- Title
- MaxEnt elicited priors with Mathematica - derivation and use
- Creator
- Stokes, Barrie
- Relation
- 35th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (Maxent 2015). Proceedings of the 35th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering [presented in AIP Conference Proceedings, Vol. 1757] (Potsdam, NY 19-24 July, 2015)
- Publisher Link
- http://dx.doi.org/10.1063/1.4959047
- Publisher
- American Institute Physics (AIP)
- Resource Type
- conference paper
- Date
- 2016
- Description
- In two previous papers [Stokes 1, 2] a general method of obtaining univariate MaxEnt distributions was presented and applied. The approach involved solving a collection of Lagrange Multiplier equations for a set of ordinates associated with a set of regular abscissae, using the Mathematica function FindRoot. The method exploits the fact that Mathematica allows an InterpolationFunction to be fitted to a list of the form, say, {{0, ord₁}, {0.1, ord₂}, {0.2, ord₃}, … where the ordinates ordi are symbolic. The resulting InterpolationFunction can be manipulated just like any conventionally defined function, so that means, variances, CDF values, or other quantities elicited from a domain expert can be expressed in terms of the ordi. This paper presents an improved method for finding these MaxEnt distributions, and shows how the MaxEnt PDF can be expressed as a piecewise polynomial function, or a “one-piece” polynomial function using step-type basis functions. Some further Mathematica string manipulation can render such expressions in R [3] or BUGS [4] syntax for use, say, as a prior distribution in a Bayesian analysis.
- Subject
- MaxEnt distributions; <i>Mathematica</i>; Lagrange multiplier equations
- Identifier
- http://hdl.handle.net/1959.13/1326367
- Identifier
- uon:25414
- Identifier
- ISBN:9780753414150
- Language
- eng
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