Expert elicitation and its interface with technology : a review with a view to designing Elicitator

Expert knowledge is valuable in many modelling endeavours, particularly where data is not extensive or sufficiently robust. In Bayesian statistics, expert opinion may be formulated as informative priors, to provide an honest reflection of the current state of knowledge, before updating this with new information. Technology is increasingly being exploited to help support the process of eliciting such information. This paper reviews the benefits that have been gained from utilizing technology in this way. These benefits can be structured within a six-step elicitation design framework proposed recently (Low Choy et al., 2009). We assume that the purpose of elicitation is to formulate a Bayesian statistical prior, either to provide a standalone expert-defined model, or for updating new data within a Bayesian analysis. We also assume that the model has been pre-specified before selecting the software. In this case, technology has the most to offer to: targeting what experts know (E2), eliciting and encoding expert opinions (E4), whilst enhancing accuracy (E5), and providing an effective and efficient protocol (E6). Benefits include: -providing an environment with familiar nuances (to make the expert comfortable) where experts can explore their knowledge from various perspectives (E2); -automating tedious or repetitive tasks, thereby minimizing calculation errors, as well as encouraging interaction between elicitors and experts (E5); -cognitive gains by educating users, enabling instant feedback (E2, E4-E5), and providing alternative methods of communicating assessments and feedback information, since experts think and learn differently; and -ensuring a repeatable and transparent protocol is used (E6).

Probability and statistics

Now in its sixth edition, the Traffic Engineering Handbook continues to be a must have publication in the transportation industry, as it has been for the past 60 years. The new edition provides updated information for people entering the practice and for those already practicing. The handbook is a convenient desk reference, as well as an all in one source of principles and proven techniques in traffic engineering. Most chapters are presented in a new format, which divides the chapters into four areas-basics, current practice, emerging trends and information sources. Chapter topics include road users, vehicle characteristics, statistics, planning for operations, communications, safety, regulations, traffic calming, access management, geometrics, signs and markings, signals, parking, traffic demand, maintenance and studies. In addition, as the focus in transportation has shifted from project based to operations based, two new chapters have been added-"Planning for Operations" and "Managing Traffic Demand to Address Congestion: Providing Travelers with Choices." The Traffic Engineering Handbook continues to be one of the primary reference sources for study to become a certified Professional Traffic Operations Engineer™. Chapters are authored by notable and experienced authors, and reviewed and edited by a distinguished panel of traffic engineering experts.

Forecasting negative effects of monotony and sensation seeking on performance during a vigilance task

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

The use of ZIP and CART to model cryptosporidiosis in relation to climatic variables

This research assesses the potential impact of weekly weather variability on the incidence of cryptosporidiosis disease using time series zero-inflated Poisson (ZIP) and classification and regression tree (CART) models. Data on weather variables, notified cryptosporidiosis cases and population size in Brisbane were supplied by the Australian Bureau of Meteorology, Queensland Department of Health, and Australian Bureau of Statistics, respectively. Both time series ZIP and CART models show a clear association between weather variables (maximum temperature, relative humidity, rainfall and wind speed) and cryptosporidiosis disease. The time series CART models indicated that, when weekly maximum temperature exceeded 31°C and relative humidity was less than 63%, the relative risk of cryptosporidiosis rose by 13.64 (expected morbidity: 39.4; 95% confidence interval: 30.9–47.9). These findings may have applications as a decision support tool in planning disease control and risk management programs for cryptosporidiosis disease.

Advanced mathematical modelling and experimental investigation of new torque arms for shaft-mounted drives

Shaft-mounted gearboxes are widely used in industry. The torque arm that holds the reactive torque on the housing of the gearbox, if properly positioned creates the reactive force that lifts the gearbox and unloads the bearings of the output shaft. The shortcoming of these torque arms is that if the gearbox is reversed the direction of the reactive force on the torque arm changes to opposite and added to the weight of the gearbox overloads the bearings shortening their operating life. In this paper, a new patented design of torque arms that develop a controlled lifting force and counteract the weight of the gearbox regardless of the direction of the output shaft rotation is described. Several mathematical models of the conventional and new torque arms were developed and verified experimentally on a specially built test rig that enables modelling of the radial compliance of the gearbox bearings and elastic elements of the torque arms. Comparison showed a good agreement between theoretical and experimental results.

Estimation of parameters for macroparasite population evolution using approximate Bayesian computation

We estimate the parameters of a stochastic process model for a macroparasite population within a host using approximate Bayesian computation (ABC). The immunity of the host is an unobserved model variable and only mature macroparasites at sacrifice of the host are counted. With very limited data, process rates are inferred reasonably precisely. Modeling involves a three variable Markov process for which the observed data likelihood is computationally intractable. ABC methods are particularly useful when the likelihood is analytically or computationally intractable. The ABC algorithm we present is based on sequential Monte Carlo, is adaptive in nature, and overcomes some drawbacks of previous approaches to ABC. The algorithm is validated on a test example involving simulated data from an autologistic model before being used to infer parameters of the Markov process model for experimental data. The fitted model explains the observed extra-binomial variation in terms of a zero-one immunity variable, which has a short-lived presence in the host.

Mathematical modelling of chronic wound healing

Chronicwounds fail to proceed through an orderly process to produce anatomic and functional integrity and are a significant socioeconomic problem. There is much debate about the best way to treat these wounds. In this thesis we review earlier mathematical models of angiogenesis and wound healing. Many of these models assume a chemotactic response of endothelial cells, the primary cell type involved in angiogenesis. Modelling this chemotactic response leads to a system of advection-dominated partial differential equations and we review numerical methods to solve these equations and argue that the finite volume method with flux limiting is best-suited to these problems. One treatment of chronic wounds that is shrouded with controversy is hyperbaric oxygen therapy (HBOT). There is currently no conclusive data showing that HBOT can assist chronic wound healing, but there has been some clinical success. In this thesis we use several mathematical models of wound healing to investigate the use of hyperbaric oxygen therapy to assist the healing process - a novel threespecies model and a more complex six-species model. The second model accounts formore of the biological phenomena but does not lend itself tomathematical analysis. Bothmodels are then used tomake predictions about the efficacy of hyperbaric oxygen therapy and the optimal treatment protocol. Based on our modelling, we are able to make several predictions including that intermittent HBOT will assist chronic wound healing while normobaric oxygen is ineffective in treating such wounds, treatment should continue until healing is complete and finding the right protocol for an individual patient is crucial if HBOT is to be effective. Analysis of the models allows us to derive constraints for the range of HBOT protocols that will stimulate healing, which enables us to predict which patients are more likely to have a positive response to HBOT and thus has the potential to assist in improving both the success rate and thus the cost-effectiveness of this therapy.

Risk factor analysis and spatiotemporal CART model of cryptosporidiosis in Queensland, Australia

Background: It remains unclear whether it is possible to develop a spatiotemporal epidemic prediction model for cryptosporidiosis disease. This paper examined the impact of social economic and weather factors on cryptosporidiosis and explored the possibility of developing such a model using social economic and weather data in Queensland, Australia. ----- ----- Methods: Data on weather variables, notified cryptosporidiosis cases and social economic factors in Queensland were supplied by the Australian Bureau of Meteorology, Queensland Department of Health, and Australian Bureau of Statistics, respectively. Three-stage spatiotemporal classification and regression tree (CART) models were developed to examine the association between social economic and weather factors and monthly incidence of cryptosporidiosis in Queensland, Australia. The spatiotemporal CART model was used for predicting the outbreak of cryptosporidiosis in Queensland, Australia. ----- ----- Results: The results of the classification tree model (with incidence rates defined as binary presence/absence) showed that there was an 87% chance of an occurrence of cryptosporidiosis in a local government area (LGA) if the socio-economic index for the area (SEIFA) exceeded 1021, while the results of regression tree model (based on non-zero incidence rates) show when SEIFA was between 892 and 945, and temperature exceeded 32°C, the relative risk (RR) of cryptosporidiosis was 3.9 (mean morbidity: 390.6/100,000, standard deviation (SD): 310.5), compared to monthly average incidence of cryptosporidiosis. When SEIFA was less than 892 the RR of cryptosporidiosis was 4.3 (mean morbidity: 426.8/100,000, SD: 319.2). A prediction map for the cryptosporidiosis outbreak was made according to the outputs of spatiotemporal CART models. ----- ----- Conclusions: The results of this study suggest that spatiotemporal CART models based on social economic and weather variables can be used for predicting the outbreak of cryptosporidiosis in Queensland, Australia.

Multivariate Markov Process Models for the transmission of methicillin-resistant Staphylococcus Aureus in a hospital ward

Methicillin-resistant Staphylococcus Aureus (MRSA) is a pathogen that continues to be of major concern in hospitals. We develop models and computational schemes based on observed weekly incidence data to estimate MRSA transmission parameters. We extend the deterministic model of McBryde, Pettitt, and McElwain (2007, Journal of Theoretical Biology 245, 470–481) involving an underlying population of MRSA colonized patients and health-care workers that describes, among other processes, transmission between uncolonized patients and colonized health-care workers and vice versa. We develop new bivariate and trivariate Markov models to include incidence so that estimated transmission rates can be based directly on new colonizations rather than indirectly on prevalence. Imperfect sensitivity of pathogen detection is modeled using a hidden Markov process. The advantages of our approach include (i) a discrete valued assumption for the number of colonized health-care workers, (ii) two transmission parameters can be incorporated into the likelihood, (iii) the likelihood depends on the number of new cases to improve precision of inference, (iv) individual patient records are not required, and (v) the possibility of imperfect detection of colonization is incorporated. We compare our approach with that used by McBryde et al. (2007) based on an approximation that eliminates the health-care workers from the model, uses Markov chain Monte Carlo and individual patient data. We apply these models to MRSA colonization data collected in a small intensive care unit at the Princess Alexandra Hospital, Brisbane, Australia.

Approximate Bayesian computation using indirect inference

We present a novel approach for developing summary statistics for use in approximate Bayesian computation (ABC) algorithms by using indirect inference. ABC methods are useful for posterior inference in the presence of an intractable likelihood function. In the indirect inference approach to ABC the parameters of an auxiliary model fitted to the data become the summary statistics. Although applicable to any ABC technique, we embed this approach within a sequential Monte Carlo algorithm that is completely adaptive and requires very little tuning. This methodological development was motivated by an application involving data on macroparasite population evolution modelled by a trivariate stochastic process for which there is no tractable likelihood function. The auxiliary model here is based on a beta–binomial distribution. The main objective of the analysis is to determine which parameters of the stochastic model are estimable from the observed data on mature parasite worms.

Application of higher order statistics/spectra in biomedical signals : a review

For many decades correlation and power spectrum have been primary tools for digital signal processing applications in the biomedical area. The information contained in the power spectrum is essentially that of the autocorrelation sequence; which is sufficient for complete statistical descriptions of Gaussian signals of known means. However, there are practical situations where one needs to look beyond autocorrelation of a signal to extract information regarding deviation from Gaussianity and the presence of phase relations. Higher order spectra, also known as polyspectra, are spectral representations of higher order statistics, i.e. moments and cumulants of third order and beyond. HOS (higher order statistics or higher order spectra) can detect deviations from linearity, stationarity or Gaussianity in the signal. Most of the biomedical signals are non-linear, non-stationary and non-Gaussian in nature and therefore it can be more advantageous to analyze them with HOS compared to the use of second order correlations and power spectra. In this paper we have discussed the application of HOS for different bio-signals. HOS methods of analysis are explained using a typical heart rate variability (HRV) signal and applications to other signals are reviewed.

Combining expert opinions in prior elicitation

A method of eliciting prior distributions for Bayesian models using expert knowledge is proposed. Elicitation is a widely studied problem, from a psychological perspective as well as from a statistical perspective. Here, we are interested in combining opinions from more than one expert using an explicitly model-based approach so that we may account for various sources of variation affecting elicited expert opinions. We use a hierarchical model to achieve this. We apply this approach to two problems. The first problem involves a food risk assessment problem involving modelling dose-response for Listeria monocytogenes contamination of mice. The second concerns the time taken by PhD students to submit their thesis in a particular school.

Early childhood teachers' mathematical content knowledge

The process of becoming numerate begins in the early years. According to Vygotskian theory (1978), teachers are More Knowledgeable Others who provide and support learning experiences that influence children’s mathematical learning. This paper reports on research that investigates three early childhood teachers mathematics content knowledge. An exploratory, single case study utilised data collected from interviews, and email correspondence to investigate the teachers’ mathematics content knowledge. The data was reviewed according to three analytical strategies: content analysis, pattern matching, and comparative analysis. Findings indicated there was variation in teachers’ content knowledge across the five mathematical strands and that teachers might not demonstrate the depth of content knowledge that is expected of four year specially trained early years’ teachers. A significant factor that appeared to influence these teachers’ content knowledge was their teaching experience. Therefore, an avenue for future research is the investigation of factors that influence teachers’ content numeracy knowledge.

Comparison of scoring systems for invasive pests using ROC analysis and Monte Carlo simulation

Different international plant protection organisations advocate different schemes for conducting pest risk assessments. Most of these schemes use structured questionnaire in which experts are asked to score several items using an ordinal scale. The scores are then combined using a range of procedures, such as simple arithmetic mean, weighted averages, multiplication of scores, and cumulative sums. The most useful schemes will correctly identify harmful pests and identify ones that are not. As the quality of a pest risk assessment can depend on the characteristics of the scoring system used by the risk assessors (i.e., on the number of points of the scale and on the method used for combining the component scores), it is important to assess and compare the performance of different scoring systems. In this article, we proposed a new method for assessing scoring systems. Its principle is to simulate virtual data using a stochastic model and, then, to estimate sensitivity and specificity values from these data for different scoring systems. The interest of our approach was illustrated in a case study where several scoring systems were compared. Data for this analysis were generated using a probabilistic model describing the pest introduction process. The generated data were then used to simulate the outcome of scoring systems and to assess the accuracy of the decisions about positive and negative introduction. The results showed that ordinal scales with at most 5 or 6 points were sufficient and that the multiplication-based scoring systems performed better than their sum-based counterparts. The proposed method could be used in the future to assess a great diversity of scoring systems.

Non-invasive assessment of tear film surface quality

The tear film plays an important role preserving the health of the ocular surface and maintaining the optimal refractive power of the cornea. Moreover dry eye syndrome is one of the most commonly reported eye health problems. This syndrome is caused by abnormalities in the properties of the tear film. Current clinical tools to assess the tear film properties have shown certain limitations. The traditional invasive methods for the assessment of tear film quality, which are used by most clinicians, have been criticized for the lack of reliability and/or repeatability. A range of non-invasive methods of tear assessment have been investigated, but also present limitations. Hence no “gold standard” test is currently available to assess the tear film integrity. Therefore, improving techniques for the assessment of the tear film quality is of clinical significance and the main motivation for the work described in this thesis. In this study the tear film surface quality (TFSQ) changes were investigated by means of high-speed videokeratoscopy (HSV). In this technique, a set of concentric rings formed in an illuminated cone or a bowl is projected on the anterior cornea and their reflection from the ocular surface imaged on a charge-coupled device (CCD). The reflection of the light is produced in the outer most layer of the cornea, the tear film. Hence, when the tear film is smooth the reflected image presents a well structure pattern. In contrast, when the tear film surface presents irregularities, the pattern also becomes irregular due to the light scatter and deviation of the reflected light. The videokeratoscope provides an estimate of the corneal topography associated with each Placido disk image. Topographical estimates, which have been used in the past to quantify tear film changes, may not always be suitable for the evaluation of all the dynamic phases of the tear film. However the Placido disk image itself, which contains the reflected pattern, may be more appropriate to assess the tear film dynamics. A set of novel routines have been purposely developed to quantify the changes of the reflected pattern and to extract a time series estimate of the TFSQ from the video recording. The routine extracts from each frame of the video recording a maximized area of analysis. In this area a metric of the TFSQ is calculated. Initially two metrics based on the Gabor filter and Gaussian gradient-based techniques, were used to quantify the consistency of the pattern’s local orientation as a metric of TFSQ. These metrics have helped to demonstrate the applicability of HSV to assess the tear film, and the influence of contact lens wear on TFSQ. The results suggest that the dynamic-area analysis method of HSV was able to distinguish and quantify the subtle, but systematic degradation of tear film surface quality in the inter-blink interval in contact lens wear. It was also able to clearly show a difference between bare eye and contact lens wearing conditions. Thus, the HSV method appears to be a useful technique for quantitatively investigating the effects of contact lens wear on the TFSQ. Subsequently a larger clinical study was conducted to perform a comparison between HSV and two other non-invasive techniques, lateral shearing interferometry (LSI) and dynamic wavefront sensing (DWS). Of these non-invasive techniques, the HSV appeared to be the most precise method for measuring TFSQ, by virtue of its lower coefficient of variation. While the LSI appears to be the most sensitive method for analyzing the tear build-up time (TBUT). The capability of each of the non-invasive methods to discriminate dry eye from normal subjects was also investigated. The receiver operating characteristic (ROC) curves were calculated to assess the ability of each method to predict dry eye syndrome. The LSI technique gave the best results under both natural blinking conditions and in suppressed blinking conditions, which was closely followed by HSV. The DWS did not perform as well as LSI or HSV. The main limitation of the HSV technique, which was identified during the former clinical study, was the lack of the sensitivity to quantify the build-up/formation phase of the tear film cycle. For that reason an extra metric based on image transformation and block processing was proposed. In this metric, the area of analysis was transformed from Cartesian to Polar coordinates, converting the concentric circles pattern into a quasi-straight lines image in which a block statistics value was extracted. This metric has shown better sensitivity under low pattern disturbance as well as has improved the performance of the ROC curves. Additionally a theoretical study, based on ray-tracing techniques and topographical models of the tear film, was proposed to fully comprehend the HSV measurement and the instrument’s potential limitations. Of special interested was the assessment of the instrument’s sensitivity under subtle topographic changes. The theoretical simulations have helped to provide some understanding on the tear film dynamics, for instance the model extracted for the build-up phase has helped to provide some insight into the dynamics during this initial phase. Finally some aspects of the mathematical modeling of TFSQ time series have been reported in this thesis. Over the years, different functions have been used to model the time series as well as to extract the key clinical parameters (i.e., timing). Unfortunately those techniques to model the tear film time series do not simultaneously consider the underlying physiological mechanism and the parameter extraction methods. A set of guidelines are proposed to meet both criteria. Special attention was given to a commonly used fit, the polynomial function, and considerations to select the appropriate model order to ensure the true derivative of the signal is accurately represented. The work described in this thesis has shown the potential of using high-speed videokeratoscopy to assess tear film surface quality. A set of novel image and signal processing techniques have been proposed to quantify different aspects of the tear film assessment, analysis and modeling. The dynamic-area HSV has shown good performance in a broad range of conditions (i.e., contact lens, normal and dry eye subjects). As a result, this technique could be a useful clinical tool to assess tear film surface quality in the future.