Density Reconstructions with Errors in the Data

Entropy

Erika Gomes-Gon๺lves²  Henryk Gzyl¹ 

[1] Centro de Finanzas, IESA, Ave. Iesa San Bernardino, Caracas 1010, Venezuela;Business Administration, Univ. Carlos III de Madrid, Calle Madrid 126, 28093 Getafe, Spain; E-Mails:

关键词: density reconstruction;    error estimation;    maximum entropy;   

DOI  :  10.3390/e16063257

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland