def likefunc(self,n,s,dels,delb):
"""log-likelihood function for individual parameter points in the model.
Contains the two nuisance parameters dels and delb, which
parameterise the systematic errors. Marginalise these out to be
Bayesian, or profile them to be pseudo-frequentist (they still
have priors).
The parameter 's' (signal mean) should then be the only free
parameter left.
Args:
n - observed number of events
i - which signal region we are currently looking at
dels - systematic error parameter for signal
delb - systematic error parameter for background
s - expected number of events due to signal
ssys - estimated gaussian uncertainty on expected number of signal events (effectively a prior)
b - expected number of events due to background
bsys - estimated gaussian uncertainty on expected number of background events (effectively a prior)
bstat - estimated "statistical" gaussian uncertainty on expected number of background events (also effectively a prior)
K - signal efficiency scaling factor
"""
#bsystot = np.sqrt(self.bsys**2 + self.bstat**2) # assume priors are independent
siglike = logpoissonlike(n,self.sK*s*(1+dels*self.ssys)+self.b*(1+delb*self.bsystot)) # poisson signal + background log likelihood
#Need to change the scaling of the prior to match the simulated data.
#Makes no difference to inferences.
Pdels = pymc.normal_like(dels,0,1) #+ 0.5*np.log(2*np.pi) #standard normal gaussian log prior on dels
Pdelb = pymc.normal_like(delb,0,1) #+ 0.5*np.log(2*np.pi) #standard normal gaussian log prior on delb
if siglike + Pdels + Pdelb < -1e200:
print dels, delb
print siglike,Pdels,Pdelb, self.sK*s*(1+dels*self.ssys)+self.b*(1+delb*self.bsystot)
raise
return siglike + Pdels + Pdelb
def plot_ratio_analysis(
data_samples=(100, ), dataset_samples=(100, ), datasets=100):
x, y = np.meshgrid(data_samples, dataset_samples)
z = np.empty(x.shape, dtype=np.float)
for i, data_sample in enumerate(data_samples):
for j, dataset_sample in enumerate(dataset_samples):
data = np.random.randn(x[j, i])
errors = []
sl_sum = 0
pt_sum = 0
for rep in range(1, 200):
# Chose two random mu pts
mu1 = (np.random.rand() - .5) * 3
mu2 = (np.random.rand() - .5) * 3
# Evaluate true likelihood
pt1 = pm.normal_like(data, mu=mu1, tau=1)
pt2 = pm.normal_like(data, mu=mu2, tau=1)
ptr = pt1 / pt2
pt_sum += pt1
pt_sum += pt2
#print ptr
# Evaluate synth likelihood
ps1 = synth_likelihood(data,
mu1,
1,
dataset_samples=y[j, i],
samples=datasets)
ps2 = synth_likelihood(data,
mu2,
1,
dataset_samples=y[j, i],
samples=datasets)
sl_sum += ps1
sl_sum += ps2
pts = ps1 / ps2
#print pts
errors.append((pts - ptr)**2)
print pt_sum
print sl_sum
z[j, i] = np.mean(errors)
print x[j, i], y[j, i], z[j, i]
print x
print y
print z
cont = plt.contourf(x, y, z)
plt.colorbar(cont)
plt.xlabel('Number of samples per dataset')
plt.ylabel('Size of input data.')
def plot_erroranalysis(
data_samples=(10, ), dataset_samples=(10, ), datasets=200):
x = dataset_samples
y = np.empty(x.shape, dtype=np.float)
for data_sample in data_samples:
data = np.random.randn(data_sample)
for i, dataset_sample in enumerate(dataset_samples):
errors = []
sl_sum = 0
pt_sum = 0
for rep in range(1, 400):
# Chose two random mu pts
mu1 = 0
mu2 = (np.random.rand() - .5)
# Evaluate true likelihood
pt1 = pm.normal_like(data, mu=mu1, tau=1**-2)
pt2 = pm.normal_like(data, mu=mu2, tau=1**-2)
ptr = pt1 / pt2
pt_sum += pt1
pt_sum += pt2
#print ptr
# Evaluate synth likelihood
ps1 = synth_likelihood(data,
mu1,
1,
dataset_samples=x[i],
samples=datasets)
ps2 = synth_likelihood(data,
mu2,
1,
dataset_samples=x[i],
samples=datasets)
sl_sum += ps1
sl_sum += ps2
pts = ps1 / ps2
#print pts
errors.append((pts - ptr)**2)
print pt_sum
print sl_sum
y[i] = np.mean(errors)
plt.plot(x, y, label='%i' % data_sample)
plt.xlabel('Number of samples per dataset')
plt.ylabel('MSE')
plt.legend()
def X(value=X_true, K=K, A=A, mu = mu_x_init, tau = tau_x_init):
"""Autoregression"""
# Initial data
logp=normal_like(value[:K], mu, tau)
# Difference equation
for i in xrange(K,T):
logp += normal_like(value[i], sum(A[:K]*value[i-K:i]), 1.)
return logp
def test_states_missing():
""" Test that the state sequence step function properly handles missing
observations.
"""
np.random.seed(2352523)
model_true = simple_state_seq_model()
trans_mat_true = model_true['trans_mat_obs']
mu_true = model_true['mu'].value
states_true = model_true['states_rv'].value
y_true = model_true['y_rv'].value
N_obs_half = model_true['N_obs'] // 2
y_mask = np.arange(model_true['N_obs']) > N_obs_half
y_obs = np.ma.masked_array(y_true, mask=y_mask)
model_test = simple_state_seq_model(y_obs=y_obs)
mcmc_step = pymc.MCMC(model_test)
mcmc_step.draw_from_prior()
mcmc_step.use_step_method(HMMStatesStep, model_test['states_rv'])
(states_step, ) = mcmc_step.step_method_dict[model_test['states_rv']]
assert isinstance(states_step, HMMStatesStep)
#
# First, let's check that the logp function is working.
# In this case, that also means missing values were forward-filled.
#
ind = np.arange(np.alen(y_obs))
ind[y_obs.mask] = 0
y_logps_0_true = np.array([
pymc.normal_like(y, model_test['mu_vals'][0], 100)
for t, y in enumerate(y_obs)
])
y_logps_0_true[y_obs.mask] = 0.
y_logps_1_true = np.array([
pymc.normal_like(y, model_test['mu_vals'][1], 100)
for t, y in enumerate(y_obs)
])
y_logps_1_true[y_obs.mask] = 0.
states_step.compute_y_logp()
y_logps_est = states_step.y_logp_vals
assert_allclose(y_logps_est[0], y_logps_0_true)
assert_allclose(y_logps_est[1], y_logps_1_true)
mcmc_step.sample(2 * model_true['N_obs'])
assert_hpd(mcmc_step.states_rv, states_true, alpha=0.1)
def X(value=X_true, K=K, A=A, mu = mu_x_init, tau = tau_x_init):
"""Autoregression"""
# Initial data
logp=normal_like(value[:K], mu, tau)
# Difference equation
for i in xrange(K,T):
logp += normal_like(value[i], sum(A[:K]*value[i-K:i]), 1.)
return logp
def X_obs(pi=pi, sigma=sigma, value=X):
logp = mc.normal_like(pl.array(value).ravel(),
(pl.ones([N,J*T])*pl.array(pi).ravel()).ravel(),
(pl.ones([N,J*T])*pl.array(sigma).ravel()).ravel()**-2)
return logp
logp = pl.zeros(N)
for n in range(N):
logp[n] = mc.normal_like(pl.array(value[n]).ravel(),
pl.array(pi+beta).ravel(),
pl.array(sigma).ravel()**-2)
return mc.flib.logsum(logp - pl.log(N))
def test_states_trans_steps():
"""Test sampling of mixture states and transition matrices
exclusively and simultaneously. I.e. no regression terms/means
or variances to estimate, only the state sequence and transition
probability matrix.
"""
np.random.seed(2352523)
model_true = simple_state_trans_model()
trans_mat_true = model_true['trans_mat_rv'].value
mu_true = model_true['mu'].value
states_true = model_true['states_rv'].value
y_obs = model_true['y_rv'].value
model_test = simple_state_trans_model(y_obs=y_obs)
mcmc_step = pymc.MCMC(model_test)
mcmc_step.draw_from_prior()
mcmc_step.use_step_method(HMMStatesStep, mcmc_step.states_rv)
(states_step, ) = mcmc_step.step_method_dict[mcmc_step.states_rv]
assert isinstance(states_step, HMMStatesStep)
mcmc_step.use_step_method(TransProbMatStep, mcmc_step.trans_mat_rv)
(trans_mat_step, ) = mcmc_step.step_method_dict[mcmc_step.trans_mat_rv]
assert isinstance(trans_mat_step, TransProbMatStep)
#
# First, let's check that the logp function is working.
#
y_logps_0_true = np.array([
pymc.normal_like(y_obs[t], model_test['mu_vals'][0], 100)
for t in xrange(model_test['N_obs'])
])
y_logps_1_true = np.array([
pymc.normal_like(y_obs[t], model_test['mu_vals'][1], 100)
for t in xrange(model_test['N_obs'])
])
states_step.compute_y_logp()
y_logps_est = states_step.y_logp_vals
assert_allclose(y_logps_est[0], y_logps_0_true)
assert_allclose(y_logps_est[1], y_logps_1_true)
mcmc_step.sample(2000)
assert_hpd(mcmc_step.states_rv, states_true, alpha=0.1)
assert_hpd(mcmc_step.trans_mat_rv, trans_mat_true, alpha=0.1)
def X_obs(pi=pi, sigma=sigma, value=X):
logp = mc.normal_like(
pl.array(value).ravel(),
(pl.ones([N, J * T]) * pl.array(pi).ravel()).ravel(),
(pl.ones([N, J * T]) * pl.array(sigma).ravel()).ravel()**-2)
return logp
logp = pl.zeros(N)
for n in range(N):
logp[n] = mc.normal_like(
pl.array(value[n]).ravel(),
pl.array(pi + beta).ravel(),
pl.array(sigma).ravel()**-2)
return mc.flib.logsum(logp - pl.log(N))
def plot_ratio_analysis(data_samples=(100,), dataset_samples=(100,), datasets=100):
x, y = np.meshgrid(data_samples, dataset_samples)
z = np.empty(x.shape, dtype=np.float)
for i, data_sample in enumerate(data_samples):
for j, dataset_sample in enumerate(dataset_samples):
data = np.random.randn(x[j, i])
errors = []
sl_sum = 0
pt_sum = 0
for rep in range(1, 200):
# Chose two random mu pts
mu1 = (np.random.rand()-.5) * 3
mu2 = (np.random.rand()-.5) * 3
# Evaluate true likelihood
pt1 = pm.normal_like(data, mu=mu1, tau=1)
pt2 = pm.normal_like(data, mu=mu2, tau=1)
ptr = pt1 / pt2
pt_sum += pt1
pt_sum += pt2
#print ptr
# Evaluate synth likelihood
ps1 = synth_likelihood(data, mu1, 1, dataset_samples=y[j, i], samples=datasets)
ps2 = synth_likelihood(data, mu2, 1, dataset_samples=y[j, i], samples=datasets)
sl_sum += ps1
sl_sum += ps2
pts = ps1 / ps2
#print pts
errors.append((pts - ptr)**2)
print pt_sum
print sl_sum
z[j, i] = np.mean(errors)
print x[j, i], y[j,i], z[j, i]
print x
print y
print z
cont = plt.contourf(x, y, z)
plt.colorbar(cont)
plt.xlabel('Number of samples per dataset')
plt.ylabel('Size of input data.')
def logdoublenormal(x,mean,sigmaP,sigmaM):
#mean is measured value
#x is computed theory value
#sigmaP and sigmaM are distances from mean to upper and lower 1 sigma (68%)
#confidence limits.
if x==None: return -1e300
if x>=mean:
tauP = 1./sigmaP**2
#need to remove the normalisation factor so we get the same normalisation
#for each half of the likelihood.
loglike = pymc.normal_like(x,mean,tauP) - pymc.normal_like(mean,mean,tauP)
if x<mean:
tauM = 1./sigmaM**2
loglike = pymc.normal_like(x,mean,tauM) - pymc.normal_like(mean,mean,tauM)
return loglike
def obs(f=rate_stoch,
age_indices=age_indices,
age_weights=age_weights,
value=d_val,
tau=1./(d_se)**2):
f_i = dismod3.utils.rate_for_range(f, age_indices, age_weights)
return mc.normal_like(value, f_i, tau)
def x(N=N, mu=moo, tau=tau, n=n, value=np.log(data)):
k = N-n
dev = (value[0]-mu)*np.sqrt(tau)
out = gammaln(N+1) - gammaln(k) + (k-1)*np.log(pm.utils.normcdf(dev)) + pm.normal_like(value, mu, tau)
if np.isnan(out):
raise ValueError
return out
def obs(value=data.y,
i_obs=i_obs,
mu=mu,
sigma_explained=sigma_explained,
sigma_e=sigma_e):
return mc.normal_like(value[i_obs], mu[i_obs],
1. / (sigma_explained[i_obs]**2. + sigma_e**-2.))
def obs(f=rate_stoch,
age_indices=age_indices,
age_weights=age_weights,
value=d_val,
tau=1. / (d_se)**2):
f_i = dismod3.utils.rate_for_range(f, age_indices, age_weights)
return mc.normal_like(value, f_i, tau)
def covariate_constraint(mu=vars['mu_age'], alpha=vars['alpha'], beta=vars['beta'],
U_all=U_all,
X_sex_max=X_sex_max,
X_sex_min=X_sex_min,
lower=np.log(model.parameters[name]['level_bounds']['lower']),
upper=np.log(model.parameters[name]['level_bounds']['upper'])):
log_mu_max = np.log(mu.max())
log_mu_min = np.log(mu.min())
alpha = np.array([float(x) for x in alpha])
if len(alpha) > 0:
for U_i in U_all:
log_mu_max += max(0, alpha[U_i].max())
log_mu_min += min(0, alpha[U_i].min())
# this estimate is too crude, and is causing problems
#if len(beta) > 0:
# log_mu_max += np.sum(np.maximum(X_max*beta, X_min*beta))
# log_mu_min += np.sum(np.minimum(X_max*beta, X_min*beta))
# but leaving out the sex effect results in strange problems, too
log_mu_max += X_sex_max*float(beta[sex_index])
log_mu_min += X_sex_min*float(beta[sex_index])
lower_violation = min(0., log_mu_min - lower)
upper_violation = max(0., log_mu_max - upper)
return mc.normal_like([lower_violation, upper_violation], 0., 1.e-6**-2)
def get_likelihood_M0(map_M0, x, pwr, sigma, tau, obstype):
A0 = get_variables_M0(map_M0)
A0 = curve_fit_M0(x, pwr, A0, sigma)
if obstype == '.logiobs':
return pymc.normal_like(pwr, get_spectrum_M0(x, A0), tau)
else:
return pymc.lognormal_like(pwr, get_spectrum_M0(x, A0), tau)
def get_likelihood_M2(map_M2, x, pwr, sigma, tau, obstype):
A2 = get_variables_M2(map_M2)
A2 = curve_fit_M2(x, pwr, A2, sigma)
if obstype == '.logiobs':
return pymc.normal_like(pwr, get_spectrum_M2(x, A2), tau)
else:
return pymc.lognormal_like(pwr, get_spectrum_M2(x, A2), tau)
def get_likelihood_M1(map_M1, x, pwr, sigma, tau, obstype):
A1 = get_variables_M1(map_M1)
A1 = curve_fit_M1(x, pwr, A1, sigma)
if obstype == '.logiobs':
return pymc.normal_like(pwr, get_spectrum_M1(x, A1), tau)
else:
return pymc.lognormal_like(pwr, get_spectrum_M1(x, A1), tau)
def model(params=params,
vars=vars,
paramnames=paramnames,
filters=filters,
value=1.0):
# Set the parameters in the model
for i, param in enumerate(paramnames):
if debug:
print("setting ", param, " to ", params[i])
self.model.parameters[param] = params[i]
logp = 0
numpts = 0
for i, f in enumerate(filters):
mod, err, mask = self.model(f, self.sn.data[f].MJD)
m = mask * self.sn.data[f].mask
if not np.sometrue(m):
continue
numpts += np.sum(m)
tau = np.power(vars[i] + np.power(self.sn.data[f].e_mag, 2),
-1)
logp += pymc.normal_like(self.sn.data[f].mag[m], mod[m],
tau[m])
#if numpts < len(paramnames):
# return -np.inf
return logp
def mixture(value=1., gamma=gamma, pi=[0.2, 0.8], mu=[-2., 3.],
sigma=[0.01, 0.01]):
"""
The log probability of a mixture of normal densities.
:param value: The point of evaluation.
:type value : float
:param gamma: The parameter characterizing the SMC one-parameter
family.
:type gamma : float
:param pi : The weights of the components.
:type pi : 1D :class:`numpy.ndarray`
:param mu : The mean of each component.
:type mu : 1D :class:`numpy.ndarray`
:param sigma: The standard deviation of each component.
:type sigma : 1D :class:`numpy.ndarray`
"""
# Make sure everything is a numpy array
pi = np.array(pi)
mu = np.array(mu)
sigma = np.array(sigma)
# The number of components in the mixture
n = pi.shape[0]
# pymc.normal_like requires the precision not the variance:
tau = np.sqrt(1. / sigma ** 2)
# The following looks a little bit awkward because of the need for
# numerical stability:
p = np.log(pi)
p += np.array([pymc.normal_like(value, mu[i], tau[i])
for i in range(n)])
p = math.fsum(np.exp(p))
# logp should never be negative, but it can be zero...
if p <= 0.:
return -np.inf
return gamma * math.log(p)
def deriv_sign_rate(f=rate,
age_indices=age_indices,
tau=1.e14,
deriv=deriv,
sign=sign):
df = pl.diff(f[age_indices], deriv)
return mc.normal_like(pl.absolute(df) * (sign * df < 0), 0., tau)
def mixture(value=1., gamma=gamma, pi=[0.2, 0.8], mu=[-2., 3.],
sigma=[0.01, 0.01]):
"""
The log probability of a mixture of normal densities.
:param value: The point of evaluation.
:type value : float
:param gamma: The parameter characterizing the SMC one-parameter
family.
:type gamma : float
:param pi : The weights of the components.
:type pi : 1D :class:`numpy.ndarray`
:param mu : The mean of each component.
:type mu : 1D :class:`numpy.ndarray`
:param sigma: The standard deviation of each component.
:type sigma : 1D :class:`numpy.ndarray`
"""
# Make sure everything is a numpy array
pi = np.array(pi)
mu = np.array(mu)
sigma = np.array(sigma)
# The number of components in the mixture
n = pi.shape[0]
# pymc.normal_like requires the precision not the variance:
tau = np.sqrt(1. / sigma ** 2)
# The following looks a little bit awkward because of the need for
# numerical stability:
p = np.log(pi)
p += np.array([pymc.normal_like(value, mu[i], tau[i])
for i in range(n)])
p = math.fsum(np.exp(p))
# logp should never be negative, but it can be zero...
if p <= 0.:
return -np.inf
return gamma * math.log(p)
def obs(f=vars['rate_stoch'],
age_indices=age_indices,
age_weights=age_weights,
value=np.log(dm.value_per_1(d)),
tau=se**-2, data=d):
f_i = rate_for_range(f, age_indices, age_weights)
return mc.normal_like(value, np.log(f_i), tau)
def multi_normal_like(values, vec_mu, tau):
"""logp for multi normal"""
logp = 0
for i in range(len(vec_mu)):
logp += pm.normal_like(values[i, :], vec_mu[i], tau)
return logp
def multi_normal_like(values, vec_mu, tau):
"""logp for multi normal"""
logp = 0
for i in range(len(vec_mu)):
logp += pm.normal_like(values[i,:], vec_mu[i], tau)
return logp
def smooth_gamma(gamma=flat_gamma, knots=knots, tau=smoothing**-2):
# the following is to include a "noise floor" so that level value
# zero prior does not exert undue influence on age pattern
# smoothing
gamma = gamma.clip(pl.log(pl.exp(gamma).mean()/10.), pl.inf) # only include smoothing on values within 10x of mean
return mc.normal_like(pl.sqrt(pl.sum(pl.diff(gamma)**2 / pl.diff(knots))), 0, tau)
def covariate_constraint(
mu=vars['mu_age'],
alpha=vars['alpha'],
beta=vars['beta'],
U_all=U_all,
X_sex_max=X_sex_max,
X_sex_min=X_sex_min,
lower=np.log(model.parameters[name]['level_bounds']['lower']),
upper=np.log(model.parameters[name]['level_bounds']['upper'])):
log_mu_max = np.log(mu.max())
log_mu_min = np.log(mu.min())
alpha = np.array([float(x) for x in alpha])
if len(alpha) > 0:
for U_i in U_all:
log_mu_max += max(0, alpha[U_i].max())
log_mu_min += min(0, alpha[U_i].min())
# this estimate is too crude, and is causing problems
#if len(beta) > 0:
# log_mu_max += np.sum(np.maximum(X_max*beta, X_min*beta))
# log_mu_min += np.sum(np.minimum(X_max*beta, X_min*beta))
# but leaving out the sex effect results in strange problems, too
log_mu_max += X_sex_max * float(beta[sex_index])
log_mu_min += X_sex_min * float(beta[sex_index])
lower_violation = min(0., log_mu_min - lower)
upper_violation = max(0., log_mu_max - upper)
return mc.normal_like([lower_violation, upper_violation], 0.,
1.e-6**-2)
def plot_erroranalysis(data_samples=(10,), dataset_samples=(10,), datasets=200):
x = dataset_samples
y = np.empty(x.shape, dtype=np.float)
for data_sample in data_samples:
data = np.random.randn(data_sample)
for i, dataset_sample in enumerate(dataset_samples):
errors = []
sl_sum = 0
pt_sum = 0
for rep in range(1, 400):
# Chose two random mu pts
mu1 = 0
mu2 = (np.random.rand()-.5)
# Evaluate true likelihood
pt1 = pm.normal_like(data, mu=mu1, tau=1**-2)
pt2 = pm.normal_like(data, mu=mu2, tau=1**-2)
ptr = pt1 / pt2
pt_sum += pt1
pt_sum += pt2
#print ptr
# Evaluate synth likelihood
ps1 = synth_likelihood(data, mu1, 1, dataset_samples=x[i], samples=datasets)
ps2 = synth_likelihood(data, mu2, 1, dataset_samples=x[i], samples=datasets)
sl_sum += ps1
sl_sum += ps2
pts = ps1 / ps2
#print pts
errors.append((pts - ptr)**2)
print pt_sum
print sl_sum
y[i] = np.mean(errors)
plt.plot(x, y, label='%i' % data_sample)
plt.xlabel('Number of samples per dataset')
plt.ylabel('MSE')
plt.legend()
def obs(f=vars['rate_stoch'],
age_indices=age_indices,
age_weights=age_weights,
value=pl.log(dm.value_per_1(d)),
tau=se**-2,
data=d):
f_i = dismod3.utils.rate_for_range(f, age_indices, age_weights)
return mc.normal_like(value, pl.log(f_i), tau)
def get_likelihood_M0(map_M0, x, pwr, sigma, obstype):
tau = 1.0 / (sigma ** 2)
A0 = get_variables_M0(map_M0)[0:3]
A0 = curve_fit_M0(x, pwr, A0, sigma)
if obstype == '.logiobs':
return pymc.normal_like(pwr, get_spectrum_M0(x, A0), tau)
else:
return pymc.lognormal_like(pwr, get_spectrum_M0(x, A0), tau)
def r_like(b1=beta1_summ, n=obs_summ['n']):
"""Likelihood for correlation coefficients of summarized data"""
# Convert slope to r
rho = b1 * stdev_phe / stdev_iq
# Fisher transformation to allow for normality assumption
eps = np.arctan(rho) - np.arctan(obs_summ['correlation'])
# Difference should be mean-zero
return normal_like(eps, mu=np.zeros(len(n)), tau=n - 3)
def r_like(b1=beta1_summ, n=obs_summ['n']):
"""Likelihood for correlation coefficients of summarized data"""
# Convert slope to r
rho = b1*stdev_phe/stdev_iq
# Fisher transformation to allow for normality assumption
eps = np.arctan(rho) - np.arctan(obs_summ['correlation'])
# Difference should be mean-zero
return normal_like(eps, mu=np.zeros(len(n)), tau=n-3)
def test_states_single_step():
"""Test custom sampling of mixture states (in isolation).
"""
np.random.seed(2352523)
model_true = simple_state_seq_model()
trans_mat_true = model_true['trans_mat_obs']
mu_true = model_true['mu'].value
states_true = model_true['states_rv'].value
y_obs = model_true['y_rv'].value
model_test = simple_state_seq_model(y_obs=y_obs)
mcmc_step = pymc.MCMC(model_test)
mcmc_step.draw_from_prior()
mcmc_step.use_step_method(HMMStatesStep, model_test['states_rv'])
(states_step, ) = mcmc_step.step_method_dict[model_test['states_rv']]
assert isinstance(states_step, HMMStatesStep)
#
# First, let's check that the logp function is working.
#
y_logps_0_true = np.array([
pymc.normal_like(y_obs[t], model_test['mu_vals'][0], 100)
for t in xrange(model_test['N_obs'])
])
y_logps_1_true = np.array([
pymc.normal_like(y_obs[t], model_test['mu_vals'][1], 100)
for t in xrange(model_test['N_obs'])
])
states_step.compute_y_logp()
y_logps_est = states_step.y_logp_vals
assert_allclose(y_logps_est[0], y_logps_0_true)
assert_allclose(y_logps_est[1], y_logps_1_true)
mcmc_step.sample(2000)
assert_hpd(mcmc_step.states_rv, states_true, alpha=0.01)
def smooth_gamma(gamma=flat_gamma, knots=knots, tau=smoothing**-2):
# the following is to include a "noise floor" so that level value
# zero prior does not exert undue influence on age pattern
# smoothing
gamma = gamma.clip(
pl.log(pl.exp(gamma).mean() / 10.),
pl.inf) # only include smoothing on values within 10x of mean
return mc.normal_like(
pl.sqrt(pl.sum(pl.diff(gamma)**2 / pl.diff(knots))), 0, tau)
def yhat(x=self.x,
y=self.y,
ysigma=self.ysigma,
m=self.m,
sigma=self.intrinsic_sigma):
yhat = m * x
return np.sum([
pymc.normal_like(yhat[i], y[i], 1. / (ysigma[i]**2 + sigma**2))
for i in range(len(y))
])
def obs(value=logit_val, logit_se=logit_se,
X=covariates(d),
alpha=alpha, beta=beta, gamma=gamma, sigma=sigma,
age_indices=age_indices,
age_weights=age_weights):
# calculate study-specific rate function
mu = predict_logit_rate(X, alpha, beta, gamma)
mu_i = rate_for_range(mu, age_indices, age_weights)
tau_i = 1. / (sigma**2 + logit_se**2)
logp = mc.normal_like(x=value, mu=mu_i, tau=tau_i)
return logp
def model(params=params, vars=vars, paramnames=paramnames, filters=filters,
value=1.0):
# Set the parameters in the model
for i,param in enumerate(paramnames):
if debug:
print "setting ",param, " to ",params[i]
self.model.parameters[param] = params[i]
logp = 0
numpts = 0
for i,f in enumerate(filters):
mod,err,mask = self.model(f, self.sn.data[f].MJD)
m = mask*self.sn.data[f].mask
if not np.sometrue(m):
continue
numpts += np.sum(m)
tau = np.power(vars[i] + np.power(self.sn.data[f].e_mag,2),-1)
logp += pymc.normal_like(self.sn.data[f].mag[m],mod[m],tau[m])
#if numpts < len(paramnames):
# return -np.inf
return logp
def parent_similarity(mu_child=mu_child, mu_parent=mu_parent,
tau=tau):
log_mu_child = pl.log(mu_child.clip(offset, pl.inf))
log_mu_parent = pl.log(mu_parent.clip(offset, pl.inf))
return mc.normal_like(log_mu_child, log_mu_parent, tau)
def gamma_potential(gamma=gamma, mu_gamma=mu_gamma, tau_gamma=1./sigma_gamma[param_mesh]**2, param_mesh=param_mesh):
return mc.normal_like(gamma[param_mesh], mu_gamma[param_mesh], tau_gamma)
def gamma_potential(gamma=gamma, mu_gamma=mu_gamma, tau_gamma=1./sigma_gamma[param_mesh]**2, param_mesh=param_mesh):
return mc.normal_like(gamma[param_mesh], mu_gamma[param_mesh], tau_gamma)
def X_obs(value=X_obs_vals, mu=X, tau=1.):
"""Data"""
return normal_like(value, mu[::obs_interval], tau)
def delta_pot(delta=delta, mu=mu_delta, tau=sigma_delta**-2):
return mc.normal_like(delta, mu, tau)
def mu_potential(mu1=rate_vars['unbounded_rate'], mu2=rate_vars['rate_stoch']):
return mc.normal_like(mu1, mu2, .0001**-2)
def mu_potential(mu1=rate_vars['unbounded_rate'],
mu2=rate_vars['rate_stoch']):
return mc.normal_like(mu1, mu2, .0001**-2)
def alpha_potential(alpha=alpha[i], mu=old_alpha_i.parents['mu'], tau=old_alpha_i.parents['tau']):
return mc.normal_like(alpha, mu, tau)
def my_trunc_norm(value=value, mu=mu, tau=tau, a=a, b=b):
if a <= value <= b:
return mc.normal_like(value, mu, tau)
else:
return -np.inf
def alpha_potential(alpha=alpha[i], mu=old_alpha_i.parents['mu'], tau=old_alpha_i.parents['tau']):
return mc.normal_like(alpha, mu, tau)
def my_trunc_norm(value=value, mu=mu, tau=tau, a=a, b=b):
if a <= value <= b:
return mc.normal_like(value, mu, tau)
else:
return -np.inf
def emp_prior_potential(f=rate_stoch, mu=emp_prior["mu"], tau=1.0 / np.array(emp_prior["se"]) ** 2):
return mc.normal_like(f, mu, tau)
def smooth_across_regions(rate_list=rate_stochs):
logp = 0.
for ii in range(len(rate_list)):
for jj in range(ii+1, len(rate_list)):
logp += mc.normal_like(np.diff(np.log(rate_list[ii]))-np.diff(np.log(rate_list[jj])), 0., 1./(.1)**2)
return logp
def logp(value, theta2, y, rho):
mean = y[1] + rho * (theta1 - y[0])
var = 1. - rho ^ 2
return normal_like(value, mean, 1. / var)
def p_obs(value=p, pi=pi, sigma=sigma, s=s, p_zeta=p_zeta):
return mc.normal_like(
pl.log(value[~i_inf] + p_zeta),
pl.log(pi[~i_inf] + p_zeta),
1.0 / (sigma ** 2.0 + (s / (value + p_zeta))[~i_inf] ** 2.0),
)
def A(value=A_init, mu=-1.*ones(K_max,dtype=float), tau=ones(K_max,dtype=float)):
"""A ~ normal(mu, tau)"""
return normal_like(value, mu, tau)
def deriv_sign_rate(f=rate,
age_indices=age_indices,
tau=1.e14,
deriv=deriv, sign=sign):
df = pl.diff(f[age_indices], deriv)
return mc.normal_like(pl.absolute(df) * (sign * df < 0), 0., tau)
def y_i(value=y, mu=y_hat, tau=tau_y):
return pymc.normal_like(value, mu, tau)
def output(value=y, model_output=model_output, sigma=sigma, gamma=gamma):
return gamma * pm.normal_like(y, model_output, 1. / (sigma ** 2.))
def parent_similarity(mu_child=mu_child, mu_parent=mu_parent, tau=tau):
log_mu_child = np.log(mu_child.clip(offset, np.inf))
log_mu_parent = np.log(mu_parent.clip(offset, np.inf))
return mc.normal_like(log_mu_child, log_mu_parent, tau)