Bayesian multinomial logit: Theory and route choice example

Statisticians along with other scientists have made significant computational advances that enable the estimation of formerly complex statistical models. The Bayesian inference framework combined with Markov chain Monte Carlo estimation methods such as the Gibbs sampler enable the estimation of discrete choice models such as the multinomial logit (MNL) model. MNL models are frequently applied in transportation research to model choice outcomes such as mode, destination, or route choices or to model categorical outcomes such as crash outcomes. Recent developments allow for the modification of the potentially limiting assumptions of MNL such as the independence from irrelevant alternatives (IIA) property. However, relatively little transportation-related research has focused on Bayesian MNL models, the tractability of which is of great value to researchers and practitioners alike. This paper addresses MNL model specification issues in the Bayesian framework, such as the value of including prior information on parameters, allowing for nonlinear covariate effects, and extensions to random parameter models, so changing the usual limiting IIA assumption. This paper also provides an example that demonstrates, using route-choice data, the considerable potential of the Bayesian MNL approach with many transportation applications. This paper then concludes with a discussion of the pros and cons of this Bayesian approach and identifies when its application is worthwhile

Alleviating ‘overfitting’ via genetically-regularised neural network

A hybrid genetic algorithm/scaled conjugate gradient regularisation method is designed to alleviate ANN `over-fitting'. In application to day-ahead load forecasting, the proposed algorithm performs better than early-stopping and Bayesian regularisation, showing promising initial results.

A parallel computation of power system equations

Streaming SIMD Extensions (SSE) is a unique feature embedded in the Pentium III and P4 classes of microprocessors. By fully exploiting SSE, parallel algorithms can be implemented on a standard personal computer and a theoretical speedup of four can be achieved. In this paper, we demonstrate the implementation of a parallel LU matrix decomposition algorithm for solving power systems network equations with SSE and discuss advantages and disadvantages of this approach.

Bayesian spatiotemporal analysis of socio-ecologic drivers of Ross River Virus transmission in Queensland, Australia

This study aims to examine the impact of socio-ecologic factors on the transmission of Ross River virus (RRV) infection and to identify areas prone to social and ecologic-driven epidemics in Queensland, Australia. We used a Bayesian spatiotemporal conditional autoregressive model to quantify the relationship between monthly variation of RRV incidence and socio-ecologic factors and to determine spatiotemporal patterns. Our results show that the average increase in monthly RRV incidence was 2.4% (95% credible interval (CrI): 0.1–4.5%) and 2.0% (95% CrI: 1.6–2.3%) for a 1°C increase in monthly average maximum temperature and a 10 mm increase in monthly average rainfall, respectively. A significant spatiotemporal variation and interactive effect between temperature and rainfall on RRV incidence were found. No association between Socio-economic Index for Areas (SEIFA) and RRV was observed. The transmission of RRV in Queensland, Australia appeared to be primarily driven by ecologic variables rather than social factors.

Bayesian filtering over compressed appearance states

This paper presents a framework for performing real-time recursive estimation of landmarks’ visual appearance. Imaging data in its original high dimensional space is probabilistically mapped to a compressed low dimensional space through the definition of likelihood functions. The likelihoods are subsequently fused with prior information using a Bayesian update. This process produces a probabilistic estimate of the low dimensional representation of the landmark visual appearance. The overall filtering provides information complementary to the conventional position estimates which is used to enhance data association. In addition to robotics observations, the filter integrates human observations in the appearance estimates. The appearance tracks as computed by the filter allow landmark classification. The set of labels involved in the classification task is thought of as an observation space where human observations are made by selecting a label. The low dimensional appearance estimates returned by the filter allow for low cost communication in low bandwidth sensor networks. Deployment of the filter in such a network is demonstrated in an outdoor mapping application involving a human operator, a ground and an air vehicle.

Learning articulated motion structures with Bayesian Networks

This paper presents a general methodology for learning articulated motions that, despite having non-linear correlations, are cyclical and have a defined pattern of behavior Using conventional algorithms to extract features from images, a Bayesian classifier is applied to cluster and classify features of the moving object. Clusters are then associated in different frames and structure learning algorithms for Bayesian networks are used to recover the structure of the motion. This framework is applied to the human gait analysis and tracking but applications include any coordinated movement such as multi-robots behavior analysis.

A Bayesian approach for place recognition

This paper presents a robust place recognition algorithm for mobile robots. The framework proposed combines nonlinear dimensionality reduction, nonlinear regression under noise, and variational Bayesian learning to create consistent probabilistic representations of places from images. These generative models are learnt from a few images and used for multi-class place recognition where classification is computed from a set of feature-vectors. Recognition can be performed in near real-time and accounts for complexity such as changes in illumination, occlusions and blurring. The algorithm was tested with a mobile robot in indoor and outdoor environments with sequences of 1579 and 3820 images respectively. This framework has several potential applications such as map building, autonomous navigation, search-rescue tasks and context recognition.

Applying incremental EM to Bayesian classifiers in the learning of hyperspectral remote sensing data

In this paper, we apply the incremental EM method to Bayesian Network Classifiers to learn and interpret hyperspectral sensor data in robotic planetary missions. Hyperspectral image spectroscopy is an emerging technique for geological investigations from airborne or orbital sensors. Many spacecraft carry spectroscopic equipment as wavelengths outside the visible light in the electromagnetic spectrum give much greater information about an object. The algorithm used is an extension to the standard Expectation Maximisation (EM). The incremental method allows us to learn and interpret the data as they become available. Two Bayesian network classifiers were tested: the Naive Bayes, and the Tree-Augmented-Naive Bayes structures. Our preliminary experiments show that incremental learning with unlabelled data can improve the accuracy of the classifier.

Bayesian network for risk of diarrhea associated with the use of recycled water

Estimating potential health risks associated with recycled (reused) water is highly complex given the multiple factors affecting water quality. We take a conceptual model, which represents the factors and pathways by which recycled water may pose a risk of contracting gastroenteritis, convert the conceptual model to a Bayesian net, and quantify the model using one expert’s opinion. This allows us to make various predictions as to the risks posed under various scenarios. Bayesian nets provide an additional way of modeling the determinants of recycled water quality and elucidating their relative influence on a given disease outcome. The important contribution to Bayesian net methodology is that all model predictions, whether risk or relative risk estimates, are expressed as credible intervals.

Hierarchical Bayesian models for estimating the extent of plant pest invasions

Plant biosecurity requires statistical tools to interpret field surveillance data in order to manage pest incursions that threaten crop production and trade. Ultimately, management decisions need to be based on the probability that an area is infested or free of a pest. Current informal approaches to delimiting pest extent rely upon expert ecological interpretation of presence / absence data over space and time. Hierarchical Bayesian models provide a cohesive statistical framework that can formally integrate the available information on both pest ecology and data. The overarching method involves constructing an observation model for the surveillance data, conditional on the hidden extent of the pest and uncertain detection sensitivity. The extent of the pest is then modelled as a dynamic invasion process that includes uncertainty in ecological parameters. Modelling approaches to assimilate this information are explored through case studies on spiralling whitefly, Aleurodicus dispersus and red banded mango caterpillar, Deanolis sublimbalis. Markov chain Monte Carlo simulation is used to estimate the probable extent of pests, given the observation and process model conditioned by surveillance data. Statistical methods, based on time-to-event models, are developed to apply hierarchical Bayesian models to early detection programs and to demonstrate area freedom from pests. The value of early detection surveillance programs is demonstrated through an application to interpret surveillance data for exotic plant pests with uncertain spread rates. The model suggests that typical early detection programs provide a moderate reduction in the probability of an area being infested but a dramatic reduction in the expected area of incursions at a given time. Estimates of spiralling whitefly extent are examined at local, district and state-wide scales. The local model estimates the rate of natural spread and the influence of host architecture, host suitability and inspector efficiency. These parameter estimates can support the development of robust surveillance programs. Hierarchical Bayesian models for the human-mediated spread of spiralling whitefly are developed for the colonisation of discrete cells connected by a modified gravity model. By estimating dispersal parameters, the model can be used to predict the extent of the pest over time. An extended model predicts the climate restricted distribution of the pest in Queensland. These novel human-mediated movement models are well suited to demonstrating area freedom at coarse spatio-temporal scales. At finer scales, and in the presence of ecological complexity, exploratory models are developed to investigate the capacity for surveillance information to estimate the extent of red banded mango caterpillar. It is apparent that excessive uncertainty about observation and ecological parameters can impose limits on inference at the scales required for effective management of response programs. The thesis contributes novel statistical approaches to estimating the extent of pests and develops applications to assist decision-making across a range of plant biosecurity surveillance activities. Hierarchical Bayesian modelling is demonstrated as both a useful analytical tool for estimating pest extent and a natural investigative paradigm for developing and focussing biosecurity programs.

Structural reliability prediction of a steel bridge element using Dynamic Object Oriented Bayesian Network (DOOBN)

Different from conventional methods for structural reliability evaluation, such as, first/second-order reliability methods (FORM/SORM) or Monte Carlo simulation based on corresponding limit state functions, a novel approach based on dynamic objective oriented Bayesian network (DOOBN) for prediction of structural reliability of a steel bridge element has been proposed in this paper. The DOOBN approach can effectively model the deterioration processes of a steel bridge element and predict their structural reliability over time. This approach is also able to achieve Bayesian updating with observed information from measurements, monitoring and visual inspection. Moreover, the computational capacity embedded in the approach can be used to facilitate integrated management and maintenance optimization in a bridge system. A steel bridge girder is used to validate the proposed approach. The predicted results are compared with those evaluated by FORM method.

Probabilistic subgroup identification using Bayesian finite mixture modelling : a case study in Parkinson’s disease phenotype identification

This article explores the use of probabilistic classification, namely finite mixture modelling, for identification of complex disease phenotypes, given cross-sectional data. In particular, if focuses on posterior probabilities of subgroup membership, a standard output of finite mixture modelling, and how the quantification of uncertainty in these probabilities can lead to more detailed analyses. Using a Bayesian approach, we describe two practical uses of this uncertainty: (i) as a means of describing a person’s membership to a single or multiple latent subgroups and (ii) as a means of describing identified subgroups by patient-centred covariates not included in model estimation. These proposed uses are demonstrated on a case study in Parkinson’s disease (PD), where latent subgroups are identified using multiple symptoms from the Unified Parkinson’s Disease Rating Scale (UPDRS).

Adaptive Bayesian compound designs for dose finding studies

We consider the problem of how to efficiently and safely design dose finding studies. Both current and novel utility functions are explored using Bayesian adaptive design methodology for the estimation of a maximum tolerated dose (MTD). In particular, we explore widely adopted approaches such as the continual reassessment method and minimizing the variance of the estimate of an MTD. New utility functions are constructed in the Bayesian framework and are evaluated against current approaches. To reduce computing time, importance sampling is implemented to re-weight posterior samples thus avoiding the need to draw samples using Markov chain Monte Carlo techniques. Further, as such studies are generally first-in-man, the safety of patients is paramount. We therefore explore methods for the incorporation of safety considerations into utility functions to ensure that only safe and well-predicted doses are administered. The amalgamation of Bayesian methodology, adaptive design and compound utility functions is termed adaptive Bayesian compound design (ABCD). The performance of this amalgamation of methodology is investigated via the simulation of dose finding studies. The paper concludes with a discussion of results and extensions that could be included into our approach.