Infinite combinatorics in mathematical biology

Biosystems ◽  
2021 ◽  
pp. 104392
Author(s):  
Saharon Shelah ◽  
Lutz Strüngmann
Keyword(s):  
Mathematical Biology ◽  
Infinite Combinatorics

Binomial subsampling

2006 ◽  
Vol 462 (2068) ◽  
pp. 1181-1195 ◽  
Author(s):  
Carsten Wiuf ◽  
Michael P.H Stumpf
Keyword(s):  
Mathematical Biology ◽  
Power Series ◽  
Generating Functions ◽  
Binomial Distribution ◽  
Random Variable ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
The Family ◽  
Necessary And Sufficient ◽  
Finite Moments

In this paper, we discuss statistical families with the property that if the distribution of a random variable X is in , 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.

scholarly journals Experimenting with Mathematical Biology

PRIMUS ◽  
2015 ◽  
Vol 26 (1) ◽  
pp. 83-103 ◽  
Author(s):  
Rebecca Sanft ◽  
Anne Walter
Keyword(s):  
Mathematical Biology

Infinite Combinatorics and Graphs

2000 ◽  
pp. 161-210
Author(s):  
John M. Harris ◽  
Jeffry L. Hirst ◽  
Michael J. Mossinghoff
Keyword(s):  
Infinite Combinatorics

Mathematical biology

1991 ◽  
Vol 103 (1) ◽  
pp. 153-155
Author(s):  
Bard Ermentrout
Keyword(s):  
Mathematical Biology
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