In this paper, computational aspects of the panel aggregation problem are addressed. Motivated primarily by applications of risk assessment, an algorithm is developed for aggregating large corpora of internally incoherent probability assessments. The algorithm is characterized by a provable performance guarantee, and is demonstrated to be orders of magnitude faster than existing tools when tested on several real-world data-sets. In addition, unexpected connections between research in risk assessment and wireless sensor networks are exposed, as several key ideas are illustrated to be useful in both fields.
@cite_20 consider a Bayesian approach to reconciling probability forecasts, whereby noisy" observations @math are assumed to arise from a coherent set @math . CAP can be viewed as a special-case of their model, since as discussed above, the solution to ) admits a Bayesian interpretation as the maximum-likelihood coherent forecasts given additive white noise corrupted observations @math . However, note that @cite_20 sought to eliminate incoherence from a single judge, whereas CAP was introduced to address the panel aggregation problem. Moreover, Osherson and Vardi were motivated by non-statistical interpretations of CAP and as here, addressed the computational issue of implementing CAP.
@cite_20
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In single-molecule microscopy it is necessary to locate with high precision point sources from noisy observations of the spectrum of the signal at frequencies capped by @math , which is just about the frequency of natural light. This paper rigorously establishes that this super-resolution problem can be solved via linear programming in a stable manner. We prove that the quality of the reconstruction crucially depends on the Rayleigh regularity of the support of the signal; that is, on the maximum number of sources that can occur within a square of side length about @math . The theoretical performance guarantee is complemented with a converse result showing that our simple convex program convex is nearly optimal. Finally, numerical experiments illustrate our methods.