def _model_setup(self):
with self._model:
# COSMOLOGY
omega_m = pm.Uniform("OmegaM", lower=0, upper=1.)
# My custom distance mod. function to enable
# ADVI and HMC sampling.
dm = distmod_constant_flat(omega_m, self._h0, self._zcmb)
# PHILIPS PARAMETERS
# M0 is the location parameter for the distribution
# sys_scat is the scale parameter for the M0 distribution
# rather than "unexpalined variance"
M0 = pm.Normal("M0", mu=-19.3, sd=2.)
sys_scat = pm.HalfCauchy('sys_scat', beta=2.5) # Gelman recommendation for variance parameter
M_true = pm.Normal('M_true', M0, sys_scat, shape=self._n_SN)
# following Rubin's Unity model... best idea? not sure
taninv_alpha = pm.Uniform("taninv_alpha", lower=-.2, upper=.3)
taninv_beta = pm.Uniform("taninv_beta", lower=-1.4, upper=1.4)
# Transform variables
alpha = pm.Deterministic('alpha', T.tan(taninv_alpha))
beta = pm.Deterministic('beta', T.tan(taninv_beta))
# Again using Rubin's Unity model.
# After discussion with Rubin, the idea is that
# these parameters are ideally sampled from a Gaussian,
# but we know they are not entirely correct. So instead,
# the Cauchy is less informative around the mean, while
# still having informative tails.
xm = pm.Cauchy('xm', alpha=0, beta=1)
cm = pm.Cauchy('cm', alpha=0, beta=1)
Rx_log = pm.Uniform('Rx_log', lower=-0.5, upper=0.5)
Rc_log = pm.Uniform('Rc_log', lower=-1.5, upper=1.5)
# Transformed variables
Rx = pm.Deterministic("Rx", T.pow(10., Rx_log))
Rc = pm.Deterministic("Rc", T.pow(10., Rc_log))
x_true = pm.Normal('x_true', mu=xm, sd=Rx, shape=self._n_SN)
c_true = pm.Normal('c_true', mu=cm, sd=Rc, shape=self._n_SN)
# Do the correction
mb = pm.Deterministic("mb", M_true + dm - alpha * x_true + beta * c_true)
# Likelihood and measurement error
obsc = pm.Normal("obsc", mu=c_true, sd=self._dcolor, observed=self._color)
obsx = pm.Normal("obsx", mu=x_true, sd=self._dx1, observed=self._x1)
obsm = pm.Normal("obsm", mu=mb, sd=self._dmb_obs, observed=self._mb_obs)
def _model_setup(self):
with self._model:
# COSMOLOGY
omega_m = pm.Uniform("OmegaM", lower=0, upper=1.)
# My custom distance mod. function to enable
# ADVI and HMC sampling.
# We are going to have to break this into
# four likelihoods
dm_0 = distmod_constant_flat(omega_m, self._h0, self._zcmb_survey[0])
dm_1 = distmod_constant_flat(omega_m, self._h0, self._zcmb_survey[1])
dm_2 = distmod_constant_flat(omega_m, self._h0, self._zcmb_survey[2])
dm_3 = distmod_constant_flat(omega_m, self._h0, self._zcmb_survey[3])
# PHILIPS PARAMETERS
# M0 is the location parameter for the distribution
# sys_scat is the scale parameter for the M0 distribution
# rather than "unexpalined variance"
M0 = pm.Uniform("M0", lower=-20., upper=-18.)
sys_scat = pm.HalfCauchy('sys_scat', beta=2.5) # Gelman recommendation for variance parameter
M_true_0 = pm.Normal('M_true_0', M0, sys_scat, shape=self._n_SN_survey[0])
M_true_1 = pm.Normal('M_true_1', M0, sys_scat, shape=self._n_SN_survey[1])
M_true_2 = pm.Normal('M_true_2', M0, sys_scat, shape=self._n_SN_survey[2])
M_true_3 = pm.Normal('M_true_3', M0, sys_scat, shape=self._n_SN_survey[3])
# following Rubin's Unity model... best idea? not sure
taninv_alpha = pm.Uniform("taninv_alpha", lower=-.2, upper=.3)
taninv_beta = pm.Uniform("taninv_beta", lower=-1.4, upper=1.4)
# Transform variables
alpha = pm.Deterministic('alpha', T.tan(taninv_alpha))
beta = pm.Deterministic('beta', T.tan(taninv_beta))
# Again using Rubin's Unity model.
# After discussion with Rubin, the idea is that
# these parameters are ideally sampled from a Gaussian,
# but we know they are not entirely correct. So instead,
# the Cauchy is less informative around the mean, while
# still having informative tails.
xm = pm.Cauchy('xm', alpha=0, beta=1)
cm = pm.Cauchy('cm', alpha=0, beta=1, shape=4)
s = pm.Uniform('s', lower=-2, upper=2, shape=4)
c_shift_0 = cm[0] + s[0] * self._zcmb_survey[0]
c_shift_1 = cm[1] + s[1] * self._zcmb_survey[1]
c_shift_2 = cm[2] + s[2] * self._zcmb_survey[2]
c_shift_3 = cm[3] + s[3] * self._zcmb_survey[3]
Rx_log = pm.Uniform('Rx_log', lower=-0.5, upper=0.5)
Rc_log = pm.Uniform('Rc_log', lower=-1.5, upper=1.5, shape=4)
# Transformed variables
Rx = pm.Deterministic("Rx", T.pow(10., Rx_log))
Rc = pm.Deterministic("Rc", T.pow(10., Rc_log))
x_true_0 = pm.Normal('x_true_0', mu=xm, sd=Rx, shape=self._n_SN_survey[0])
c_true_0 = pm.Normal('c_true_0', mu=c_shift_0, sd=Rc[0], shape=self._n_SN_survey[0])
x_true_1 = pm.Normal('x_true_1', mu=xm, sd=Rx, shape=self._n_SN_survey[1])
c_true_1 = pm.Normal('c_true_1', mu=c_shift_1, sd=Rc[1], shape=self._n_SN_survey[1])
x_true_2 = pm.Normal('x_true_2', mu=xm, sd=Rx, shape=self._n_SN_survey[2])
c_true_2 = pm.Normal('c_true_2', mu=c_shift_2, sd=Rc[2], shape=self._n_SN_survey[2])
x_true_3 = pm.Normal('x_true_3', mu=xm, sd=Rx, shape=self._n_SN_survey[3])
c_true_3 = pm.Normal('c_true_3', mu=c_shift_3, sd=Rc[3], shape=self._n_SN_survey[3])
# Do the correction
mb_0 = pm.Deterministic("mb_0", M_true_0 + dm_0 - alpha * x_true_0 + beta * c_true_0)
mb_1 = pm.Deterministic("mb_1", M_true_1 + dm_1 - alpha * x_true_1 + beta * c_true_1)
mb_2 = pm.Deterministic("mb_2", M_true_2 + dm_2 - alpha * x_true_2 + beta * c_true_2)
mb_3 = pm.Deterministic("mb_3", M_true_3 + dm_3 - alpha * x_true_3 + beta * c_true_3)
# Likelihood and measurement error
obsc_0 = pm.Normal("obsc_0", mu=c_true_0, sd=self._dcolor_survey[0], observed=self._color_survey[0])
obsx_0 = pm.Normal("obsx_0", mu=x_true_0, sd=self._dx1_survey[0], observed=self._x1_survey[0])
obsm_0 = pm.Normal("obsm_0", mu=mb_0, sd=self._dmbObs_survey[0], observed=self._mbObs_survey[0])
obsc_1 = pm.Normal("obsc_1", mu=c_true_1, sd=self._dcolor_survey[1], observed=self._color_survey[1])
obsx_1 = pm.Normal("obsx_1", mu=x_true_1, sd=self._dx1_survey[1], observed=self._x1_survey[1])
obsm_1 = pm.Normal("obsm_1", mu=mb_1, sd=self._dmbObs_survey[1], observed=self._mbObs_survey[1])
obsc_2 = pm.Normal("obsc_2", mu=c_true_2, sd=self._dcolor_survey[2], observed=self._color_survey[2])
obsx_2 = pm.Normal("obsx_2", mu=x_true_2, sd=self._dx1_survey[2], observed=self._x1_survey[2])
obsm_2 = pm.Normal("obsm_2", mu=mb_2, sd=self._dmbObs_survey[2], observed=self._mbObs_survey[2])
obsc_3 = pm.Normal("obsc_3", mu=c_true_3, sd=self._dcolor_survey[3], observed=self._color_survey[3])
obsx_3 = pm.Normal("obsx_3", mu=x_true_3, sd=self._dx1_survey[3], observed=self._x1_survey[3])
obsm_3 = pm.Normal("obsm_3", mu=mb_3, sd=self._dmbObs_survey[3], observed=self._mbObs_survey[3])