def __deriv_probs_sharp_threshold(self, rho1, rho2, rho12):
"""Compute and return derivative of probability of phi(infty) with
respect to rho1, rho2 and rho12 using the sharp threshold model.
Returns
-------
dprobs_drhos : 2D float numpy array, shape = (4, 3)
"""
# 3 elements in array are derivative wrt to rho1, rho2 and rho12.
deriv_prob_noD1 = np.zeros(3, dtype=np.float)
deriv_prob_noD2 = np.zeros(3, dtype=np.float)
deriv_prob_noD1_and_noD2 = np.zeros(3, dtype=np.float)
tau1 = self.tau1
tau2 = self.tau2
tau12 = max(tau1, tau2)
if self.overlap_type == 0: # coorperative model
indices = [(k1, k2, k12) for k1 in xrange(tau1)
for k2 in xrange(tau2)
for k12 in xrange(tau12)]
deriv_prob_noD1[0] = poisson.dcdf_dmu(tau1 - 1, rho1 + rho12)
deriv_prob_noD1[1] = 0.0
deriv_prob_noD1[2] = poisson.dcdf_dmu(tau1 - 1, rho1 + rho12)
deriv_prob_noD2[0] = 0.0
deriv_prob_noD2[1] = poisson.dcdf_dmu(tau2 - 1, rho2 + rho12)
deriv_prob_noD2[2] = poisson.dcdf_dmu(tau2 - 1, rho2 + rho12)
for (k1, k2, k12) in indices:
no_penetrance = k1 + k12 < tau1 and k2 + k12 < tau2
if no_penetrance:
deriv_prob_noD1_and_noD2[0] = (
poisson.dpmf_dmu(k1, rho1) *
poisson.pmf(k2, rho2) *
poisson.pmf(k12, rho12))
deriv_prob_noD1_and_noD2[1] = (
poisson.pmf(k1, rho1) *
poisson.dpmf_dmu(k2, rho2) *
poisson.pmf(k12, rho12))
deriv_prob_noD1_and_noD2[2] = (
poisson.pmf(k1, rho1)*
poisson.pmf(k2, rho2) *
poisson.dpmf_dmu(k12, rho12))
elif self.overlap_type == 1 and rho12 > 0.0: # competition model
raise NotImplementedError("competition model not implemented.")
else: # independent model, rho12 does not contribute!
deriv_prob_noD1[0] = poisson.dcdf_dmu(tau1 - 1, rho1)
deriv_prob_noD1[1] = 0.0
deriv_prob_noD1[2] = 0.0
deriv_prob_noD2[0] = 0.0
deriv_prob_noD2[1] = poisson.dcdf_dmu(tau2 - 1, rho2)
deriv_prob_noD2[2] = 0.0
indices = [(k1, k2) for k1 in xrange(tau1)
for k2 in xrange(tau2)]
for (k1, k2) in indices:
no_penetrance = k1 < tau1 and k2 < tau2
if no_penetrance:
deriv_prob_noD1_and_noD2[0] = (
poisson.dpmf_dmu(k1, rho1) *
poisson.pmf(k2, rho2))
deriv_prob_noD1_and_noD2[1] = (
poisson.pmf(k1, rho1) *
poisson.dpmf_dmu(k2, rho2))
deriv_prob_noD1_and_noD2[2] = 0.0
# Derivative of phi_infty_probs wrt to rho1, rho2, and rho12
deriv_probs = np.zeros([4, 3], dtype=np.float)
# deriv of prob(noD1 and noD2)
deriv_probs[0] = deriv_prob_noD1_and_noD2
# deriv of prob(yesD1 and noD2)
deriv_probs[1] = deriv_prob_noD2 - deriv_prob_noD1_and_noD2
# deriv of prob(noD1 and yesD2)
deriv_probs[2] = deriv_prob_noD1 - deriv_prob_noD1_and_noD2
# deriv of prob(yesD1 and yesD2)
deriv_probs[3] = -np.sum(deriv_probs[0:3])
return deriv_probs
def __deriv_probs_sharp_threshold(self, rho1, rho2, rho12):
"""Compute and return derivative of probability of phi(infty) with
respect to rho1, rho2 and rho12 using the sharp threshold model.
Returns
-------
dprobs_drhos : 2D float numpy array, shape = (4, 3)
"""
# 3 elements in array are derivative wrt to rho1, rho2 and rho12.
deriv_prob_noD1 = np.zeros(3, dtype=np.float)
deriv_prob_noD2 = np.zeros(3, dtype=np.float)
deriv_prob_noD1_and_noD2 = np.zeros(3, dtype=np.float)
tau1 = self.tau1
tau2 = self.tau2
tau12 = max(tau1, tau2)
if self.overlap_type == 0: # coorperative model
indices = [(k1, k2, k12) for k1 in xrange(tau1)
for k2 in xrange(tau2) for k12 in xrange(tau12)]
deriv_prob_noD1[0] = poisson.dcdf_dmu(tau1 - 1, rho1 + rho12)
deriv_prob_noD1[1] = 0.0
deriv_prob_noD1[2] = poisson.dcdf_dmu(tau1 - 1, rho1 + rho12)
deriv_prob_noD2[0] = 0.0
deriv_prob_noD2[1] = poisson.dcdf_dmu(tau2 - 1, rho2 + rho12)
deriv_prob_noD2[2] = poisson.dcdf_dmu(tau2 - 1, rho2 + rho12)
for (k1, k2, k12) in indices:
no_penetrance = k1 + k12 < tau1 and k2 + k12 < tau2
if no_penetrance:
deriv_prob_noD1_and_noD2[0] = (poisson.dpmf_dmu(k1, rho1) *
poisson.pmf(k2, rho2) *
poisson.pmf(k12, rho12))
deriv_prob_noD1_and_noD2[1] = (poisson.pmf(k1, rho1) *
poisson.dpmf_dmu(k2, rho2) *
poisson.pmf(k12, rho12))
deriv_prob_noD1_and_noD2[2] = (
poisson.pmf(k1, rho1) * poisson.pmf(k2, rho2) *
poisson.dpmf_dmu(k12, rho12))
elif self.overlap_type == 1 and rho12 > 0.0: # competition model
raise NotImplementedError("competition model not implemented.")
else: # independent model, rho12 does not contribute!
deriv_prob_noD1[0] = poisson.dcdf_dmu(tau1 - 1, rho1)
deriv_prob_noD1[1] = 0.0
deriv_prob_noD1[2] = 0.0
deriv_prob_noD2[0] = 0.0
deriv_prob_noD2[1] = poisson.dcdf_dmu(tau2 - 1, rho2)
deriv_prob_noD2[2] = 0.0
indices = [(k1, k2) for k1 in xrange(tau1) for k2 in xrange(tau2)]
for (k1, k2) in indices:
no_penetrance = k1 < tau1 and k2 < tau2
if no_penetrance:
deriv_prob_noD1_and_noD2[0] = (poisson.dpmf_dmu(k1, rho1) *
poisson.pmf(k2, rho2))
deriv_prob_noD1_and_noD2[1] = (poisson.pmf(k1, rho1) *
poisson.dpmf_dmu(k2, rho2))
deriv_prob_noD1_and_noD2[2] = 0.0
# Derivative of phi_infty_probs wrt to rho1, rho2, and rho12
deriv_probs = np.zeros([4, 3], dtype=np.float)
# deriv of prob(noD1 and noD2)
deriv_probs[0] = deriv_prob_noD1_and_noD2
# deriv of prob(yesD1 and noD2)
deriv_probs[1] = deriv_prob_noD2 - deriv_prob_noD1_and_noD2
# deriv of prob(noD1 and yesD2)
deriv_probs[2] = deriv_prob_noD1 - deriv_prob_noD1_and_noD2
# deriv of prob(yesD1 and yesD2)
deriv_probs[3] = -np.sum(deriv_probs[0:3])
return deriv_probs
def __probs_sharp_threshold(self, rho1, rho2, rho12):
"""Compute and return probability of phi(infty), the age-integrated
phenotypes using the sharp threshold model.
Please refer to section 6.2 in the SI Appendix 2 of Rzhetsky et al.
2007 for details.
Returns
-------
phi_infty_probs : 1D float numpy array (size = 4)
Notes
-----
poisson.pmf(k, mu) is probability mass function of the Poisson
distribution with parameter mu evualated at k.
poisson.cdf(kmax, mu) is cumulative of Poisson probability mass
function from k = 0, 1, 2 to kmax.
"""
prob_noD1 = 0.0
prob_noD2 = 0.0
prob_noD1_and_noD2 = 0.0
tau1 = self.tau1
tau2 = self.tau2
tau12 = max(tau1, tau2)
if self.overlap_type == 0: # coorperative model
indices = [(k1, k2, k12) for k1 in xrange(tau1)
for k2 in xrange(tau2)
for k12 in xrange(tau12)]
prob_noD1 = poisson.cdf(tau1 - 1, rho1 + rho12)
prob_noD2 = poisson.cdf(tau2 - 1, rho2 + rho12)
for (k1, k2, k12) in indices:
no_penetrance = k1 + k12 < tau1 and k2 + k12 < tau2
if no_penetrance:
prob_noD1_and_noD2 += (poisson.pmf(k1, rho1) *
poisson.pmf(k2, rho2) *
poisson.pmf(k12, rho12))
elif self.overlap_type == 1 and rho12 > 0.0: # competition model
raise NotImplementedError("competition model not implemented.")
else: # independent model, rho12 does not contribute!
prob_noD1 = poisson.cdf(tau1 - 1, rho1)
prob_noD2 = poisson.cdf(tau2 - 1, rho2)
indices = [(k1, k2) for k1 in xrange(tau1)
for k2 in xrange(tau2)]
for (k1, k2) in indices:
no_penetrance = k1 < tau1 and k2 < tau2
if no_penetrance:
prob_noD1_and_noD2 += (poisson.pmf(k1, rho1) *
poisson.pmf(k2, rho2))
# Instantiate phi_infinity_probs
phi_infty_probs = np.zeros(4, dtype=np.float)
# prob(noD1 and noD2)
phi_infty_probs[0] = prob_noD1_and_noD2
# prob(yesD1 and noD2)
phi_infty_probs[1] = prob_noD2 - prob_noD1_and_noD2
# prob(noD1 and yesD2)
phi_infty_probs[2] = prob_noD1 - prob_noD1_and_noD2
# prob(yesD1 and yesD2)
# use the fact that probability must add up to 1.
phi_infty_probs[3] = 1.0 - np.sum(phi_infty_probs[0:3])
return phi_infty_probs
def __probs_sharp_threshold(self, rho1, rho2, rho12):
"""Compute and return probability of phi(infty), the age-integrated
phenotypes using the sharp threshold model.
Please refer to section 6.2 in the SI Appendix 2 of Rzhetsky et al.
2007 for details.
Returns
-------
phi_infty_probs : 1D float numpy array (size = 4)
Notes
-----
poisson.pmf(k, mu) is probability mass function of the Poisson
distribution with parameter mu evualated at k.
poisson.cdf(kmax, mu) is cumulative of Poisson probability mass
function from k = 0, 1, 2 to kmax.
"""
prob_noD1 = 0.0
prob_noD2 = 0.0
prob_noD1_and_noD2 = 0.0
tau1 = self.tau1
tau2 = self.tau2
tau12 = max(tau1, tau2)
if self.overlap_type == 0: # coorperative model
indices = [(k1, k2, k12) for k1 in xrange(tau1)
for k2 in xrange(tau2) for k12 in xrange(tau12)]
prob_noD1 = poisson.cdf(tau1 - 1, rho1 + rho12)
prob_noD2 = poisson.cdf(tau2 - 1, rho2 + rho12)
for (k1, k2, k12) in indices:
no_penetrance = k1 + k12 < tau1 and k2 + k12 < tau2
if no_penetrance:
prob_noD1_and_noD2 += (poisson.pmf(k1, rho1) *
poisson.pmf(k2, rho2) *
poisson.pmf(k12, rho12))
elif self.overlap_type == 1 and rho12 > 0.0: # competition model
raise NotImplementedError("competition model not implemented.")
else: # independent model, rho12 does not contribute!
prob_noD1 = poisson.cdf(tau1 - 1, rho1)
prob_noD2 = poisson.cdf(tau2 - 1, rho2)
indices = [(k1, k2) for k1 in xrange(tau1) for k2 in xrange(tau2)]
for (k1, k2) in indices:
no_penetrance = k1 < tau1 and k2 < tau2
if no_penetrance:
prob_noD1_and_noD2 += (poisson.pmf(k1, rho1) *
poisson.pmf(k2, rho2))
# Instantiate phi_infinity_probs
phi_infty_probs = np.zeros(4, dtype=np.float)
# prob(noD1 and noD2)
phi_infty_probs[0] = prob_noD1_and_noD2
# prob(yesD1 and noD2)
phi_infty_probs[1] = prob_noD2 - prob_noD1_and_noD2
# prob(noD1 and yesD2)
phi_infty_probs[2] = prob_noD1 - prob_noD1_and_noD2
# prob(yesD1 and yesD2)
# use the fact that probability must add up to 1.
phi_infty_probs[3] = 1.0 - np.sum(phi_infty_probs[0:3])
return phi_infty_probs