Correcting Parameters of Events Based on the Entropy of Microlensing Ensemble

Details Correcting Parameters of Events Based on the Entropy of Microlensing Ensemble Correcting Parameters of Events Based on the Entropy of Microlensing Ensemble

Jun 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002apj...572..514p&link_type=abstract

The Astrophysical Journal, Volume 572, Issue 1, pp. 514-520.

Astronomy and Astrophysics

Astronomy

Cosmology: Dark Matter, Gravitation, Cosmology: Gravitational Lensing, Methods: Statistical, Stars: Fundamental Parameters

Scientific paper

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, umin. We refer to the case when undetected biases in the umin 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 umin 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.

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