Density Reconstructions with Errors in the Data

The maximum entropy method was originally proposed as a variational technique to determine probability densities from the knowledge of a few expected values. The applications of the method beyond its original role in statistical physics are manifold. An interesting feature of the method is its poten...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2014-06, Vol.16 (6), p.3257-3272
Main Authors: Gomes-Gonçalves, Erika, Gzyl, Henryk, Mayoral, Silvia
Format: Article
Language:English
Subjects:
Density
density reconstruction
Entropy
Error analysis
error estimation
Errors
Laplace transforms
maximum entropy
Maximum entropy method
Permissible error
Stemming
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Summary:The maximum entropy method was originally proposed as a variational technique to determine probability densities from the knowledge of a few expected values. The applications of the method beyond its original role in statistical physics are manifold. An interesting feature of the method is its potential to incorporate errors in the data. Here, we examine two possible ways of doing that. The two approaches have different intuitive interpretations, and one of them allows for error estimation. Our motivating example comes from the field of risk analysis, but the statement of the problem might as well come from any branch of applied sciences. We apply the methodology to a problem consisting of the determination of a probability density from a few values of its numerically-determined Laplace transform. This problem can be mapped onto a problem consisting of the determination of a probability density on [0, 1] from the knowledge of a few of its fractional moments up to some measurement errors stemming from insufficient data.
ISSN:1099-4300
1099-4300
DOI:10.3390/e16063257