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ID: 5534.0, MPI für Astrophysik / Cosmology
Correcting parameters of events based on the entropy of microlensing ensemble
Authors:Popowski, P.; Alcock, C.
Date of Publication (YYYY-MM-DD):2002
Title of Journal:The Astrophysical Journal
Journal Abbrev.:Astrophys. J.
Issue / Number:1
Start Page:514
End Page:520
Review Status:Peer-review
Audience:Experts Only
Abstract / Description:We entertain the idea that robust theoretical expectations can become a tool in removing hidden observational or data- reduction biases. We illustrate this approach for a specific problem associated with gravitational microlensing. Using the fact that a group is more than just a collection of individuals, we derive formulae for correcting the distribution of the dimensionless impact parameters of events, u(min). We refer to the case when undetected biases in the u(min) distribution can be alleviated by multiplication of impact parameters of all events by a common constant factor. We show that in this case the general maximum likelihood problem of solving an infinite number of equations reduces to two constraints, and we find an analytic solution. Under the above assumptions, this solution represents a state in which the entropy of a microlensing ensemble is at its maximum; that is, the distribution of u(min) resembles a specific, theoretically expected, boxlike distribution to the highest possible extent. We also show that this technique does not allow one to correct the parameters of individual events on an event-by-event basis, independently from each other.
Free Keywords:dark matter; gravitation; gravitational lensing; methods : statistical; stars : fundamental parameters
External Publication Status:published
Document Type:Article
Communicated by:N. N.
Affiliations:MPI für Astrophysik
External Affiliations:Lawrence Livermore Natl Lab, 7000 East Ave, Livermore, CA 94550; USA; Lawrence Livermore Natl Lab, Livermore, CA 94550 USA; Max Planck Inst Astrophys, D-85741 Garching, Germany; Univ Penn, Dept Phys & Astron, Philadelphia, PA 19104 USA
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