Multiple Testing

Multiple Testing is implemented to analyse the characteristics of the maxima population as a whole. First, the intensity of the maxima is compared to the expected distribution \(f\), and the probability of a maxima happening at random in a Gaussian map is computed (as opposed to the maximum being produced by a point source): this is the pvalue. These can be studied individually or as a population. For the latter, we implement the Benjamini-Hochberg procedure of multiple testing.

There are three types of functions regarding pvalues and multiple testing:

  1. Functions to calculate the theoretical distribution of maxima \(f\).

  2. Functions to calculate the pvalue.

  3. A functions to apply the multiple testing approach.

Theoretical distribution \(f\)

f_fromks(k1, k2)

Get the theoretical maxima distribution f, from the values of k_1, k_2.

f_fromcl(cls)

Get the theoretical maxima distribution f, from the angular power spectra C_l of a map.

f_fromSW(j, B[, gamma, p])

Get the theoretical maxima distribution for a Sachs-Wolfe-like spectra filtered with a Mexican needlet.

pvalues

pvalues(xvec, f[, returnerror])

Calculate the p-values for a certain maxima distribution f, of diferent values of the intensity.

max_getpvalue(maxima, f[, n_exact, step, …])

Get the p-values for the maxima for a given expected distribution.

Multiple testing

benjamini_hochberg(maxima, alpha[, plot])

Select a subset of the maxima to be candidates to Point Source.