def allele_frequency_probabilityln(allele_frequency_counts, theta=0.001):
"""Log space version to avoid inevitable overflows with coverage >100.
Implements Ewens' Sampling Formula. allele_frequency_counts is a
dictionary mapping count -> number of alleles with this count in the
population."""
thetaln = math.log(theta)
M = sum([frequency * count for frequency, count in allele_frequency_counts.iteritems()])
return factorialln(M) \
- (thetaln + sum([math.log(theta + h) for h in range(1, M)])) \
+ sum([powln(thetaln, count) - powln(math.log(frequency), count) + factorialln(count) \
for frequency, count in allele_frequency_counts.iteritems()])
def allele_frequency_probabilityln(allele_frequency_counts, theta=0.001):
"""Log space version to avoid inevitable overflows with coverage >100.
Implements Ewens' Sampling Formula. allele_frequency_counts is a
dictionary mapping count -> number of alleles with this count in the
population."""
thetaln = math.log(theta)
M = sum([
frequency * count
for frequency, count in allele_frequency_counts.iteritems()
])
return factorialln(M) \
- (thetaln + sum([math.log(theta + h) for h in range(1, M)])) \
+ sum([powln(thetaln, count) - powln(math.log(frequency), count) + factorialln(count) \
for frequency, count in allele_frequency_counts.iteritems()])
def multinomial_coefficientln(n, counts):
return factorialln(n) - sum(map(factorialln, counts))
def multinomialln(probs, obs):
return factorialln(sum(obs)) - sum(map(factorialln, obs)) + sum(
[math.log(math.pow(p, x)) for p, x in zip(probs, obs)])
def multinomial_coefficientln(n, counts):
return factorialln(n) - sum(map(factorialln, counts))
def multinomialln(probs, obs):
return factorialln(sum(obs)) - sum(map(factorialln, obs)) + sum([math.log(math.pow(p, x)) for p,x in zip(probs, obs)])