From Data to Assessments and Decisions: Epi-Spline Technology
Abstract
Analysts in every field face the challenge of how to best use available data to estimate performance, quantify uncertainty, and predict the future. The data are almost never ``just right,'' but rather scarce, excessive, corrupted, uncertain, and incomplete. External information derived from experiences, established ``laws,'' and physical restrictions offer opportunities to remedy the situation and should be utilized. Applications in sustainable energy, natural resources, image reconstruction, financial planning, uncertainty quantification, and reliability engineering are rich with problems where decisions rely on data analysis under such circumstances. We address these problems within a framework that identifies a function that according to some criterion best represents the given data set and satisfies constraints derived from the data as well as external information. Epi-splines provide the linchpin that allows us to handle shape restrictions, information growth, and approximations.
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