Bayesian Inference for Complex Systems

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Data processing is ubiquitous across society. Of course, data may contain errors or may have only a certain degree of accuracy. For data processing to be trustworthy, it is vital to quantify such uncertainties, to understand the ways in which cumulative accretion of uncertainty can breach uncertainty thresholds, and to devise ways to efficiently inject greater levels of certainty into uncertain systems. The basic contours of this problem fall within Bayesian Inference but solutions often are difficult to scale to large complex systems. We propose a new approach which is compositional in that we conduct Bayesian Inference on large complex systems by combining inference on the smaller - and hence easier to model and reason about - subsystems. This supports reuse - eg small changes to particular components in a system only require small changes to generate revised uncertainty predictions. A key distinctive advantage is that our models of Bayesian Inference are computational in that the model automatically supports code extraction. This distinguishes our approach from many others which stop before the production of software. Applying compositionality to the underpinning computational dynamics is highly novel and likely to produce new forms of structured computation of uncertainty bringing reuse to our model and our code. Ultimately, this creates a library of well-behaved components for constructing bespoke systems with lower costs for uncertainty quantification.