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Bayesian methods are revolutionising computing science and engineering and are fast becoming the lingua franca for modelling scientific, engineering and business problems involving uncertainty. Applications in a wide variety of areas are blossoming: speech recognition, automated vision, information retrieval, sensor fusion, system filtering, fault diagnosis, medical diagnosis, bioinformatics, financial risk management, etc. The investigators have been involved in applications of Bayesian techniques for AI, expert systems, quality control and risk analysis [13, 14, 15]. Much of this work has used Bayesian Networks (BNs), which are graphical models that represent complex causal relationships between uncertain variables [34]. BN algorithms enable rigorous Bayesian inference across these variables. Developments in the last fifteen years of computationally intensive methods have increased the popularity of the Bayesian paradigm in academia.Yet, despite all these great strides, Bayesian modelling has failed to cross the chasm and become a mainstream technology usable by non-specialists for everyday modelling problems. .One of the main barriers to applying Bayesian methods more widely in business and industry is the lack of general-purpose tools and algorithms that allow non-specialists to conduct statistical inference and modelling on complex real-world problems. Designing, implementing and applying Bayesian statistics and probabilistic models using current tools and technology is a challenging and sometimes daunting task. These challenges are rooted in a number of interrelated and overlapping problems:1. Most of the available tools for Bayesian inference on complex stochastic models, such as the popular WinBUGS software package, are based on intensive sampling algorithms collectively known as Markov Chain Monte Carlo (MCMC) methods. These methods require drawing tens of thousands of dependent samples from, usually, high dimensional probability distributions [16]. To obtain reliable results these tools rely on expert knowledge to calibrate the tool according to the model and data set and to monitor the outputs to ensure the model converges to a stable solution.2. In many real-world applications it is fundamental to be able to monitor the evolution of a complex situation over time, reliably detect abnormal behaviour and diagnose failure modes. Current methods to perform 'online' inference or to monitor stochastic dynamic systems are based on simulation methods known as particle filters [17], which again also rely on a high level of statistical knowledge and suffer from similar problems as MCMC.3. Most real-world applications involve continuous quantities as well as discrete ones. Models that contain both continuous and discrete variables are called hybrid. Currently, tools supporting universal inference in hybrid models are not available. Where easy-to-use graphical tools are available, in the form of BNs, the incorporation of continuous variables and inference from large data sets is near impossible [18].Recently, we have made advances in applying Bayesian inference of a new powerful computational algorithm based on dynamic discretisation. This work has extended the capability and applicability of hybrid Bayesian networks to capture complex Bayesian statistical modelling and data analysis techniques, such as hierarchical mixture modelling and time series analysis, and it represents a potentially viable alternative to MCMC approaches [16]. We believe this work can form the basis of a crucial breakthrough in tackling the deeply rooted problems described above.Hence, the project name / DyFUSION / reflects our twin goals of dynamic fusion of data/judgement and the diffusion of Bayesian methods from academia to commerce and industry.
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