Boosting the margin: A new explanation for the effectiveness of voting methods

One of the surprising recurring phenomena observed in experiments with boosting is that the test error of the generated classifier usually does not increase as its size becomes very large, and often is observed to decrease even after the training error reaches zero. In this paper, we show that this phenomenon is related to the distribution of margins of the training examples with respect to the generated voting classification rule, where the margin of an example is simply the difference between the number of correct votes and the maximum number of votes received by any incorrect label. We show that techniques used in the analysis of Vapnik's support vector classifiers and of neural networks with small weights can be applied to voting methods to relate the margin distribution to the test error. We also show theoretically and experimentally that boosting is especially effective at increasing the margins of the training examples. Finally, we compare our explanation to those based on the bias-variance decomposition.

Stochastic simulation of chemical reactions in spatially complex media

Discrete stochastic simulations, via techniques such as the Stochastic Simulation Algorithm (SSA) are a powerful tool for understanding the dynamics of chemical kinetics when there are low numbers of certain molecular species. However, an important constraint is the assumption of well-mixedness and homogeneity. In this paper, we show how to use Monte Carlo simulations to estimate an anomalous diffusion parameter that encapsulates the crowdedness of the spatial environment. We then use this parameter to replace the rate constants of bimolecular reactions by a time-dependent power law to produce an SSA valid in cases where anomalous diffusion occurs or the system is not well-mixed (ASSA). Simulations then show that ASSA can successfully predict the temporal dynamics of chemical kinetics in a spatially constrained environment.

Stochastic modelling of T cell homeostasis for two competing clonotypes via the master equation

Stochastic models for competing clonotypes of T cells by multivariate, continuous-time, discrete state, Markov processes have been proposed in the literature by Stirk, Molina-París and van den Berg (2008). A stochastic modelling framework is important because of rare events associated with small populations of some critical cell types. Usually, computational methods for these problems employ a trajectory-based approach, based on Monte Carlo simulation. This is partly because the complementary, probability density function (PDF) approaches can be expensive but here we describe some efficient PDF approaches by directly solving the governing equations, known as the Master Equation. These computations are made very efficient through an approximation of the state space by the Finite State Projection and through the use of Krylov subspace methods when evolving the matrix exponential. These computational methods allow us to explore the evolution of the PDFs associated with these stochastic models, and bimodal distributions arise in some parameter regimes. Time-dependent propensities naturally arise in immunological processes due to, for example, age-dependent effects. Incorporating time-dependent propensities into the framework of the Master Equation significantly complicates the corresponding computational methods but here we describe an efficient approach via Magnus formulas. Although this contribution focuses on the example of competing clonotypes, the general principles are relevant to multivariate Markov processes and provide fundamental techniques for computational immunology.

Stochastic simulation for spatial modelling of dynamic process in a living cell

One of the fundamental motivations underlying computational cell biology is to gain insight into the complicated dynamical processes taking place, for example, on the plasma membrane or in the cytosol of a cell. These processes are often so complicated that purely temporal mathematical models cannot adequately capture the complex chemical kinetics and transport processes of, for example, proteins or vesicles. On the other hand, spatial models such as Monte Carlo approaches can have very large computational overheads. This chapter gives an overview of the state of the art in the development of stochastic simulation techniques for the spatial modelling of dynamic processes in a living cell.

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.

Comparison of three-dimensional profiles over time

In this paper, we describe an analysis for data collected on a three-dimensional spatial lattice with treatments applied at the horizontal lattice points. Spatial correlation is accounted for using a conditional autoregressive model. Observations are defined as neighbours only if they are at the same depth. This allows the corresponding variance components to vary by depth. We use the Markov chain Monte Carlo method with block updating, together with Krylov subspace methods, for efficient estimation of the model. The method is applicable to both regular and irregular horizontal lattices and hence to data collected at any set of horizontal sites for a set of depths or heights, for example, water column or soil profile data. The model for the three-dimensional data is applied to agricultural trial data for five separate days taken roughly six months apart in order to determine possible relationships over time. The purpose of the trial is to determine a form of cropping that leads to less moist soils in the root zone and beyond.We estimate moisture for each date, depth and treatment accounting for spatial correlation and determine relationships of these and other parameters over time.

Bayesian hierarchical models in statistical quality control methods to improve healthcare in hospitals

Quality oriented management systems and methods have become the dominant business and governance paradigm. From this perspective, satisfying customers’ expectations by supplying reliable, good quality products and services is the key factor for an organization and even government. During recent decades, Statistical Quality Control (SQC) methods have been developed as the technical core of quality management and continuous improvement philosophy and now are being applied widely to improve the quality of products and services in industrial and business sectors. Recently SQC tools, in particular quality control charts, have been used in healthcare surveillance. In some cases, these tools have been modified and developed to better suit the health sector characteristics and needs. It seems that some of the work in the healthcare area has evolved independently of the development of industrial statistical process control methods. Therefore analysing and comparing paradigms and the characteristics of quality control charts and techniques across the different sectors presents some opportunities for transferring knowledge and future development in each sectors. Meanwhile considering capabilities of Bayesian approach particularly Bayesian hierarchical models and computational techniques in which all uncertainty are expressed as a structure of probability, facilitates decision making and cost-effectiveness analyses. Therefore, this research investigates the use of quality improvement cycle in a health vii setting using clinical data from a hospital. The need of clinical data for monitoring purposes is investigated in two aspects. A framework and appropriate tools from the industrial context are proposed and applied to evaluate and improve data quality in available datasets and data flow; then a data capturing algorithm using Bayesian decision making methods is developed to determine economical sample size for statistical analyses within the quality improvement cycle. Following ensuring clinical data quality, some characteristics of control charts in the health context including the necessity of monitoring attribute data and correlated quality characteristics are considered. To this end, multivariate control charts from an industrial context are adapted to monitor radiation delivered to patients undergoing diagnostic coronary angiogram and various risk-adjusted control charts are constructed and investigated in monitoring binary outcomes of clinical interventions as well as postintervention survival time. Meanwhile, adoption of a Bayesian approach is proposed as a new framework in estimation of change point following control chart’s signal. This estimate aims to facilitate root causes efforts in quality improvement cycle since it cuts the search for the potential causes of detected changes to a tighter time-frame prior to the signal. This approach enables us to obtain highly informative estimates for change point parameters since probability distribution based results are obtained. Using Bayesian hierarchical models and Markov chain Monte Carlo computational methods, Bayesian estimators of the time and the magnitude of various change scenarios including step change, linear trend and multiple change in a Poisson process are developed and investigated. The benefits of change point investigation is revisited and promoted in monitoring hospital outcomes where the developed Bayesian estimator reports the true time of the shifts, compared to priori known causes, detected by control charts in monitoring rate of excess usage of blood products and major adverse events during and after cardiac surgery in a local hospital. The development of the Bayesian change point estimators are then followed in a healthcare surveillances for processes in which pre-intervention characteristics of patients are viii affecting the outcomes. In this setting, at first, the Bayesian estimator is extended to capture the patient mix, covariates, through risk models underlying risk-adjusted control charts. Variations of the estimator are developed to estimate the true time of step changes and linear trends in odds ratio of intensive care unit outcomes in a local hospital. Secondly, the Bayesian estimator is extended to identify the time of a shift in mean survival time after a clinical intervention which is being monitored by riskadjusted survival time control charts. In this context, the survival time after a clinical intervention is also affected by patient mix and the survival function is constructed using survival prediction model. The simulation study undertaken in each research component and obtained results highly recommend the developed Bayesian estimators as a strong alternative in change point estimation within quality improvement cycle in healthcare surveillances as well as industrial and business contexts. The superiority of the proposed Bayesian framework and estimators are enhanced when probability quantification, flexibility and generalizability of the developed model are also considered. The empirical results and simulations indicate that the Bayesian estimators are a strong alternative in change point estimation within quality improvement cycle in healthcare surveillances. The superiority of the proposed Bayesian framework and estimators are enhanced when probability quantification, flexibility and generalizability of the developed model are also considered. The advantages of the Bayesian approach seen in general context of quality control may also be extended in the industrial and business domains where quality monitoring was initially developed.

Bayesian algorithms with applications

Advances in algorithms for approximate sampling from a multivariable target function have led to solutions to challenging statistical inference problems that would otherwise not be considered by the applied scientist. Such sampling algorithms are particularly relevant to Bayesian statistics, since the target function is the posterior distribution of the unobservables given the observables. In this thesis we develop, adapt and apply Bayesian algorithms, whilst addressing substantive applied problems in biology and medicine as well as other applications. For an increasing number of high-impact research problems, the primary models of interest are often sufficiently complex that the likelihood function is computationally intractable. Rather than discard these models in favour of inferior alternatives, a class of Bayesian "likelihoodfree" techniques (often termed approximate Bayesian computation (ABC)) has emerged in the last few years, which avoids direct likelihood computation through repeated sampling of data from the model and comparing observed and simulated summary statistics. In Part I of this thesis we utilise sequential Monte Carlo (SMC) methodology to develop new algorithms for ABC that are more efficient in terms of the number of model simulations required and are almost black-box since very little algorithmic tuning is required. In addition, we address the issue of deriving appropriate summary statistics to use within ABC via a goodness-of-fit statistic and indirect inference. Another important problem in statistics is the design of experiments. That is, how one should select the values of the controllable variables in order to achieve some design goal. The presences of parameter and/or model uncertainty are computational obstacles when designing experiments but can lead to inefficient designs if not accounted for correctly. The Bayesian framework accommodates such uncertainties in a coherent way. If the amount of uncertainty is substantial, it can be of interest to perform adaptive designs in order to accrue information to make better decisions about future design points. This is of particular interest if the data can be collected sequentially. In a sense, the current posterior distribution becomes the new prior distribution for the next design decision. Part II of this thesis creates new algorithms for Bayesian sequential design to accommodate parameter and model uncertainty using SMC. The algorithms are substantially faster than previous approaches allowing the simulation properties of various design utilities to be investigated in a more timely manner. Furthermore the approach offers convenient estimation of Bayesian utilities and other quantities that are particularly relevant in the presence of model uncertainty. Finally, Part III of this thesis tackles a substantive medical problem. A neurological disorder known as motor neuron disease (MND) progressively causes motor neurons to no longer have the ability to innervate the muscle fibres, causing the muscles to eventually waste away. When this occurs the motor unit effectively ‘dies’. There is no cure for MND, and fatality often results from a lack of muscle strength to breathe. The prognosis for many forms of MND (particularly amyotrophic lateral sclerosis (ALS)) is particularly poor, with patients usually only surviving a small number of years after the initial onset of disease. Measuring the progress of diseases of the motor units, such as ALS, is a challenge for clinical neurologists. Motor unit number estimation (MUNE) is an attempt to directly assess underlying motor unit loss rather than indirect techniques such as muscle strength assessment, which generally is unable to detect progressions due to the body’s natural attempts at compensation. Part III of this thesis builds upon a previous Bayesian technique, which develops a sophisticated statistical model that takes into account physiological information about motor unit activation and various sources of uncertainties. More specifically, we develop a more reliable MUNE method by applying marginalisation over latent variables in order to improve the performance of a previously developed reversible jump Markov chain Monte Carlo sampler. We make other subtle changes to the model and algorithm to improve the robustness of the approach.

Three dimensional simulation of a parabolic trough concentrator thermal collector

Parabolic Trough Concentrators (PTC) are the most proven solar collectors for solar thermal power plants, and are suitable for concentrating photovoltaic (CPV) applications. PV cells are sensitive to spatial uniformity of incident light and the cell operating temperature. This requires the design of CPV-PTCs to be optimised both optically and thermally. Optical modelling can be performed using Monte Carlo Ray Tracing (MCRT), with conjugate heat transfer (CHT) modelling using the computational fluid dynamics (CFD) to analyse the overall designs. This paper develops and evaluates a CHT simulation for a concentrating solar thermal PTC collector. It uses the ray tracing work by Cheng et al. (2010) and thermal performance data for LS-2 parabolic trough used in the SEGS III-VII plants from Dudley et al. (1994). This is a preliminary step to developing models to compare heat transfer performances of faceted absorbers for concentrating photovoltaic (CPV) applications. Reasonable agreement between the simulation results and the experimental data confirms the reliability of the numerical model. The model explores different physical issues as well as computational issues for this particular kind of system modeling. The physical issues include the resultant non-uniformity of the boundary heat flux profile and the temperature profile around the tube, and uneven heating of the HTF. The numerical issues include, most importantly, the design of the computational domain/s, and the solution techniques of the turbulence quantities and the near-wall physics. This simulation confirmed that optical simulation and the computational CHT simulation of the collector can be accomplished independently.

Dosimetric effects of a high-density spinal implant

In this study, a treatment plan for a spinal lesion, with all beams transmitted though a titanium vertebral reconstruction implant, was used to investigate the potential effect of a high-density implant on a three-dimensional dose distribution for a radiotherapy treatment. The BEAMnrc/DOSXYZnrc and MCDTK Monte Carlo codes were used to simulate the treatment using both a simplified, recltilinear model and a detailed model incorporating the full complexity of the patient anatomy and treatment plan. The resulting Monte Carlo dose distributions showed that the commercial treatment planning system failed to accurately predict both the depletion of dose downstream of the implant and the increase in scattered dose adjacent to the implant. Overall, the dosimetric effect of the implant was underestimated by the commercial treatment planning system and overestimated by the simplified Monte Carlo model. The value of performing detailed Monte Carlo calculations, using the full patient and treatment geometry, was demonstrated.

In-cylinder pressure and inter-cycle variability analysis for a compression ignition engine : Bayesian approaches

This thesis introduced Bayesian statistics as an analysis technique to isolate resonant frequency information in in-cylinder pressure signals taken from internal combustion engines. Applications of these techniques are relevant to engine design (performance and noise), energy conservation (fuel consumption) and alternative fuel evaluation. The use of Bayesian statistics, over traditional techniques, allowed for a more in-depth investigation into previously difficult to isolate engine parameters on a cycle-by-cycle basis. Specifically, these techniques facilitated the determination of the start of pre-mixed and diffusion combustion and for the in-cylinder temperature profile to be resolved on individual consecutive engine cycles. Dr Bodisco further showed the utility of the Bayesian analysis techniques by applying them to in-cylinder pressure signals taken from a compression ignition engine run with fumigated ethanol.

A methodological approach to reporting corrected small field relative outputs

Purpose The goal of this work was to set out a methodology for measuring and reporting small field relative output and to assess the application of published correction factors across a population of linear accelerators. Methods and materials Measurements were made at 6 MV on five Varian iX accelerators using two PTW T60017 unshielded diodes. Relative output readings and profile measurements were made for nominal square field sizes of side 0.5 to 1.0 cm. The actual in-plane (A) and cross-plane (B) field widths were taken to be the FWHM at the 50% isodose level. An effective field size, defined as FSeff=A·B, was calculated and is presented as a field size metric. FSeffFSeff was used to linearly interpolate between published Monte Carlo (MC) calculated kQclin,Qmsrfclin,fmsr values to correct for the diode over-response in small fields. Results The relative output data reported as a function of the nominal field size were different across the accelerator population by up to nearly 10%. However, using the effective field size for reporting showed that the actual output ratios were consistent across the accelerator population to within the experimental uncertainty of ±1.0%. Correcting the measured relative output using kQclin,Qmsrfclin,fmsr at both the nominal and effective field sizes produce output factors that were not identical but differ by much less than the reported experimental and/or MC statistical uncertainties. Conclusions In general, the proposed methodology removes much of the ambiguity in reporting and interpreting small field dosimetric quantities and facilitates a clear dosimetric comparison across a population of linacs

Evaluation of MegaVoltage Cone Beam CT image quality with an unmodified Elekta Precise Linac and EPID : a feasibility study

In order to increase the accuracy of patient positioning for complex radiotherapy treatments various 3D imaging techniques have been developed. MegaVoltage Cone Beam CT (MVCBCT) can utilise existing hardware to implement a 3D imaging modality to aid patient positioning. MVCBCT has been investigated using an unmodified Elekta Precise linac and 15 iView amorphous silicon electronic portal imaging device (EPID). Two methods of delivery and acquisition have been investigated for imaging an anthropomorphic head phantom and quality assurance phantom. Phantom projections were successfully acquired and CT datasets reconstructed using both acquisition methods. Bone, tissue and air were 20 clearly resolvable in both phantoms even with low dose (22 MU) scans. The feasibility of MegaVoltage Cone beam CT was investigated using a standard linac, amorphous silicon EPID and a combination of a free open source reconstruction toolkit as well as custom in-house software written in Matlab. The resultant image quality has 25 been assessed and presented. Although bone, tissue and air were resolvable 2 in all scans, artifacts are present and scan doses are increased when compared with standard portal imaging. The feasibility of MVCBCT with unmodified Elekta Precise linac and EPID has been considered as well as the identification of possible areas for future development in artifact correction techniques to 30 further improve image quality.

Prostate radiotherapy treatment plan quality : effects of hip prostheses

Introduction This study aimed to examine the geometric and dosimetric results when radiotherapy treatment plans are designed for prostate cancer patients with hip prostheses. Methods Ten EBRT treatment plans for localised prostate cancer, in the presence of hip prostheses, were analysed and compared with a reference set of 196 treatment plans for localised prostate cancer in patients without prostheses. Crowe et al.’s TADA code [1] was used to extract treatment plan parameters and evaluate doses to target volumes and critical structures against recommended goals [2] and constraints [3, 4]. Results The need to avoid transmitting the radiation beam through the hip prostheses limited the range of gantry angles available for use in both the rotational (VMAT) and the non-rotational (3DCRT and IMRT) radiotherapy treatments. This geometric limitation (exemplified in the VMAT data shown in Fig. 1) reduced the overall quality of the treatment plans for patients with prostheses compared to the reference plans. All plans with prostheses failed the PTV dose homogeneity requirement [2], whereas only 4 % of the plans without prostheses failed this test. Several treatment plans for patients with hip prostheses also failed the QUANTEC requirements that less than 50 % of the rectum receive 50 Gy and less than 35 % of the rectum receive 60 Gy to keep the grade 3 toxicity rate below 10 % [3], or the Hansen and Roach requirement that less than 25 % of the bladder receive 75 Gy [4]. Discussion and conclusions The results of this study exemplify the difficulty of designing prostate radiotherapy treatment plans, where beams provide adequate doses to targeted tissues while avoiding nearby organs at risk, when the presence of hip prostheses limits the available treatment geometries. This work provides qualitative evidence of the compromised dose distributions that can result, in such cases.

The effect of very small air gaps on small field dosimetry

The purpose of this study was to investigate the effect of very small air gaps (less than 1 mm) on the dosimetry of small photon fields used for stereotactic treatments. Measurements were performed with optically stimulated luminescent dosimeters (OSLDs) for 6 MV photons on a Varian 21iX linear accelerator with a Brainlab lMLC attachment for square field sizes down to 6 mm 9 6 mm. Monte Carlo simulations were performed using EGSnrc C++ user code cavity. It was found that the Monte Carlo model used in this study accurately simulated the OSLD measurements on the linear accelerator. For the 6 mm field size, the 0.5 mm air gap upstream to the active area of the OSLD caused a 5.3 % dose reduction relative to a Monte Carlo simulation with no air gap...