Model choice problems using approximate Bayesian computation with applications to pathogen transmission data sets

Analytically or computationally intractable likelihood functions can arise in complex statistical inferential problems making them inaccessible to standard Bayesian inferential methods. Approximate Bayesian computation (ABC) methods address such inferential problems by replacing direct likelihood evaluations with repeated sampling from the model. ABC methods have been predominantly applied to parameter estimation problems and less to model choice problems due to the added difficulty of handling multiple model spaces. The ABC algorithm proposed here addresses model choice problems by extending Fearnhead and Prangle (2012, Journal of the Royal Statistical Society, Series B 74, 1–28) where the posterior mean of the model parameters estimated through regression formed the summary statistics used in the discrepancy measure. An additional stepwise multinomial logistic regression is performed on the model indicator variable in the regression step and the estimated model probabilities are incorporated into the set of summary statistics for model choice purposes. A reversible jump Markov chain Monte Carlo step is also included in the algorithm to increase model diversity for thorough exploration of the model space. This algorithm was applied to a validating example to demonstrate the robustness of the algorithm across a wide range of true model probabilities. Its subsequent use in three pathogen transmission examples of varying complexity illustrates the utility of the algorithm in inferring preference of particular transmission models for the pathogens.

A pseudo-marginal sequential Monte Carlo algorithm for random effects models in Bayesian sequential design

A computationally efficient sequential Monte Carlo algorithm is proposed for the sequential design of experiments for the collection of block data described by mixed effects models. The difficulty in applying a sequential Monte Carlo algorithm in such settings is the need to evaluate the observed data likelihood, which is typically intractable for all but linear Gaussian models. To overcome this difficulty, we propose to unbiasedly estimate the likelihood, and perform inference and make decisions based on an exact-approximate algorithm. Two estimates are proposed: using Quasi Monte Carlo methods and using the Laplace approximation with importance sampling. Both of these approaches can be computationally expensive, so we propose exploiting parallel computational architectures to ensure designs can be derived in a timely manner. We also extend our approach to allow for model uncertainty. This research is motivated by important pharmacological studies related to the treatment of critically ill patients.

Incorporating human-factors in car-following models : a review of recent developments and research needs

Over the past decades there has been a considerable development in the modeling of car-following (CF) behavior as a result of research undertaken by both traffic engineers and traffic psychologists. While traffic engineers seek to understand the behavior of a traffic stream, traffic psychologists seek to describe the human abilities and errors involved in the driving process. This paper provides a comprehensive review of these two research streams. It is necessary to consider human-factors in {CF} modeling for a more realistic representation of {CF} behavior in complex driving situations (for example, in traffic breakdowns, crash-prone situations, and adverse weather conditions) to improve traffic safety and to better understand widely-reported puzzling traffic flow phenomena, such as capacity drop, stop-and-go oscillations, and traffic hysteresis. While there are some excellent reviews of {CF} models available in the literature, none of these specifically focuses on the human factors in these models. This paper addresses this gap by reviewing the available literature with a specific focus on the latest advances in car-following models from both the engineering and human behavior points of view. In so doing, it analyses the benefits and limitations of various models and highlights future research needs in the area.

Theorizing the use of multiple conceptual models in combination

Conceptual modelling continues to be an important means for graphically capturing the requirements of an information system. Observations of modelling practice suggest that modellers often use multiple conceptual models in combination, because they articulate different aspects of real-world domains. Yet, the available empirical as well as theoretical research in this area has largely studied the use of single models, or single modelling grammars. We develop a Theory of Combined Ontological Coverage by extending an existing theory of ontological expressiveness of conceptual modelling grammars. Our new theory posits that multiple conceptual models are used to increase the maximum coverage of the real-world domain being modelled, whilst trying to minimize the ontological overlap between the models. We illustrate how the theory can be applied to analyse sets of conceptual models. We develop three propositions of the theory about evaluations of model combinations in terms of users’ selection, understandability and usefulness of conceptual models.

Adaptive estimation of hidden semi-Markov chains with parameterised transition probabilities and exponential decaying states

This paper develops maximum likelihood (ML) estimation schemes for finite-state semi-Markov chains in white Gaussian noise. We assume that the semi-Markov chain is characterised by transition probabilities of known parametric from with unknown parameters. We reformulate this hidden semi-Markov model (HSM) problem in the scalar case as a two-vector homogeneous hidden Markov model (HMM) problem in which the state consist of the signal augmented by the time to last transition. With this reformulation we apply the expectation Maximumisation (EM ) algorithm to obtain ML estimates of the transition probabilities parameters, Markov state levels and noise variance. To demonstrate our proposed schemes, motivated by neuro-biological applications, we use a damped sinusoidal parameterised function for the transition probabilities.

Reduced complexity on-line estimation of hidden Markov model parameters

In this paper we propose and study low complexity algorithms for on-line estimation of hidden Markov model (HMM) parameters. The estimates approach the true model parameters as the measurement noise approaches zero, but otherwise give improved estimates, albeit with bias. On a nite data set in the high noise case, the bias may not be signi cantly more severe than for a higher complexity asymptotically optimal scheme. Our algorithms require O(N3) calculations per time instant, where N is the number of states. Previous algorithms based on earlier hidden Markov model signal processing methods, including the expectation-maximumisation (EM) algorithm require O(N4) calculations per time instant.

MIMO and SISO identification of radiation force terms for models of marine structures in waves

This paper presents a discussion on the use of MIMO and SISO techniques for identification of the radiation force terms in models for surface vessels. We compare and discuss two techniques recently proposed in literature for this application: time domain identification and frequency domain identification. We compare the methods in terms of estimates model order, accuracy of the fit, use of the available information, and ease of use and implementation.

Principles of goal-directed spatial robot navigation in biomimetic models

Mobile robots and animals alike must effectively navigate their environments in order to achieve their goals. For animals goal-directed navigation facilitates finding food, seeking shelter or migration; similarly robots perform goal-directed navigation to find a charging station, get out of the rain or guide a person to a destination. This similarity in tasks extends to the environment as well; increasingly, mobile robots are operating in the same underwater, ground and aerial environments that animals do. Yet despite these similarities, goal-directed navigation research in robotics and biology has proceeded largely in parallel, linked only by a small amount of interdisciplinary research spanning both areas. Most state-of-the-art robotic navigation systems employ a range of sensors, world representations and navigation algorithms that seem far removed from what we know of how animals navigate; their navigation systems are shaped by key principles of navigation in ‘real-world’ environments including dealing with uncertainty in sensing, landmark observation and world modelling. By contrast, biomimetic animal navigation models produce plausible animal navigation behaviour in a range of laboratory experimental navigation paradigms, typically without addressing many of these robotic navigation principles. In this paper, we attempt to link robotics and biology by reviewing the current state of the art in conventional and biomimetic goal-directed navigation models, focusing on the key principles of goal-oriented robotic navigation and the extent to which these principles have been adapted by biomimetic navigation models and why.

Computation of Mathematical Models for Complex Industrial Processes

Designed for undergraduate and postgraduate students, academic researchers and industrial practitioners, this book provides comprehensive case studies on numerical computing of industrial processes and step-by-step procedures for conducting industrial computing. It assumes minimal knowledge in numerical computing and computer programming, making it easy to read, understand and follow. Topics discussed include fundamentals of industrial computing, finite difference methods, the Wavelet-Collocation Method, the Wavelet-Galerkin Method, High Resolution Methods, and comparative studies of various methods. These are discussed using examples of carefully selected models from real processes of industrial significance. The step-by-step procedures in all these case studies can be easily applied to other industrial processes without a need for major changes and thus provide readers with useful frameworks for the applications of engineering computing in fundamental research problems and practical development scenarios.

Fourier active appearance models

Gaining invariance to camera and illumination variations has been a well investigated topic in Active Appearance Model (AAM) fitting literature. The major problem lies in the inability of the appearance parameters of the AAM to generalize to unseen conditions. An attractive approach for gaining invariance is to fit an AAM to a multiple filter response (e.g. Gabor) representation of the input image. Naively applying this concept with a traditional AAM is computationally prohibitive, especially as the number of filter responses increase. In this paper, we present a computationally efficient AAM fitting algorithm based on the Lucas-Kanade (LK) algorithm posed in the Fourier domain that affords invariance to both expression and illumination. We refer to this as a Fourier AAM (FAAM), and show that this method gives substantial improvement in person specific AAM fitting performance over traditional AAM fitting methods.