A Monte-Carlo tree search in argumentation

Monte-Carlo Tree Search (MCTS) is a heuristic to search in large trees. We apply it to argumentative puzzles where MCTS pursues the best argumentation with respect to a set of arguments to be argued. To make our ideas as widely applicable as possible, we integrate MCTS to an abstract setting for argumentation where the content of arguments is left unspecified. Experimental results show the pertinence of this integration for learning argumentations by comparing it with a basic reinforcement learning.

Monte Carlo analysis of a puzzle game

When a puzzle game is created, its design parameters must be chosen to allow solvable and interesting challenges to be created for the player. We investigate the use of random sampling as a computationally inexpensive means of automated game analysis, to evaluate the BoxOff family of puzzle games. This analysis reveals useful insights into the game, such as the surprising fact that almost 100% of randomly generated challenges have a solution, but less than 10% will be solved using strictly random play, validating the inventor’s design choices. We show the 1D game to be trivial and the 3D game to be viable.

Modeling dynamic demand response using Monte Carlo simulation and interval mathematics for boundary estimation

With the rapid development of various technologies and applications in smart grid implementation, demand response has attracted growing research interests because of its potentials in enhancing power grid reliability with reduced system operation costs. This paper presents a new demand response model with elastic economic dispatch in a locational marginal pricing market. It models system economic dispatch as a feedback control process, and introduces a flexible and adjustable load cost as a controlled signal to adjust demand response. Compared with the conventional “one time use” static load dispatch model, this dynamic feedback demand response model may adjust the load to a desired level in a finite number of time steps and a proof of convergence is provided. In addition, Monte Carlo simulation and boundary calculation using interval mathematics are applied for describing uncertainty of end-user's response to an independent system operator's expected dispatch. A numerical analysis based on the modified Pennsylvania-Jersey-Maryland power pool five-bus system is introduced for simulation and the results verify the effectiveness of the proposed model. System operators may use the proposed model to obtain insights in demand response processes for their decision-making regarding system load levels and operation conditions.

Bayesian model comparison in cosmology with Population Monte Carlo

We use Bayesian model selection techniques to test extensions of the standard flat LambdaCDM paradigm. Dark-energy and curvature scenarios, and primordial perturbation models are considered. To that end, we calculate the Bayesian evidence in favour of each model using Population Monte Carlo (PMC), a new adaptive sampling technique which was recently applied in a cosmological context. The Bayesian evidence is immediately available from the PMC sample used for parameter estimation without further computational effort, and it comes with an associated error evaluation. Besides, it provides an unbiased estimator of the evidence after any fixed number of iterations and it is naturally parallelizable, in contrast with MCMC and nested sampling methods. By comparison with analytical predictions for simulated data, we show that our results obtained with PMC are reliable and robust. The variability in the evidence evaluation and the stability for various cases are estimated both from simulations and from data. For the cases we consider, the log-evidence is calculated with a precision of better than 0.08. Using a combined set of recent CMB, SNIa and BAO data, we find inconclusive evidence between flat LambdaCDM and simple dark-energy models. A curved Universe is moderately to strongly disfavoured with respect to a flat cosmology. Using physically well-motivated priors within the slow-roll approximation of inflation, we find a weak preference for a running spectral index. A Harrison-Zel'dovich spectrum is weakly disfavoured. With the current data, tensor modes are not detected; the large prior volume on the tensor-to-scalar ratio r results in moderate evidence in favour of r=0.

Evaluating Specification Tests for Markov-Switching Time-Series Models

We evaluate the performance of several specification tests for Markov regime-switching time-series models. We consider the Lagrange multiplier (LM) and dynamic specification tests of Hamilton (1996) and Ljung–Box tests based on both the generalized residual and a standard-normal residual constructed using the Rosenblatt transformation. The size and power of the tests are studied using Monte Carlo experiments. We find that the LM tests have the best size and power properties. The Ljung–Box tests exhibit slight size distortions, though tests based on the Rosenblatt transformation perform better than the generalized residual-based tests. The tests exhibit impressive power to detect both autocorrelation and autoregressive conditional heteroscedasticity (ARCH). The tests are illustrated with a Markov-switching generalized ARCH (GARCH) model fitted to the US dollar–British pound exchange rate, with the finding that both autocorrelation and GARCH effects are needed to adequately fit the data.

A hidden Markov model and relative entropy rate approach to vision-based dim target detection for UAV sense-and-avoid

Uninhabited aerial vehicles (UAVs) are a cutting-edge technology that is at the forefront of aviation/aerospace research and development worldwide. Many consider their current military and defence applications as just a token of their enormous potential. Unlocking and fully exploiting this potential will see UAVs in a multitude of civilian applications and routinely operating alongside piloted aircraft. The key to realising the full potential of UAVs lies in addressing a host of regulatory, public relation, and technological challenges never encountered be- fore. Aircraft collision avoidance is considered to be one of the most important issues to be addressed, given its safety critical nature. The collision avoidance problem can be roughly organised into three areas: 1) Sense; 2) Detect; and 3) Avoid. Sensing is concerned with obtaining accurate and reliable information about other aircraft in the air; detection involves identifying potential collision threats based on available information; avoidance deals with the formulation and execution of appropriate manoeuvres to maintain safe separation. This thesis tackles the detection aspect of collision avoidance, via the development of a target detection algorithm that is capable of real-time operation onboard a UAV platform. One of the key challenges of the detection problem is the need to provide early warning. This translates to detecting potential threats whilst they are still far away, when their presence is likely to be obscured and hidden by noise. Another important consideration is the choice of sensors to capture target information, which has implications for the design and practical implementation of the detection algorithm. The main contributions of the thesis are: 1) the proposal of a dim target detection algorithm combining image morphology and hidden Markov model (HMM) filtering approaches; 2) the novel use of relative entropy rate (RER) concepts for HMM filter design; 3) the characterisation of algorithm detection performance based on simulated data as well as real in-flight target image data; and 4) the demonstration of the proposed algorithm's capacity for real-time target detection. We also consider the extension of HMM filtering techniques and the application of RER concepts for target heading angle estimation. In this thesis we propose a computer-vision based detection solution, due to the commercial-off-the-shelf (COTS) availability of camera hardware and the hardware's relatively low cost, power, and size requirements. The proposed target detection algorithm adopts a two-stage processing paradigm that begins with an image enhancement pre-processing stage followed by a track-before-detect (TBD) temporal processing stage that has been shown to be effective in dim target detection. We compare the performance of two candidate morphological filters for the image pre-processing stage, and propose a multiple hidden Markov model (MHMM) filter for the TBD temporal processing stage. The role of the morphological pre-processing stage is to exploit the spatial features of potential collision threats, while the MHMM filter serves to exploit the temporal characteristics or dynamics. The problem of optimising our proposed MHMM filter has been examined in detail. Our investigation has produced a novel design process for the MHMM filter that exploits information theory and entropy related concepts. The filter design process is posed as a mini-max optimisation problem based on a joint RER cost criterion. We provide proof that this joint RER cost criterion provides a bound on the conditional mean estimate (CME) performance of our MHMM filter, and this in turn establishes a strong theoretical basis connecting our filter design process to filter performance. Through this connection we can intelligently compare and optimise candidate filter models at the design stage, rather than having to resort to time consuming Monte Carlo simulations to gauge the relative performance of candidate designs. Moreover, the underlying entropy concepts are not constrained to any particular model type. This suggests that the RER concepts established here may be generalised to provide a useful design criterion for multiple model filtering approaches outside the class of HMM filters. In this thesis we also evaluate the performance of our proposed target detection algorithm under realistic operation conditions, and give consideration to the practical deployment of the detection algorithm onboard a UAV platform. Two fixed-wing UAVs were engaged to recreate various collision-course scenarios to capture highly realistic vision (from an onboard camera perspective) of the moments leading up to a collision. Based on this collected data, our proposed detection approach was able to detect targets out to distances ranging from about 400m to 900m. These distances, (with some assumptions about closing speeds and aircraft trajectories) translate to an advanced warning ahead of impact that approaches the 12.5 second response time recommended for human pilots. Furthermore, readily available graphic processing unit (GPU) based hardware is exploited for its parallel computing capabilities to demonstrate the practical feasibility of the proposed target detection algorithm. A prototype hardware-in- the-loop system has been found to be capable of achieving data processing rates sufficient for real-time operation. There is also scope for further improvement in performance through code optimisations. Overall, our proposed image-based target detection algorithm offers UAVs a cost-effective real-time target detection capability that is a step forward in ad- dressing the collision avoidance issue that is currently one of the most significant obstacles preventing widespread civilian applications of uninhabited aircraft. We also highlight that the algorithm development process has led to the discovery of a powerful multiple HMM filtering approach and a novel RER-based multiple filter design process. The utility of our multiple HMM filtering approach and RER concepts, however, extend beyond the target detection problem. This is demonstrated by our application of HMM filters and RER concepts to a heading angle estimation problem.

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.

Maintenance strategy optimization using a continuous-state partially observable semi-Markov decision process

Due to the limitation of current condition monitoring technologies, the estimates of asset health states may contain some uncertainties. A maintenance strategy ignoring this uncertainty of asset health state can cause additional costs or downtime. The partially observable Markov decision process (POMDP) is a commonly used approach to derive optimal maintenance strategies when asset health inspections are imperfect. However, existing applications of the POMDP to maintenance decision-making largely adopt the discrete time and state assumptions. The discrete-time assumption requires the health state transitions and maintenance activities only happen at discrete epochs, which cannot model the failure time accurately and is not cost-effective. The discrete health state assumption, on the other hand, may not be elaborate enough to improve the effectiveness of maintenance. To address these limitations, this paper proposes a continuous state partially observable semi-Markov decision process (POSMDP). An algorithm that combines the Monte Carlo-based density projection method and the policy iteration is developed to solve the POSMDP. Different types of maintenance activities (i.e., inspections, replacement, and imperfect maintenance) are considered in this paper. The next maintenance action and the corresponding waiting durations are optimized jointly to minimize the long-run expected cost per unit time and availability. The result of simulation studies shows that the proposed maintenance optimization approach is more cost-effective than maintenance strategies derived by another two approximate methods, when regular inspection intervals are adopted. The simulation study also shows that the maintenance cost can be further reduced by developing maintenance strategies with state-dependent maintenance intervals using the POSMDP. In addition, during the simulation studies the proposed POSMDP shows the ability to adopt a cost-effective strategy structure when multiple types of maintenance activities are involved.

A fully Bayesian approach to inference for Coxian phase-type distributions with covariate dependent mean

Phase-type distributions represent the time to absorption for a finite state Markov chain in continuous time, generalising the exponential distribution and providing a flexible and useful modelling tool. We present a new reversible jump Markov chain Monte Carlo scheme for performing a fully Bayesian analysis of the popular Coxian subclass of phase-type models; the convenient Coxian representation involves fewer parameters than a more general phase-type model. The key novelty of our approach is that we model covariate dependence in the mean whilst using the Coxian phase-type model as a very general residual distribution. Such incorporation of covariates into the model has not previously been attempted in the Bayesian literature. A further novelty is that we also propose a reversible jump scheme for investigating structural changes to the model brought about by the introduction of Erlang phases. Our approach addresses more questions of inference than previous Bayesian treatments of this model and is automatic in nature. We analyse an example dataset comprising lengths of hospital stays of a sample of patients collected from two Australian hospitals to produce a model for a patient's expected length of stay which incorporates the effects of several covariates. This leads to interesting conclusions about what contributes to length of hospital stay with implications for hospital planning. We compare our results with an alternative classical analysis of these data.