Multitask learning with expert advice

We consider the problem of prediction with expert advice in the setting where a forecaster is presented with several online prediction tasks. Instead of competing against the best expert separately on each task, we assume the tasks are related, and thus we expect that a few experts will perform well on the entire set of tasks. That is, our forecaster would like, on each task, to compete against the best expert chosen from a small set of experts. While we describe the "ideal" algorithm and its performance bound, we show that the computation required for this algorithm is as hard as computation of a matrix permanent. We present an efficient algorithm based on mixing priors, and prove a bound that is nearly as good for the sequential task presentation case. We also consider a harder case where the task may change arbitrarily from round to round, and we develop an efficient approximate randomized algorithm based on Markov chain Monte Carlo techniques.

Stochastic simulation of chemical reactions in spatially complex media

Discrete stochastic simulations, via techniques such as the Stochastic Simulation Algorithm (SSA) are a powerful tool for understanding the dynamics of chemical kinetics when there are low numbers of certain molecular species. However, an important constraint is the assumption of well-mixedness and homogeneity. In this paper, we show how to use Monte Carlo simulations to estimate an anomalous diffusion parameter that encapsulates the crowdedness of the spatial environment. We then use this parameter to replace the rate constants of bimolecular reactions by a time-dependent power law to produce an SSA valid in cases where anomalous diffusion occurs or the system is not well-mixed (ASSA). Simulations then show that ASSA can successfully predict the temporal dynamics of chemical kinetics in a spatially constrained environment.

Stochastic simulation for spatial modelling of dynamic process in a living cell

One of the fundamental motivations underlying computational cell biology is to gain insight into the complicated dynamical processes taking place, for example, on the plasma membrane or in the cytosol of a cell. These processes are often so complicated that purely temporal mathematical models cannot adequately capture the complex chemical kinetics and transport processes of, for example, proteins or vesicles. On the other hand, spatial models such as Monte Carlo approaches can have very large computational overheads. This chapter gives an overview of the state of the art in the development of stochastic simulation techniques for the spatial modelling of dynamic processes in a living cell.

LMP estimation considering the uncertainty of wind power

One of the impediments to large-scale use of wind generation within power system is its variable and uncertain real-time availability. Due to the low marginal cost of wind power, its output will change the merit order of power markets and influence the Locational Marginal Price (LMP). For the large scale of wind power, LMP calculation can't ignore the essential variable and uncertain nature of wind power. This paper proposes an algorithm to estimate LMP. The estimation result of conventional Monte Carlo simulation is taken as benchmark to examine accuracy. Case study is conducted on a simplified SE Australian power system, and the simulation results show the feasibility of proposed method.

Optimal sitting and sizing of distributed generators considering plug-in electric vehicles

Some uncertainties such as the stochastic input/output power of a plug-in electric vehicle due to its stochastic charging and discharging schedule, that of a wind unit and that of a photovoltaic generation source, volatile fuel prices and future uncertain load growth, all together could lead to some risks in determining the optimal siting and sizing of distributed generators (DGs) in distributed systems. Given this background, under the chance constrained programming (CCP) framework, a new method is presented to handle these uncertainties in the optimal sitting and sizing problem of DGs. First, a mathematical model of CCP is developed with the minimization of DGs investment cost, operational cost and maintenance cost as well as the network loss cost as the objective, security limitations as constraints, the sitting and sizing of DGs as optimization variables. Then, a Monte Carolo simulation embedded genetic algorithm approach is developed to solve the developed CCP model. Finally, the IEEE 37-node test feeder is employed to verify the feasibility and effectiveness of the developed model and method. This work is supported by an Australian Commonwealth Scientific and Industrial Research Organisation (CSIRO) Project on Intelligent Grids Under the Energy Transformed Flagship, and Project from Jiangxi Power Company.

Bayesian hierarchical models in statistical quality control methods to improve healthcare in hospitals

Quality oriented management systems and methods have become the dominant business and governance paradigm. From this perspective, satisfying customers’ expectations by supplying reliable, good quality products and services is the key factor for an organization and even government. During recent decades, Statistical Quality Control (SQC) methods have been developed as the technical core of quality management and continuous improvement philosophy and now are being applied widely to improve the quality of products and services in industrial and business sectors. Recently SQC tools, in particular quality control charts, have been used in healthcare surveillance. In some cases, these tools have been modified and developed to better suit the health sector characteristics and needs. It seems that some of the work in the healthcare area has evolved independently of the development of industrial statistical process control methods. Therefore analysing and comparing paradigms and the characteristics of quality control charts and techniques across the different sectors presents some opportunities for transferring knowledge and future development in each sectors. Meanwhile considering capabilities of Bayesian approach particularly Bayesian hierarchical models and computational techniques in which all uncertainty are expressed as a structure of probability, facilitates decision making and cost-effectiveness analyses. Therefore, this research investigates the use of quality improvement cycle in a health vii setting using clinical data from a hospital. The need of clinical data for monitoring purposes is investigated in two aspects. A framework and appropriate tools from the industrial context are proposed and applied to evaluate and improve data quality in available datasets and data flow; then a data capturing algorithm using Bayesian decision making methods is developed to determine economical sample size for statistical analyses within the quality improvement cycle. Following ensuring clinical data quality, some characteristics of control charts in the health context including the necessity of monitoring attribute data and correlated quality characteristics are considered. To this end, multivariate control charts from an industrial context are adapted to monitor radiation delivered to patients undergoing diagnostic coronary angiogram and various risk-adjusted control charts are constructed and investigated in monitoring binary outcomes of clinical interventions as well as postintervention survival time. Meanwhile, adoption of a Bayesian approach is proposed as a new framework in estimation of change point following control chart’s signal. This estimate aims to facilitate root causes efforts in quality improvement cycle since it cuts the search for the potential causes of detected changes to a tighter time-frame prior to the signal. This approach enables us to obtain highly informative estimates for change point parameters since probability distribution based results are obtained. Using Bayesian hierarchical models and Markov chain Monte Carlo computational methods, Bayesian estimators of the time and the magnitude of various change scenarios including step change, linear trend and multiple change in a Poisson process are developed and investigated. The benefits of change point investigation is revisited and promoted in monitoring hospital outcomes where the developed Bayesian estimator reports the true time of the shifts, compared to priori known causes, detected by control charts in monitoring rate of excess usage of blood products and major adverse events during and after cardiac surgery in a local hospital. The development of the Bayesian change point estimators are then followed in a healthcare surveillances for processes in which pre-intervention characteristics of patients are viii affecting the outcomes. In this setting, at first, the Bayesian estimator is extended to capture the patient mix, covariates, through risk models underlying risk-adjusted control charts. Variations of the estimator are developed to estimate the true time of step changes and linear trends in odds ratio of intensive care unit outcomes in a local hospital. Secondly, the Bayesian estimator is extended to identify the time of a shift in mean survival time after a clinical intervention which is being monitored by riskadjusted survival time control charts. In this context, the survival time after a clinical intervention is also affected by patient mix and the survival function is constructed using survival prediction model. The simulation study undertaken in each research component and obtained results highly recommend the developed Bayesian estimators as a strong alternative in change point estimation within quality improvement cycle in healthcare surveillances as well as industrial and business contexts. The superiority of the proposed Bayesian framework and estimators are enhanced when probability quantification, flexibility and generalizability of the developed model are also considered. The empirical results and simulations indicate that the Bayesian estimators are a strong alternative in change point estimation within quality improvement cycle in healthcare surveillances. The superiority of the proposed Bayesian framework and estimators are enhanced when probability quantification, flexibility and generalizability of the developed model are also considered. The advantages of the Bayesian approach seen in general context of quality control may also be extended in the industrial and business domains where quality monitoring was initially developed.

Bayesian experimental design for models with intractable likelihoods

In this paper we present a methodology for designing experiments for efficiently estimating the parameters of models with computationally intractable likelihoods. The approach combines a commonly used methodology for robust experimental design, based on Markov chain Monte Carlo sampling, with approximate Bayesian computation (ABC) to ensure that no likelihood evaluations are required. The utility function considered for precise parameter estimation is based upon the precision of the ABC posterior distribution, which we form efficiently via the ABC rejection algorithm based on pre-computed model simulations. Our focus is on stochastic models and, in particular, we investigate the methodology for Markov process models of epidemics and macroparasite population evolution. The macroparasite example involves a multivariate process and we assess the loss of information from not observing all variables.

Bayesian algorithms with applications

Advances in algorithms for approximate sampling from a multivariable target function have led to solutions to challenging statistical inference problems that would otherwise not be considered by the applied scientist. Such sampling algorithms are particularly relevant to Bayesian statistics, since the target function is the posterior distribution of the unobservables given the observables. In this thesis we develop, adapt and apply Bayesian algorithms, whilst addressing substantive applied problems in biology and medicine as well as other applications. For an increasing number of high-impact research problems, the primary models of interest are often sufficiently complex that the likelihood function is computationally intractable. Rather than discard these models in favour of inferior alternatives, a class of Bayesian "likelihoodfree" techniques (often termed approximate Bayesian computation (ABC)) has emerged in the last few years, which avoids direct likelihood computation through repeated sampling of data from the model and comparing observed and simulated summary statistics. In Part I of this thesis we utilise sequential Monte Carlo (SMC) methodology to develop new algorithms for ABC that are more efficient in terms of the number of model simulations required and are almost black-box since very little algorithmic tuning is required. In addition, we address the issue of deriving appropriate summary statistics to use within ABC via a goodness-of-fit statistic and indirect inference. Another important problem in statistics is the design of experiments. That is, how one should select the values of the controllable variables in order to achieve some design goal. The presences of parameter and/or model uncertainty are computational obstacles when designing experiments but can lead to inefficient designs if not accounted for correctly. The Bayesian framework accommodates such uncertainties in a coherent way. If the amount of uncertainty is substantial, it can be of interest to perform adaptive designs in order to accrue information to make better decisions about future design points. This is of particular interest if the data can be collected sequentially. In a sense, the current posterior distribution becomes the new prior distribution for the next design decision. Part II of this thesis creates new algorithms for Bayesian sequential design to accommodate parameter and model uncertainty using SMC. The algorithms are substantially faster than previous approaches allowing the simulation properties of various design utilities to be investigated in a more timely manner. Furthermore the approach offers convenient estimation of Bayesian utilities and other quantities that are particularly relevant in the presence of model uncertainty. Finally, Part III of this thesis tackles a substantive medical problem. A neurological disorder known as motor neuron disease (MND) progressively causes motor neurons to no longer have the ability to innervate the muscle fibres, causing the muscles to eventually waste away. When this occurs the motor unit effectively ‘dies’. There is no cure for MND, and fatality often results from a lack of muscle strength to breathe. The prognosis for many forms of MND (particularly amyotrophic lateral sclerosis (ALS)) is particularly poor, with patients usually only surviving a small number of years after the initial onset of disease. Measuring the progress of diseases of the motor units, such as ALS, is a challenge for clinical neurologists. Motor unit number estimation (MUNE) is an attempt to directly assess underlying motor unit loss rather than indirect techniques such as muscle strength assessment, which generally is unable to detect progressions due to the body’s natural attempts at compensation. Part III of this thesis builds upon a previous Bayesian technique, which develops a sophisticated statistical model that takes into account physiological information about motor unit activation and various sources of uncertainties. More specifically, we develop a more reliable MUNE method by applying marginalisation over latent variables in order to improve the performance of a previously developed reversible jump Markov chain Monte Carlo sampler. We make other subtle changes to the model and algorithm to improve the robustness of the approach.

On the statistical determination of optimal camera configurations in large scale surveillance networks

The selection of optimal camera configurations (camera locations, orientations etc.) for multi-camera networks remains an unsolved problem. Previous approaches largely focus on proposing various objective functions to achieve different tasks. Most of them, however, do not generalize well to large scale networks. To tackle this, we introduce a statistical formulation of the optimal selection of camera configurations as well as propose a Trans-Dimensional Simulated Annealing (TDSA) algorithm to effectively solve the problem. We compare our approach with a state-of-the-art method based on Binary Integer Programming (BIP) and show that our approach offers similar performance on small scale problems. However, we also demonstrate the capability of our approach in dealing with large scale problems and show that our approach produces better results than 2 alternative heuristics designed to deal with the scalability issue of BIP.

Exact and approximate Bayesian inference for low count time series models with intractable likelihoods

In this paper we present a new simulation methodology in order to obtain exact or approximate Bayesian inference for models for low-valued count time series data that have computationally demanding likelihood functions. The algorithm fits within the framework of particle Markov chain Monte Carlo (PMCMC) methods. The particle filter requires only model simulations and, in this regard, our approach has connections with approximate Bayesian computation (ABC). However, an advantage of using the PMCMC approach in this setting is that simulated data can be matched with data observed one-at-a-time, rather than attempting to match on the full dataset simultaneously or on a low-dimensional non-sufficient summary statistic, which is common practice in ABC. For low-valued count time series data we find that it is often computationally feasible to match simulated data with observed data exactly. Our particle filter maintains $N$ particles by repeating the simulation until $N+1$ exact matches are obtained. Our algorithm creates an unbiased estimate of the likelihood, resulting in exact posterior inferences when included in an MCMC algorithm. In cases where exact matching is computationally prohibitive, a tolerance is introduced as per ABC. A novel aspect of our approach is that we introduce auxiliary variables into our particle filter so that partially observed and/or non-Markovian models can be accommodated. We demonstrate that Bayesian model choice problems can be easily handled in this framework.

Coordinated probabilistic optimal decision-making model for multi-area ATC with risk control

In the decision-making of multi-area ATC (Available Transfer Capacity) in electricity market environment, the existing resources of transmission network should be optimally dispatched and coordinately employed on the premise that the secure system operation is maintained and risk associated is controllable. The non-sequential Monte Carlo simulation is used to determine the ATC probability density distribution of specified areas under the influence of several uncertainty factors, based on which, a coordinated probabilistic optimal decision-making model with the maximal risk benefit as its objective is developed for multi-area ATC. The NSGA-II is applied to calculate the ATC of each area, which considers the risk cost caused by relevant uncertainty factors and the synchronous coordination among areas. The essential characteristics of the developed model and the employed algorithm are illustrated by the example of IEEE 118-bus test system. Simulative result shows that, the risk of multi-area ATC decision-making is influenced by the uncertainties in power system operation and the relative importance degrees of different areas.

Pseudo-marginal algorithms with multiple CPUs

The emergence of pseudo-marginal algorithms has led to improved computational efficiency for dealing with complex Bayesian models with latent variables. Here an unbiased estimator of the likelihood replaces the true likelihood in order to produce a Bayesian algorithm that remains on the marginal space of the model parameter (with latent variables integrated out), with a target distribution that is still the correct posterior distribution. Very efficient proposal distributions can be developed on the marginal space relative to the joint space of model parameter and latent variables. Thus psuedo-marginal algorithms tend to have substantially better mixing properties. However, for pseudo-marginal approaches to perform well, the likelihood has to be estimated rather precisely. This can be difficult to achieve in complex applications. In this paper we propose to take advantage of multiple central processing units (CPUs), that are readily available on most standard desktop computers. Here the likelihood is estimated independently on the multiple CPUs, with the ultimate estimate of the likelihood being the average of the estimates obtained from the multiple CPUs. The estimate remains unbiased, but the variability is reduced. We compare and contrast two different technologies that allow the implementation of this idea, both of which require a negligible amount of extra programming effort. The superior performance of this idea over the standard approach is demonstrated on simulated data from a stochastic volatility model.

A multi-objective optimization approach for coordinating available transfer capability with risk control

In the electricity market environment, coordination of system reliability and economics of a power system is of great significance in determining the available transfer capability (ATC). In addition, the risks associated with uncertainties should be properly addressed in the ATC determination process for risk-benefit maximization. Against this background, it is necessary that the ATC be optimally allocated and utilized within relative security constraints. First of all, the non-sequential Monte Carlo stimulation is employed to derive the probability density distribution of ATC of designated areas incorporating uncertainty factors. Second, on the basis of that, a multi-objective optimization model is formulated to determine the multi-area ATC so as to maximize the risk-benefits. Then, the solution to the developed model is achieved by the fast non-dominated sorting (NSGA-II) algorithm, which could decrease the risk caused by uncertainties while coordinating the ATCs of different areas. Finally, the IEEE 118-bus test system is served for demonstrating the essential features of the developed model and employed algorithm.

Optimal camera planning under versatile user constraints in multi-camera image processing systems

The selection of optimal camera configurations (camera locations, orientations, etc.) for multi-camera networks remains an unsolved problem. Previous approaches largely focus on proposing various objective functions to achieve different tasks. Most of them, however, do not generalize well to large scale networks. To tackle this, we propose a statistical framework of the problem as well as propose a trans-dimensional simulated annealing algorithm to effectively deal with it. We compare our approach with a state-of-the-art method based on binary integer programming (BIP) and show that our approach offers similar performance on small scale problems. However, we also demonstrate the capability of our approach in dealing with large scale problems and show that our approach produces better results than two alternative heuristics designed to deal with the scalability issue of BIP. Last, we show the versatility of our approach using a number of specific scenarios.