takes advantage of scientific libraries Numpy and Scipy and other high level features of the Python language. PySSM is also used as a platform for interfacing between optimised and parallelised Fortran routines. These Fortran routines heavily utilise Basic Linear Algebra (BLAS) and Linear Algebra Package (LAPACK) functions for maximum performance. PySSM contains classes for filtering, classical smoothing as well as simulation smoothing.

A sequential Monte Carlo algorithm to incorporate model uncertainty in Bayesian sequential design

Here we present a sequential Monte Carlo (SMC) algorithm that can be used for any one-at-a-time Bayesian sequential design problem in the presence of model uncertainty where discrete data are encountered. Our focus is on adaptive design for model discrimination but the methodology is applicable if one has a different design objective such as parameter estimation or prediction. An SMC algorithm is run in parallel for each model and the algorithm relies on a convenient estimator of the evidence of each model which is essentially a function of importance sampling weights. Other methods for this task such as quadrature, often used in design, suffer from the curse of dimensionality. Approximating posterior model probabilities in this way allows us to use model discrimination utility functions derived from information theory that were previously difficult to compute except for conjugate models. A major benefit of the algorithm is that it requires very little problem specific tuning. We demonstrate the methodology on three applications, including discriminating between models for decline in motor neuron numbers in patients suffering from neurological diseases such as Motor Neuron disease.

Hotspot Identification: A Full Bayesian Hierarchical Modeling Approach

This study proposes a full Bayes (FB) hierarchical modeling approach in traffic crash hotspot identification. The FB approach is able to account for all uncertainties associated with crash risk and various risk factors by estimating a posterior distribution of the site safety on which various ranking criteria could be based. Moreover, by use of hierarchical model specification, FB approach is able to flexibly take into account various heterogeneities of crash occurrence due to spatiotemporal effects on traffic safety. Using Singapore intersection crash data(1997-2006), an empirical evaluate was conducted to compare the proposed FB approach to the state-of-the-art approaches. Results show that the Bayesian hierarchical models with accommodation for site specific effect and serial correlation have better goodness-of-fit than non hierarchical models. Furthermore, all model-based approaches perform significantly better in safety ranking than the naive approach using raw crash count. The FB hierarchical models were found to significantly outperform the standard EB approach in correctly identifying hotspots.

Tooth fracture risk analysis based on a new finite element dental structure models using micro-CT data

The finite element (FE) analysis is an effective method to study the strength and predict the fracture risk of endodontically-treated teeth. This paper presents a rapid method developed to generate a comprehensive tooth FE model using data retrieved from micro-computed tomography (μCT). With this method, the inhomogeneity of material properties of teeth was included into the model without dividing the tooth model into different regions. The material properties of the tooth were assumed to be related to the mineral density. The fracture risk at different tooth portions was assessed for root canal treatments. The micro-CT images of a tooth were processed by a Matlab software programme and the CT numbers were retrieved. The tooth contours were obtained with thresholding segmentation using Amira. The inner and outer surfaces of the tooth were imported into Solidworks and a three-dimensional (3D) tooth model was constructed. An assembly of the tooth model with the periodontal ligament (PDL) layer and surrounding bone was imported into ABAQUS. The material properties of the tooth were calculated from the retrieved CT numbers via ABAQUS user's subroutines. Three root canal geometries (original and two enlargements) were investigated. The proposed method in this study can generate detailed 3D finite element models of a tooth with different root canal enlargements and filling materials, and would be very useful for the assessment of the fracture risk at different tooth portions after root canal treatments.

Bayesian experimental design for models with intractable likelihoods

In this paper we present a methodology for designing experiments for efficiently estimating the parameters of models with computationally intractable likelihoods. The approach combines a commonly used methodology for robust experimental design, based on Markov chain Monte Carlo sampling, with approximate Bayesian computation (ABC) to ensure that no likelihood evaluations are required. The utility function considered for precise parameter estimation is based upon the precision of the ABC posterior distribution, which we form efficiently via the ABC rejection algorithm based on pre-computed model simulations. Our focus is on stochastic models and, in particular, we investigate the methodology for Markov process models of epidemics and macroparasite population evolution. The macroparasite example involves a multivariate process and we assess the loss of information from not observing all variables.

Towards Bayesian experimental design for nonlinear models that require a large number of sampling times

The use of Bayesian methodologies for solving optimal experimental design problems has increased. Many of these methods have been found to be computationally intensive for design problems that require a large number of design points. A simulation-based approach that can be used to solve optimal design problems in which one is interested in finding a large number of (near) optimal design points for a small number of design variables is presented. The approach involves the use of lower dimensional parameterisations that consist of a few design variables, which generate multiple design points. Using this approach, one simply has to search over a few design variables, rather than searching over a large number of optimal design points, thus providing substantial computational savings. The methodologies are demonstrated on four applications, including the selection of sampling times for pharmacokinetic and heat transfer studies, and involve nonlinear models. Several Bayesian design criteria are also compared and contrasted, as well as several different lower dimensional parameterisation schemes for generating the many design points.

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.

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.

Sampling designs on stream networks using the pseudo-Bayesian approach

Monitoring stream networks through time provides important ecological information. The sampling design problem is to choose locations where measurements are taken so as to maximise information gathered about physicochemical and biological variables on the stream network. This paper uses a pseudo-Bayesian approach, averaging a utility function over a prior distribution, in finding a design which maximizes the average utility. We use models for correlations of observations on the stream network that are based on stream network distances and described by moving average error models. Utility functions used reflect the needs of the experimenter, such as prediction of location values or estimation of parameters. We propose an algorithmic approach to design with the mean utility of a design estimated using Monte Carlo techniques and an exchange algorithm to search for optimal sampling designs. In particular we focus on the problem of finding an optimal design from a set of fixed designs and finding an optimal subset of a given set of sampling locations. As there are many different variables to measure, such as chemical, physical and biological measurements at each location, designs are derived from models based on different types of response variables: continuous, counts and proportions. We apply the methodology to a synthetic example and the Lake Eacham stream network on the Atherton Tablelands in Queensland, Australia. We show that the optimal designs depend very much on the choice of utility function, varying from space filling to clustered designs and mixtures of these, but given the utility function, designs are relatively robust to the type of response variable.

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.