/
moth_em.py
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/
moth_em.py
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### EXAMPLE 4.2 EM ALGORITHM (PEPPERED MOTHS)
#########################################################################
# x = observed phenotype counts (carbonaria, insularia, typica)
# n = expected genotype frequencies (CC, CI, CT, II, IT, TT)
# p = allele probabilities (carbonaria, insularia, typica)
# itr = number of iterations
# allele_e = computes expected genotype frequencies
# allele_m = computes allele probabilities
#########################################################################
import numpy as np
C, I, T = 0, 1, 2
## EXPECTATION AND MAXIMIZATION FUNCTIONS
def allele_e(x, p):
En_cc = (x[C]*(p[C]**2)) / ((p[C]**2) + 2*p[C]*p[I] + 2*p[C]*p[T])
En_ci = (2*x[C]*p[C]*p[I]) / ((p[C]**2) + 2*p[C]*p[I] + 2*p[C]*p[T])
En_ct = (2*x[C]*p[C]*p[T]) / ((p[C]**2) + 2*p[C]*p[I] + 2*p[C]*p[T])
En_ii = (x[I]*(p[I]**2)) / ((p[I]**2) + 2*p[I]*p[T])
En_it = (2*x[I]*p[I]*p[T]) / ((p[I]**2) + 2*p[I]*p[T])
return(En_cc, En_ci, En_ct, En_ii, En_it, x[2])
CC, CI, CT, II, IT, TT = range(6)
def allele_m (x, n):
p_c = (2*n[CC] + n[CI] + n[CT]) / (2*x.sum())
p_i = (2*n[II] + n[IT] + n[CI]) / (2*x.sum())
p_t = (2*n[-1] + n[CT] + n[IT]) / (2*x.sum())
return(p_c, p_i, p_t)
def run(itr=40):
x = np.array([85, 196, 341])
n = np.zeros(6)
p = np.ones(3)*(1/3)
for i in range(itr):
n = allele_e(x,p)
p = allele_m(x,n)
return p
if __name__ == '__main__':
print(run())