A Decision-Centric Framework for Density Forecasting

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1 December 2010
Gabriel Terejanu, Puneet Singla, Tarunraj Singh, Peter D. Scott

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In general, the uncertainty propagation problem, in which the uncertain initial condition evolves through a dynamic system driven by noise, is seen strictly from the producer’s perspective. This means that uncertainty propagation algorithms are derived and evaluated based on statistical measures independent of the user’s decision needs. However accurate the uncertainty evolution given by a particular method, it may be less than optimal to the user or the decision maker, who takes decisions based on an implicit or explicit utility function. While in a static environment, one may be able to select an appropriate method for uncertainty propagation, in a dynamic environment with an ever-changing utility function this becomes a challenging task.

The goal of the present work is to reconcile the two views into a decision-centric framework which provides both a more accurate approximation to the relevant probability density function and a more precise expected utility value for the decision maker. A numerical example using a puff-based dispersion model, for forecasting downwind concentrations of toxic materials, demonstrates the capacity of this approach to focus computational resources on regions of particular interest such as high population density. A second example shows improvement over alternative methods as measured by a variety of utility-weighted metrics.