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Entropy 2014, 16(6), 3257-3272; doi:10.3390/e16063257
Article

Density Reconstructions with Errors in the Data

1
, 2,*  and 1
Received: 2 May 2014; in revised form: 3 June 2014 / Accepted: 9 June 2014 / Published: 12 June 2014
(This article belongs to the Special Issue Maximum Entropy and Its Application)
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Abstract: 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.
Keywords: density reconstruction; error estimation; maximum entropy density reconstruction; error estimation; maximum entropy
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Gomes-Gonçalves, E.; Gzyl, H.; Mayoral, S. Density Reconstructions with Errors in the Data. Entropy 2014, 16, 3257-3272.

AMA Style

Gomes-Gonçalves E, Gzyl H, Mayoral S. Density Reconstructions with Errors in the Data. Entropy. 2014; 16(6):3257-3272.

Chicago/Turabian Style

Gomes-Gonçalves, Erika; Gzyl, Henryk; Mayoral, Silvia. 2014. "Density Reconstructions with Errors in the Data." Entropy 16, no. 6: 3257-3272.


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