Transdimensional sequential Monte Carlo using variational Bayes — SMCVB

A new transdimensional Sequential Monte Carlo (SMC) algorithm called SM- CVB is proposed. In an SMC approach, a weighted sample of particles is generated from a sequence of probability distributions which ‘converge’ to the target distribution of interest, in this case a Bayesian posterior distri- bution. The approach is based on the use of variational Bayes to propose new particles at each iteration of the SMCVB algorithm in order to target the posterior more efficiently. The variational-Bayes-generated proposals are not limited to a fixed dimension. This means that the weighted particle sets that arise can have varying dimensions thereby allowing us the option to also estimate an appropriate dimension for the model. This novel algorithm is outlined within the context of finite mixture model estimation. This pro- vides a less computationally demanding alternative to using reversible jump Markov chain Monte Carlo kernels within an SMC approach. We illustrate these ideas in a simulated data analysis and in applications.

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.

Property cash flow studies : focusing on model consistency and data accuracy

The high degree of variability and inconsistency in cash flow study usage by property professionals demands improvement in knowledge and processes. Until recently limited research was being undertaken on the use of cash flow studies in property valuations but the growing acceptance of this approach for major investment valuations has resulted in renewed interest in this topic. Studies on valuation variations identify data accuracy, model consistency and bias as major concerns. In cash flow studies there are practical problems with the input data and the consistency of the models. This study will refer to the recent literature and identify the major factors in model inconsistency and data selection. A detailed case study will be used to examine the effects of changes in structure and inputs. The key variable inputs will be identified and proposals developed to improve the selection process for these key variables. The variables will be selected with the aid of sensitivity studies and alternative ways of quantifying the key variables explained. The paper recommends, with reservations, the use of probability profiles of the variables and the incorporation of this data in simulation exercises. The use of Monte Carlo simulation is demonstrated and the factors influencing the structure of the probability distributions of the key variables are outline. This study relates to ongoing research into functional performance of commercial property within an Australian Cooperative Research Centre.

Whole of life cycle cost analysis in bridge rehabilitation

The report presents a methodology for whole of life cycle cost analysis of alternative treatment options for bridge structures, which require rehabilitation. The methodology has been developed after a review of current methods and establishing that a life cycle analysis based on a probabilistic risk approach has many advantages including the essential ability to consider variability of input parameters. The input parameters for the analysis are identified as initial cost, maintenance, monitoring and repair cost, user cost and failure cost. The methodology utilizes the advanced simulation technique of Monte Carlo simulation to combine a number of probability distributions to establish the distribution of whole of life cycle cost. In performing the simulation, the need for a powerful software package, which would work with spreadsheet program, has been identified. After exploring several products on the market, @RISK software has been selected for the simulation. In conclusion, the report presents a typical decision making scenario considering two alternative treatment options.

Identification of critical input variables for risk-based cost estimates for road maintenance and rehabilitation

An estimation of costs for maintenance and rehabilitation is subject to variation due to the uncertainties of input parameters. This paper presents the results of an analysis to identify input parameters that affect the prediction of variation in road deterioration. Road data obtained from 1688 km of a national highway located in the tropical northeast of Queensland in Australia were used in the analysis. Data were analysed using a probability-based method, the Monte Carlo simulation technique and HDM-4’s roughness prediction model. The results of the analysis indicated that among the input parameters the variability of pavement strength, rut depth, annual equivalent axle load and initial roughness affected the variability of the predicted roughness. The second part of the paper presents an analysis to assess the variation in cost estimates due to the variability of the overall identified critical input parameters.

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.

CTCombine : rotating and combining CT data with an accurate detector model, to simulate radiotherapy portal imaging at non-zero beam angles

Established Monte Carlo user codes BEAMnrc and DOSXYZnrc permit the accurate and straightforward simulation of radiotherapy experiments and treatments delivered from multiple beam angles. However, when an electronic portal imaging detector (EPID) is included in these simulations, treatment delivery from non-zero beam angles becomes problematic. This study introduces CTCombine, a purpose-built code for rotating selected CT data volumes, converting CT numbers to mass densities, combining the results with model EPIDs and writing output in a form which can easily be read and used by the dose calculation code DOSXYZnrc. The geometric and dosimetric accuracy of CTCombine’s output has been assessed by simulating simple and complex treatments applied to a rotated planar phantom and a rotated humanoid phantom and comparing the resulting virtual EPID images with the images acquired using experimental measurements and independent simulations of equivalent phantoms. It is expected that CTCombine will be useful for Monte Carlo studies of EPID dosimetry as well as other EPID imaging applications.

Reliability driven reconfiguration of rural power distribution systems

This paper presents a reliability-based reconfiguration methodology for power distribution systems. Probabilistic reliability models of the system components are considered and Monte Carlo method is used while evaluating the reliability of the distribution system. The reconfiguration is aimed at maximizing the reliability of the power supplied to the customers. A binary particle swarm optimization (BPSO) algorithm is used as a tool to determine the optimal configuration of the sectionalizing and tie switches in the system. The proposed methodology is applied on a modified IEEE 13-bus distribution system.