A Bayesian model predicts the response of axons to molecular gradients

Axon guidance by molecular gradients plays a crucial role in wiring up the nervous system. However, the mechanisms axons use to detect gradients are largely unknown. We first develop a Bayesian “ideal observer” analysis of gradient detection by axons, based on the hypothesis that a principal constraint on gradient detection is intrinsic receptor binding noise. Second, from this model, we derive an equation predicting how the degree of response of an axon to a gradient should vary with gradient steepness and absolute concentration. Third, we confirm this prediction quantitatively by performing the first systematic experimental analysis of how axonal response varies with both these quantities. These experiments demonstrate a degree of sensitivity much higher than previously reported for any chemotacting system. Together, these results reveal both the quantitative constraints that must be satisfied for effective axonal guidance and the computational principles that may be used by the underlying signal transduction pathways, and allow predictions for the degree of response of axons to gradients in a wide variety of in vivo and in vitro settings.

The Bayesian conditional independence model for measurement error: applications in ecology

The measurement error model is a well established statistical method for regression problems in medical sciences, although rarely used in ecological studies. While the situations in which it is appropriate may be less common in ecology, there are instances in which there may be benefits in its use for prediction and estimation of parameters of interest. We have chosen to explore this topic using a conditional independence model in a Bayesian framework using a Gibbs sampler, as this gives a great deal of flexibility, allowing us to analyse a number of different models without losing generality. Using simulations and two examples, we show how the conditional independence model can be used in ecology, and when it is appropriate.

High-probability regret bounds for bandit online linear optimization

We present a modification of the algorithm of Dani et al. [8] for the online linear optimization problem in the bandit setting, which with high probability has regret at most O ∗ ( √ T) against an adaptive adversary. This improves on the previous algorithm [8] whose regret is bounded in expectation against an oblivious adversary. We obtain the same dependence on the dimension (n 3/2) as that exhibited by Dani et al. The results of this paper rest firmly on those of [8] and the remarkable technique of Auer et al. [2] for obtaining high probability bounds via optimistic estimates. This paper answers an open question: it eliminates the gap between the high-probability bounds obtained in the full-information vs bandit settings.

An economic evaluation of the Safe Motherhood programme in Guangxi, China

Maternal and infant mortality is a global health issue with a significant social and economic impact. Each year, over half a million women worldwide die due to complications related to pregnancy or childbirth, four million infants die in the first 28 days of life, and eight million infants die in the first year. Ninety-nine percent of maternal and infant deaths are in developing countries. Reducing maternal and infant mortality is among the key international development goals. In China, the national maternal mortality ratio and infant mortality rate were reduced greatly in the past two decades, yet a large discrepancy remains between urban and rural areas. To address this problem, a large-scale Safe Motherhood Programme was initiated in 2000. The programme was implemented in Guangxi in 2003. Interventions in the programme included both demand-side and supply side-interventions focusing on increasing health service use and improving birth outcomes. Little is known about the effects and economic outcomes of the Safe Motherhood Programme in Guangxi, although it has been implemented for seven years. The aim of this research is to estimate the effectiveness and cost-effectiveness of the interventions in the Safe Motherhood Programme in Guangxi, China. The objectives of this research include: 1. To evaluate whether the changes of health service use and birth outcomes are associated with the interventions in the Safe Motherhood Programme. 2. To estimate the cost-effectiveness of the interventions in the Safe Motherhood Programme and quantify the uncertainty surrounding the decision. 3. To assess the expected value of perfect information associated with both the whole decision and individual parameters, and interpret the findings to inform priority setting in further research and policy making in this area. A quasi-experimental study design was used in this research to assess the effectiveness of the programme in increasing health service use and improving birth outcomes. The study subjects were 51 intervention counties and 30 control counties. Data on the health service use, birth outcomes and socio-economic factors from 2001 to 2007 were collected from the programme database and statistical yearbooks. Based on the profile plots of the data, general linear mixed models were used to evaluate the effectiveness of the programme while controlling for the effects of baseline levels of the response variables, change of socio-economic factors over time and correlations among repeated measurements from the same county. Redundant multicollinear variables were deleted from the mixed model using the results of the multicollinearity diagnoses. For each response variable, the best covariance structure was selected from 15 alternatives according to the fit statistics including Akaike information criterion, Finite-population corrected Akaike information criterion, and Schwarz.s Bayesian information criterion. Residual diagnostics were used to validate the model assumptions. Statistical inferences were made to show the effect of the programme on health service use and birth outcomes. A decision analytic model was developed to evaluate the cost-effectiveness of the programme, quantify the decision uncertainty, and estimate the expected value of perfect information associated with the decision. The model was used to describe the transitions between health states for women and infants and reflect the change of both costs and health benefits associated with implementing the programme. Result gained from the mixed models and other relevant evidence identified were synthesised appropriately to inform the input parameters of the model. Incremental cost-effectiveness ratios of the programme were calculated for the two groups of intervention counties over time. Uncertainty surrounding the parameters was dealt with using probabilistic sensitivity analysis, and uncertainty relating to model assumptions was handled using scenario analysis. Finally the expected value of perfect information for both the whole model and individual parameters in the model were estimated to inform priority setting in further research in this area.The annual change rates of the antenatal care rate and the institutionalised delivery rate were improved significantly in the intervention counties after the programme was implemented. Significant improvements were also found in the annual change rates of the maternal mortality ratio, the infant mortality rate, the incidence rate of neonatal tetanus and the mortality rate of neonatal tetanus in the intervention counties after the implementation of the programme. The annual change rate of the neonatal mortality rate was also improved, although the improvement was only close to statistical significance. The influences of the socio-economic factors on the health service use indicators and birth outcomes were identified. The rural income per capita had a significant positive impact on the health service use indicators, and a significant negative impact on the birth outcomes. The number of beds in healthcare institutions per 1,000 population and the number of rural telephone subscribers per 1,000 were found to be positively significantly related to the institutionalised delivery rate. The length of highway per square kilometre negatively influenced the maternal mortality ratio. The percentage of employed persons in the primary industry had a significant negative impact on the institutionalised delivery rate, and a significant positive impact on the infant mortality rate and neonatal mortality rate. The incremental costs of implementing the programme over the existing practice were US $11.1 million from the societal perspective, and US $13.8 million from the perspective of the Ministry of Health. Overall, 28,711 life years were generated by the programme, producing an overall incremental cost-effectiveness ratio of US $386 from the societal perspective, and US $480 from the perspective of the Ministry of Health, both of which were below the threshold willingness-to-pay ratio of US $675. The expected net monetary benefit generated by the programme was US $8.3 million from the societal perspective, and US $5.5 million from the perspective of the Ministry of Health. The overall probability that the programme was cost-effective was 0.93 and 0.89 from the two perspectives, respectively. The incremental cost-effectiveness ratio of the programme was insensitive to the different estimates of the three parameters relating to the model assumptions. Further research could be conducted to reduce the uncertainty surrounding the decision, in which the upper limit of investment was US $0.6 million from the societal perspective, and US $1.3 million from the perspective of the Ministry of Health. It is also worthwhile to get a more precise estimate of the improvement of infant mortality rate. The population expected value of perfect information for individual parameters associated with this parameter was US $0.99 million from the societal perspective, and US $1.14 million from the perspective of the Ministry of Health. The findings from this study have shown that the interventions in the Safe Motherhood Programme were both effective and cost-effective in increasing health service use and improving birth outcomes in rural areas of Guangxi, China. Therefore, the programme represents a good public health investment and should be adopted and further expanded to an even broader area if possible. This research provides economic evidence to inform efficient decision making in improving maternal and infant health in developing countries.

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.

Using Bayesian methods for the estimation of uncertainty in complex statistical models

The research objectives of this thesis were to contribute to Bayesian statistical methodology by contributing to risk assessment statistical methodology, and to spatial and spatio-temporal methodology, by modelling error structures using complex hierarchical models. Specifically, I hoped to consider two applied areas, and use these applications as a springboard for developing new statistical methods as well as undertaking analyses which might give answers to particular applied questions. Thus, this thesis considers a series of models, firstly in the context of risk assessments for recycled water, and secondly in the context of water usage by crops. The research objective was to model error structures using hierarchical models in two problems, namely risk assessment analyses for wastewater, and secondly, in a four dimensional dataset, assessing differences between cropping systems over time and over three spatial dimensions. The aim was to use the simplicity and insight afforded by Bayesian networks to develop appropriate models for risk scenarios, and again to use Bayesian hierarchical models to explore the necessarily complex modelling of four dimensional agricultural data. The specific objectives of the research were to develop a method for the calculation of credible intervals for the point estimates of Bayesian networks; to develop a model structure to incorporate all the experimental uncertainty associated with various constants thereby allowing the calculation of more credible credible intervals for a risk assessment; to model a single day’s data from the agricultural dataset which satisfactorily captured the complexities of the data; to build a model for several days’ data, in order to consider how the full data might be modelled; and finally to build a model for the full four dimensional dataset and to consider the timevarying nature of the contrast of interest, having satisfactorily accounted for possible spatial and temporal autocorrelations. This work forms five papers, two of which have been published, with two submitted, and the final paper still in draft. The first two objectives were met by recasting the risk assessments as directed, acyclic graphs (DAGs). In the first case, we elicited uncertainty for the conditional probabilities needed by the Bayesian net, incorporated these into a corresponding DAG, and used Markov chain Monte Carlo (MCMC) to find credible intervals, for all the scenarios and outcomes of interest. In the second case, we incorporated the experimental data underlying the risk assessment constants into the DAG, and also treated some of that data as needing to be modelled as an ‘errors-invariables’ problem [Fuller, 1987]. This illustrated a simple method for the incorporation of experimental error into risk assessments. In considering one day of the three-dimensional agricultural data, it became clear that geostatistical models or conditional autoregressive (CAR) models over the three dimensions were not the best way to approach the data. Instead CAR models are used with neighbours only in the same depth layer. This gave flexibility to the model, allowing both the spatially structured and non-structured variances to differ at all depths. We call this model the CAR layered model. Given the experimental design, the fixed part of the model could have been modelled as a set of means by treatment and by depth, but doing so allows little insight into how the treatment effects vary with depth. Hence, a number of essentially non-parametric approaches were taken to see the effects of depth on treatment, with the model of choice incorporating an errors-in-variables approach for depth in addition to a non-parametric smooth. The statistical contribution here was the introduction of the CAR layered model, the applied contribution the analysis of moisture over depth and estimation of the contrast of interest together with its credible intervals. These models were fitted using WinBUGS [Lunn et al., 2000]. The work in the fifth paper deals with the fact that with large datasets, the use of WinBUGS becomes more problematic because of its highly correlated term by term updating. In this work, we introduce a Gibbs sampler with block updating for the CAR layered model. The Gibbs sampler was implemented by Chris Strickland using pyMCMC [Strickland, 2010]. This framework is then used to consider five days data, and we show that moisture in the soil for all the various treatments reaches levels particular to each treatment at a depth of 200 cm and thereafter stays constant, albeit with increasing variances with depth. In an analysis across three spatial dimensions and across time, there are many interactions of time and the spatial dimensions to be considered. Hence, we chose to use a daily model and to repeat the analysis at all time points, effectively creating an interaction model of time by the daily model. Such an approach allows great flexibility. However, this approach does not allow insight into the way in which the parameter of interest varies over time. Hence, a two-stage approach was also used, with estimates from the first-stage being analysed as a set of time series. We see this spatio-temporal interaction model as being a useful approach to data measured across three spatial dimensions and time, since it does not assume additivity of the random spatial or temporal effects.

Preliminary study on bridge health prediction using Dynamic Objective Oriented Bayesian Network (DOOBN)

The availability of bridges is crucial to people’s daily life and national economy. Bridge health prediction plays an important role in bridge management because maintenance optimization is implemented based on prediction results of bridge deterioration. Conventional bridge deterioration models can be categorised into two groups, namely condition states models and structural reliability models. Optimal maintenance strategy should be carried out based on both condition states and structural reliability of a bridge. However, none of existing deterioration models considers both condition states and structural reliability. This study thus proposes a Dynamic Objective Oriented Bayesian Network (DOOBN) based method to overcome the limitations of the existing methods. This methodology has the ability to act upon as a flexible unifying tool, which can integrate a variety of approaches and information for better bridge deterioration prediction. Two demonstrative case studies are conducted to preliminarily justify the feasibility of the methodology

Thresholds for error probability measures of business process models

The quality of conceptual business process models is highly relevant for the design of corresponding information systems. In particular, a precise measurement of model characteristics can be beneficial from a business perspective, helping to save costs thanks to early error detection. This is just as true from a software engineering point of view. In this latter case, models facilitate stakeholder communication and software system design. Research has investigated several proposals as regards measures for business process models, from a rather correlational perspective. This is helpful for understanding, for example size and complexity as general driving forces of error probability. Yet, design decisions usually have to build on thresholds, which can reliably indicate that a certain counter-action has to be taken. This cannot be achieved only by providing measures; it requires a systematic identification of effective and meaningful thresholds. In this paper, we derive thresholds for a set of structural measures for predicting errors in conceptual process models. To this end, we use a collection of 2,000 business process models from practice as a means of determining thresholds, applying an adaptation of the ROC curves method. Furthermore, an extensive validation of the derived thresholds was conducted by using 429 EPC models from an Australian financial institution. Finally, significant thresholds were adapted to refine existing modeling guidelines in a quantitative way.

Sequential Monte Carlo for Bayesian sequentially designed experiments for discrete data

In this paper we present a sequential Monte Carlo algorithm for Bayesian sequential experimental design applied to generalised non-linear models for discrete data. The approach is computationally convenient in that the information of newly observed data can be incorporated through a simple re-weighting step. We also consider a flexible parametric model for the stimulus-response relationship together with a newly developed hybrid design utility that can produce more robust estimates of the target stimulus in the presence of substantial model and parameter uncertainty. The algorithm is applied to hypothetical clinical trial or bioassay scenarios. In the discussion, potential generalisations of the algorithm are suggested to possibly extend its applicability to a wide variety of scenarios

Bayesian mixtures for modelling complex medical data : a case study in Parkinson’s disease

Mixture models are a flexible tool for unsupervised clustering that have found popularity in a vast array of research areas. In studies of medicine, the use of mixtures holds the potential to greatly enhance our understanding of patient responses through the identification of clinically meaningful clusters that, given the complexity of many data sources, may otherwise by intangible. Furthermore, when developed in the Bayesian framework, mixture models provide a natural means for capturing and propagating uncertainty in different aspects of a clustering solution, arguably resulting in richer analyses of the population under study. This thesis aims to investigate the use of Bayesian mixture models in analysing varied and detailed sources of patient information collected in the study of complex disease. The first aim of this thesis is to showcase the flexibility of mixture models in modelling markedly different types of data. In particular, we examine three common variants on the mixture model, namely, finite mixtures, Dirichlet Process mixtures and hidden Markov models. Beyond the development and application of these models to different sources of data, this thesis also focuses on modelling different aspects relating to uncertainty in clustering. Examples of clustering uncertainty considered are uncertainty in a patient’s true cluster membership and accounting for uncertainty in the true number of clusters present. Finally, this thesis aims to address and propose solutions to the task of comparing clustering solutions, whether this be comparing patients or observations assigned to different subgroups or comparing clustering solutions over multiple datasets. To address these aims, we consider a case study in Parkinson’s disease (PD), a complex and commonly diagnosed neurodegenerative disorder. In particular, two commonly collected sources of patient information are considered. The first source of data are on symptoms associated with PD, recorded using the Unified Parkinson’s Disease Rating Scale (UPDRS) and constitutes the first half of this thesis. The second half of this thesis is dedicated to the analysis of microelectrode recordings collected during Deep Brain Stimulation (DBS), a popular palliative treatment for advanced PD. Analysis of this second source of data centers on the problems of unsupervised detection and sorting of action potentials or "spikes" in recordings of multiple cell activity, providing valuable information on real time neural activity in the brain.

A Bayesian analysis of an agricultural field trial with three spatial dimensions

Modern technology now has the ability to generate large datasets over space and time. Such data typically exhibit high autocorrelations over all dimensions. The field trial data motivating the methods of this paper were collected to examine the behaviour of traditional cropping and to determine a cropping system which could maximise water use for grain production while minimising leakage below the crop root zone. They consist of moisture measurements made at 15 depths across 3 rows and 18 columns, in the lattice framework of an agricultural field. Bayesian conditional autoregressive (CAR) models are used to account for local site correlations. Conditional autoregressive models have not been widely used in analyses of agricultural data. This paper serves to illustrate the usefulness of these models in this field, along with the ease of implementation in WinBUGS, a freely available software package. The innovation is the fitting of separate conditional autoregressive models for each depth layer, the ‘layered CAR model’, while simultaneously estimating depth profile functions for each site treatment. Modelling interest also lay in how best to model the treatment effect depth profiles, and in the choice of neighbourhood structure for the spatial autocorrelation model. The favoured model fitted the treatment effects as splines over depth, and treated depth, the basis for the regression model, as measured with error, while fitting CAR neighbourhood models by depth layer. It is hierarchical, with separate onditional autoregressive spatial variance components at each depth, and the fixed terms which involve an errors-in-measurement model treat depth errors as interval-censored measurement error. The Bayesian framework permits transparent specification and easy comparison of the various complex models compared.