TY - JOUR
T1 - Binomial subsampling
AU - Wiuf, Carsten
AU - Stumpf, Michael P.H.
PY - 2006/1/1
Y1 - 2006/1/1
N2 - In this paper, we discuss statistical families P with the property that if the distribution of a random variable X is in P, then so is the distribution of Z∼Bi(X, p) for 0≤p≤1. (Here we take Z∼Bi(X, p) to mean that given X = x, Z is a draw from the binomial distribution Bi(x, p).) It is said that the family is closed under binomial subsampling. We characterize such families in terms of probability generating functions and for families with finite moments of all orders we give a necessary and sufficient condition for the family to be closed under binomial subsampling. The results are illustrated with power series and other examples, and related to examples from mathematical biology. Finally, some issues concerning inference are discussed.
AB - In this paper, we discuss statistical families P with the property that if the distribution of a random variable X is in P, then so is the distribution of Z∼Bi(X, p) for 0≤p≤1. (Here we take Z∼Bi(X, p) to mean that given X = x, Z is a draw from the binomial distribution Bi(x, p).) It is said that the family is closed under binomial subsampling. We characterize such families in terms of probability generating functions and for families with finite moments of all orders we give a necessary and sufficient condition for the family to be closed under binomial subsampling. The results are illustrated with power series and other examples, and related to examples from mathematical biology. Finally, some issues concerning inference are discussed.
KW - Binomial distribution
KW - Biological networks
KW - Closure property
KW - Power series
KW - Sampling
UR - http://www.scopus.com/inward/record.url?scp=33845276871&partnerID=8YFLogxK
U2 - 10.1098/rspa.2005.1622
DO - 10.1098/rspa.2005.1622
M3 - Journal article
AN - SCOPUS:33845276871
SN - 1364-5021
VL - 462
SP - 1181
EP - 1195
JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
IS - 2068
ER -