Bayesian decision support for complex systems with many distributed experts

Abstract

Complex decision support systems often consist of component modules which, encoding the judgements of panels of domain experts, describe a particular sub-domain of the overall system. Ideally these modules need to be pasted together to provide a comprehensive picture of the whole process. The challenge of building such an integrated system is that, whilst the overall qualitative features are common knowledge to all, the explicit forecasts and their associated uncertainties are only expressed individually by each panel, resulting from its own analysis. The structure of the integrated system therefore needs to facilitate the coherent piecing together of these separate evaluations. If such a system is not available there is a serious danger that this might drive decision makers to incoherent and so indefensible policy choices. In this paper we develop a graphically based framework which embeds a set of conditions, consisting of the agreement usually made in practice of certain probability and utility models, that, if satisfied in a given context, are sufficient to ensure the composite system is truly coherent. Furthermore, we develop new message passing algorithms entailing the transmission of expected utility scores between the panels, that enable the uncertainties within each module to be fully accounted for in the evaluation of the available alternatives in these composite systems.

A Bayesian Hierarchical Model for Criminal Investigations

“…In other settings e.g. [22] we have been able to prove how a Bayesian integrating decision support system (IDSS) can be built to harmonise and draw evidential strength by coherently combining these sources. Current work is now focusing on developing such integrated systems for policing violent crimes.…”

Joining and Splitting Models with Markov Melding

“…Alternatively, as we outline in Supplementary Material F, we could assume that the priors differ only due to different scalings in each submodel, and so can be made consistent through rescaling, similar to when deriving multivariate distributions from copulas (Durante and Sempi, 2010). Yet another approach is a supra-Bayesian approach (Lindley et al, 1979; Leonelli, 2015), in which the decision maker models the experts’ opinions.…”

A symbolic algebra for the computation of expected utilities in multiplicative influence diagrams

“…However, there are ways around this memory problem. For example by imposing certain conditions on the model -formally discussed in [34] -computations can then be distributed. This can dramatically reduce complexity and make calculations again feasible albeit with the necessary addition of further software -designed for the particular application -which intelligently merges together the outputs of the different contributing distributed components of the system: see also [45].…”

“…In the continuous case the unknown quantities of the polynomials are low order moments. Examples of these polynomials are presented in [34]. Just as in the discrete case, the manipulations of the diagrams for policies with continuous variables and their associated asymmetries can be described as operations over the polynomials.…”