Version 1.2.7

# Epoch Folding

## Gregory & Loredo Algorithm

This implements the algorithm described by Gregory & Loredo (1992, ApJ, vol. 398, pp. 146-168) to evenly divide a lightcurve, and determine whether this description is better than a constant lightcurve.

1. sitar_glvary( t, [; tmin=#, tmax=#, mmax=#, thresh=#, nbins=#, texp=array, frac_exp=array]);
Use the Gregory-Loredo algorithm to find the odds ratios that even divisions of a lightcurve are better descriptions of the data than a constant lightcurve. A 'best estimate' lightcurve can also be output for a lightcurve with nbins.
Run as: isis> fold = sitar_glvary(t; tmin=#, tmax=#, mmax=#, thresh=#, nbins=#, texp=array, frac_exp=array);
Variables in [] are optional qualifiers.
Omitted qualifier variables take on default values.

Inputs:
• t :  Array of event times
Optional Qualifier Inputs:
•  tmin :  The minimum time to consider (Default=min(t)-1)
•  tmax :  The maximum time to consider (Default=max(t)+1)
•  mmax :  Consider lightcurve divisions from 2 to mmax evenly spaced bins. (Default=300)
•  thresh :  Truncate the maximum number of partitions considered by ignoring partitionings for which-- \sum_m(odds ratio) < max(\sum_n(odds ratio))/exp(thresh) , where n = 2 -> mmax. I.e., the more partitionings you have, the less significant the results tend to become. thresh sets a minimum probability: (1-p_min) ~ exp(thresh)*(1-p_peak). (Default=2.)
•  nbins :  Create an output lightcurve with nbins. (Default=mmax)
•  texp, :  A pair of arrays that give values for the fractional exposure frac_exp as a function of time. *** Only non-zero values of exposure will be retained ***, which will then be interpolated and used to correct the lightcurve rates. These arrays must have a minimum of five entries. (Default is for no correction.)
Outputs:
•  gl.p :  Total probability that some evenly partitioned lightcurve, with up to gl.mmax bins, is a better description than a constant lightcurve
•  gl.ppart :  The probability for an individual evenly partitioned lightcurve that it is a better description than a constant lightcurve
•  gl.lodds_sum :  The natural logarithm of the sum of the odds ratios comparing lightcurves with two or more partitions to a constant lightcurve. gl.p == exp(gl.lodds_sum)/[1+exp(gl.lodds_sum)]
•  gl.mpeak :  The number of partitions for the evenly partitioned lightcurve with the maximum probability.
•  gl.mmax :  The maximum number of partitions actually used (influenced by the setting of the thresh parameter)
•  gl.m :  The number of partitions corresponding to each evenly partitioned lightcurve considered (=[2:mmax])
•  gl.pm :  Total probability that some evenly partitioned lightcurve is a better description than a constant lightcurve for each maximum number of partitions considered ([2:mmax])
•  gl.nj :  The counts histogram corresponding to each partitioning above
•  gl.aj :  The integrated fractional exposure for each partitioning above
•  gl.a_avg :  The averaged fractional exposure.
•  gl.tmin :  The value of tmin actually used (maximum of [tmin,min(texp)]);
•  gl.tmax :  The value of tmax actually used (minimum of [tmax,max(texp)]);
•  gl.tlc :  The output lightcurve times (an array with input nbins bins)
•  gl.rate :  Best estimate of the lightcuve rates at the above times
•  gl.erate :  Best estimate of the lightcuve rate errors at the above times

This page was last updated May 2, 2017 by Michael Nowak. To comment on it or the material presented here, send email to mnowak@space.mit.edu.