A cohort, described by the sampling depth of each repertoire, turns a sequence probability
into the distribution of how many repertoires contain the sequence: a repertoire of depth d
contains a sequence of probability p with probability 1−(1−p)d. See
How public is a sequence?.
One depth per repertoire: the number of draws (cells or templates) sampled from it; finite and non-negative.
depth_bins
Repertoires of similar depth are grouped into at most this many groups (default 64), each represented by the geometric mean of its depths, to keep the calculation fast. Grouping changes the answer slightly: depth_spread reports the widest ratio of depths within a group (1.0 means none happened), and depth_bins=len(set(depths)) keeps every depth separate.
Mean and variance of the number of carriers, in closed form. p may be one probability or an array.
pmf(p)
The probability of exactly 0, 1, …, R carriers, for one probability, by numerical inversion of the generating function, accurate to double-precision round-off.
bin_mass(p, edges)
The probability of a number of carriers in each bin [edges[i], edges[i+1]); an integer edges makes that many equal-width bins.
For a whole spectrum of sequence probabilities (each probability and the number of sequences that have it), the expected number of sequences at each publicness level: one bin per number of carriers by default, levels=k for k equal-width bins, or a list of edges.
