Prior and posterior linear pooling for combining expert opinions: Uses and impact on Bayesian Networks

The use of expert knowledge to quantify a Bayesian Network (BN) is necessary when data is not available. This however raises questions regarding how opinions from multiple experts can be used in a BN. Linear pooling is a popular method for combining probability assessments from multiple experts. In particular, Prior Linear Pooling (PrLP), which pools opinions then places them into the BN is a common method. This paper firstly proposes an alternative pooling method, Posterior Linear Pooling (PoLP). This method constructs a BN for each expert, then pools the resulting probabilities at the nodes of interest. Secondly, it investigates the advantages and disadvantages of using these pooling methods to combine the opinions of multiple experts. Finally, the methods are applied to an existing BN, the Wayfinding Bayesian Network Model, to investigate the behaviour of different groups of people and how these different methods may be able to capture such differences. The paper focusses on 6 nodes Human Factors, Environmental Factors, Wayfinding, Communication, Visual Elements of Communication and Navigation Pathway, and three subgroups Gender (female, male),Travel Experience (experienced, inexperienced), and Travel Purpose (business, personal) and finds that different behaviors can indeed be captured by the different methods.

Comparison of decision tree, support vector machines, and Bayesian network approaches for classification of falls in Parkinson’s disease

Being able to accurately predict the risk of falling is crucial in patients with Parkinson’s dis- ease (PD). This is due to the unfavorable effect of falls, which can lower the quality of life as well as directly impact on survival. Three methods considered for predicting falls are decision trees (DT), Bayesian networks (BN), and support vector machines (SVM). Data on a 1-year prospective study conducted at IHBI, Australia, for 51 people with PD are used. Data processing are conducted using rpart and e1071 packages in R for DT and SVM, con- secutively; and Bayes Server 5.5 for the BN. The results show that BN and SVM produce consistently higher accuracy over the 12 months evaluation time points (average sensitivity and specificity > 92%) than DT (average sensitivity 88%, average specificity 72%). DT is prone to imbalanced data so needs to adjust for the misclassification cost. However, DT provides a straightforward, interpretable result and thus is appealing for helping to identify important items related to falls and to generate fallers’ profiles.

Statistical and Information-Theoretic Methods for Data-Analysis

In this Thesis, we develop theory and methods for computational data analysis. The problems in data analysis are approached from three perspectives: statistical learning theory, the Bayesian framework, and the information-theoretic minimum description length (MDL) principle. Contributions in statistical learning theory address the possibility of generalization to unseen cases, and regression analysis with partially observed data with an application to mobile device positioning. In the second part of the Thesis, we discuss so called Bayesian network classifiers, and show that they are closely related to logistic regression models. In the final part, we apply the MDL principle to tracing the history of old manuscripts, and to noise reduction in digital signals.

Applicability of Statistical Learning Algorithms for Spatial Variability of Rock Depth

Two algorithms are outlined, each of which has interesting features for modeling of spatial variability of rock depth. In this paper, reduced level of rock at Bangalore, India, is arrived from the 652 boreholes data in the area covering 220 sqa <.km. Support vector machine (SVM) and relevance vector machine (RVM) have been utilized to predict the reduced level of rock in the subsurface of Bangalore and to study the spatial variability of the rock depth. The support vector machine (SVM) that is firmly based on the theory of statistical learning theory uses regression technique by introducing epsilon-insensitive loss function has been adopted. RVM is a probabilistic model similar to the widespread SVM, but where the training takes place in a Bayesian framework. Prediction results show the ability of learning machine to build accurate models for spatial variability of rock depth with strong predictive capabilities. The paper also highlights the capability ofRVM over the SVM model.

Internal representations of temporal statistics and feedback calibrate motor-sensory interval timing.

Humans have been shown to adapt to the temporal statistics of timing tasks so as to optimize the accuracy of their responses, in agreement with the predictions of Bayesian integration. This suggests that they build an internal representation of both the experimentally imposed distribution of time intervals (the prior) and of the error (the loss function). The responses of a Bayesian ideal observer depend crucially on these internal representations, which have only been previously studied for simple distributions. To study the nature of these representations we asked subjects to reproduce time intervals drawn from underlying temporal distributions of varying complexity, from uniform to highly skewed or bimodal while also varying the error mapping that determined the performance feedback. Interval reproduction times were affected by both the distribution and feedback, in good agreement with a performance-optimizing Bayesian observer and actor model. Bayesian model comparison highlighted that subjects were integrating the provided feedback and represented the experimental distribution with a smoothed approximation. A nonparametric reconstruction of the subjective priors from the data shows that they are generally in agreement with the true distributions up to third-order moments, but with systematically heavier tails. In particular, higher-order statistical features (kurtosis, multimodality) seem much harder to acquire. Our findings suggest that humans have only minor constraints on learning lower-order statistical properties of unimodal (including peaked and skewed) distributions of time intervals under the guidance of corrective feedback, and that their behavior is well explained by Bayesian decision theory.

Decision-theoretic designs for phase II clinical trials allowing for competing studies

This article describes an approach to optimal design of phase II clinical trials using Bayesian decision theory. The method proposed extends that suggested by Stallard (1998, Biometrics54, 279–294) in which designs were obtained to maximize a gain function including the cost of drug development and the benefit from a successful therapy. Here, the approach is extended by the consideration of other potential therapies, the development of which is competing for the same limited resources. The resulting optimal designs are shown to have frequentist properties much more similar to those traditionally used in phase II trials.

Sequential updating via dynamic hierarchical models: A Bayesian approach to longitudinal data analysis

Most statistical analysis, theory and practice, is concerned with static models; models with a proposed set of parameters whose values are fixed across observational units. Static models implicitly assume that the quantified relationships remain the same across the design space of the data. While this is reasonable under many circumstances this can be a dangerous assumption when dealing with sequentially ordered data. The mere passage of time always brings fresh considerations and the interrelationships among parameters, or subsets of parameters, may need to be continually revised. ^ When data are gathered sequentially dynamic interim monitoring may be useful as new subject-specific parameters are introduced with each new observational unit. Sequential imputation via dynamic hierarchical models is an efficient strategy for handling missing data and analyzing longitudinal studies. Dynamic conditional independence models offers a flexible framework that exploits the Bayesian updating scheme for capturing the evolution of both the population and individual effects over time. While static models often describe aggregate information well they often do not reflect conflicts in the information at the individual level. Dynamic models prove advantageous over static models in capturing both individual and aggregate trends. Computations for such models can be carried out via the Gibbs sampler. An application using a small sample repeated measures normally distributed growth curve data is presented. ^

A test of a stochastic theory of choice,

Mode of access: Internet.

Measurements of generalisation based on information geometry

Neural networks are statistical models and learning rules are estimators. In this paper a theory for measuring generalisation is developed by combining Bayesian decision theory with information geometry. The performance of an estimator is measured by the information divergence between the true distribution and the estimate, averaged over the Bayesian posterior. This unifies the majority of error measures currently in use. The optimal estimators also reveal some intricate interrelationships among information geometry, Banach spaces and sufficient statistics.

Dynamic decision networks for decision-making in self-adaptive systems:a case study

Bayesian decision theory is increasingly applied to support decision-making processes under environmental variability and uncertainty. Researchers from application areas like psychology and biomedicine have applied these techniques successfully. However, in the area of software engineering and speci?cally in the area of self-adaptive systems (SASs), little progress has been made in the application of Bayesian decision theory. We believe that techniques based on Bayesian Networks (BNs) are useful for systems that dynamically adapt themselves at runtime to a changing environment, which is usually uncertain. In this paper, we discuss the case for the use of BNs, speci?cally Dynamic Decision Networks (DDNs), to support the decision-making of self-adaptive systems. We present how such a probabilistic model can be used to support the decision making in SASs and justify its applicability. We have applied our DDN-based approach to the case of an adaptive remote data mirroring system. We discuss results, implications and potential bene?ts of the DDN to enhance the development and operation of self-adaptive systems, by providing mechanisms to cope with uncertainty and automatically make the best decision.

Bayesian models for longitudinal data

Longitudinal data, where data are repeatedly observed or measured on a temporal basis of time or age provides the foundation of the analysis of processes which evolve over time, and these can be referred to as growth or trajectory models. One of the traditional ways of looking at growth models is to employ either linear or polynomial functional forms to model trajectory shape, and account for variation around an overall mean trend with the inclusion of random eects or individual variation on the functional shape parameters. The identification of distinct subgroups or sub-classes (latent classes) within these trajectory models which are not based on some pre-existing individual classification provides an important methodology with substantive implications. The identification of subgroups or classes has a wide application in the medical arena where responder/non-responder identification based on distinctly diering trajectories delivers further information for clinical processes. This thesis develops Bayesian statistical models and techniques for the identification of subgroups in the analysis of longitudinal data where the number of time intervals is limited. These models are then applied to a single case study which investigates the neuropsychological cognition for early stage breast cancer patients undergoing adjuvant chemotherapy treatment from the Cognition in Breast Cancer Study undertaken by the Wesley Research Institute of Brisbane, Queensland. Alternative formulations to the linear or polynomial approach are taken which use piecewise linear models with a single turning point, change-point or knot at a known time point and latent basis models for the non-linear trajectories found for the verbal memory domain of cognitive function before and after chemotherapy treatment. Hierarchical Bayesian random eects models are used as a starting point for the latent class modelling process and are extended with the incorporation of covariates in the trajectory profiles and as predictors of class membership. The Bayesian latent basis models enable the degree of recovery post-chemotherapy to be estimated for short and long-term followup occasions, and the distinct class trajectories assist in the identification of breast cancer patients who maybe at risk of long-term verbal memory impairment.

Statistical and Econometric Methods for Transportation Data Analysis, 2nd edition

Now in its second edition, this book describes tools that are commonly used in transportation data analysis. The first part of the text provides statistical fundamentals while the second part presents continuous dependent variable models. With a focus on count and discrete dependent variable models, the third part features new chapters on mixed logit models, logistic regression, and ordered probability models. The last section provides additional coverage of Bayesian statistical modeling, including Bayesian inference and Markov chain Monte Carlo methods. Data sets are available online to use with the modeling techniques discussed.

Asset renewal decision modelling with application to the water utility industry

Reliable infrastructure assets impact significantly on quality of life and provide a stable foundation for economic growth and competitiveness. Decisions about the way assets are managed are of utmost importance in achieving this. Timely renewal of infrastructure assets supports reliability and maximum utilisation of infrastructure and enables business and community to grow and prosper. This research initially examined a framework for asset management decisions and then focused on asset renewal optimisation and renewal engineering optimisation in depth. This study had four primary objectives. The first was to develop a new Asset Management Decision Framework (AMDF) for identifying and classifying asset management decisions. The AMDF was developed by applying multi-criteria decision theory, classical management theory and life cycle management. The AMDF is an original and innovative contribution to asset management in that: · it is the first framework to provide guidance for developing asset management decision criteria based on fundamental business objectives; · it is the first framework to provide a decision context identification and analysis process for asset management decisions; and · it is the only comprehensive listing of asset management decision types developed from first principles. The second objective of this research was to develop a novel multi-attribute Asset Renewal Decision Model (ARDM) that takes account of financial, customer service, health and safety, environmental and socio-economic objectives. The unique feature of this ARDM is that it is the only model to optimise timing of asset renewal with respect to fundamental business objectives. The third objective of this research was to develop a novel Renewal Engineering Decision Model (REDM) that uses multiple criteria to determine the optimal timing for renewal engineering. The unique features of this model are that: · it is a novel extension to existing real options valuation models in that it uses overall utility rather than present value of cash flows to model engineering value; and · it is the only REDM that optimises timing of renewal engineering with respect to fundamental business objectives; The final objective was to develop and validate an Asset Renewal Engineering Philosophy (AREP) consisting of three principles of asset renewal engineering. The principles were validated using a novel application of real options theory. The AREP is the only renewal engineering philosophy in existence. The original contributions of this research are expected to enrich the body of knowledge in asset management through effectively addressing the need for an asset management decision framework, asset renewal and renewal engineering optimisation based on fundamental business objectives and a novel renewal engineering philosophy.

A Python package for Bayesian estimation using Markov Chain Monte Carlo

Markov chain Monte Carlo (MCMC) estimation provides a solution to the complex integration problems that are faced in the Bayesian analysis of statistical problems. The implementation of MCMC algorithms is, however, code intensive and time consuming. We have developed a Python package, which is called PyMCMC, that aids in the construction of MCMC samplers and helps to substantially reduce the likelihood of coding error, as well as aid in the minimisation of repetitive code. PyMCMC contains classes for Gibbs, Metropolis Hastings, independent Metropolis Hastings, random walk Metropolis Hastings, orientational bias Monte Carlo and slice samplers as well as specific modules for common models such as a module for Bayesian regression analysis. PyMCMC is straightforward to optimise, taking advantage of the Python libraries Numpy and Scipy, as well as being readily extensible with C or Fortran.

Quantum models of cognition and decision

Much of our understanding of human thinking is based on probabilistic models. This innovative book by Jerome R. Busemeyer and Peter D. Bruza argues that, actually, the underlying mathematical structures from quantum theory provide a much better account of human thinking than traditional models. They introduce the foundations for modelling probabilistic-dynamic systems using two aspects of quantum theory. The first, "contextuality", is a way to understand interference effects found with inferences and decisions under conditions of uncertainty. The second, "entanglement", allows cognitive phenomena to be modelled in non-reductionist ways. Employing these principles drawn from quantum theory allows us to view human cognition and decision in a totally new light...