def step(self):
self.compute_y_logp()
t_last = 0
for stoch in self.state_seq:
t_end = t_last + np.alen(stoch.value)
time_range = xrange(t_last, t_end)
trans_mat = stoch.parents['trans_mat']
trans_mat = getattr(trans_mat, 'value', trans_mat)
P = np.column_stack((trans_mat, 1. - trans_mat.sum(axis=1)))
p0 = stoch.parents['p0']
p0 = getattr(p0, 'value', p0)
if p0 is None:
p0 = compute_steady_state(trans_mat)
p_run = p0
# Very inefficient forward pass:
for t in time_range:
logp_k_t = self.logp_filtered[t]
for k in xrange(stoch.K):
# This is the forward step (in log scale):
# p(S_t=k \mid y_{1:t}) \propto p(y_t \mid S_t=k) *
# p(S_t=k \mid y_{1:t-1})
logp_k_t[k] = self.y_logp_vals[k, t] +\
pymc.categorical_like(k, p_run)
# Here we normalize across k
logp_k_t -= reduce(np.logaddexp, logp_k_t)
# This computes p(S_{t+1} \mid y_{1:t})
p_run = np.dot(np.exp(logp_k_t), P)
np.exp(self.logp_filtered, out=self.p_filtered)
# An inefficient backward pass:
# Sample p(S_T \mid y_{1:T})
new_values = np.empty_like(stoch.value, dtype=stoch.value.dtype)
new_values[t_end-1] = pymc.rcategorical(self.p_filtered[t_end-1][:-1])
for t in xrange(t_end-2, t_last-1, -1):
# Now, sample p(S_t \mid S_{t+1}, y_{1:T}) via the relation
# p(S_t=j \mid S_{t+1}=k, y_{1:T}) \propto
# p(S_t=j \mid S_{t_1}=k, y_{1:t}) \propto
# p(S_{t+1}=k \mid S_t=j, y_{1:t}) * p(S_t=j \mid y_{1:t})
p_back = P[:, int(new_values[t + 1])] * self.p_filtered[t]
p_back /= p_back.sum()
new_values[t-t_last] = pymc.rcategorical(p_back[:-1])
stoch.value = new_values
t_last += np.alen(stoch.value)
def states_random(Ptrans=Ptrans, N_chain=N_chain):
P = np.column_stack((Ptrans, 1. - Ptrans.sum(axis=1)))
Pinit = unconditionalProbability(Ptrans)
states = np.empty(N_chain, dtype=np.uint8)
states[0] = pymc.rcategorical(Pinit)
for i in range(1, N_chain):
states[i] = pymc.rcategorical(P[states[i - 1]])
return states
def ages_and_data(N_exam, f_samp, correction_factor_array, age_lims):
"""Called by pred_samps. Simulates ages of survey participants and data given f."""
N_samp = len(f_samp)
N_age_samps = correction_factor_array.shape[1]
# Get samples for the age distribution at the observation points.
age_distribution = []
for i in xrange(N_samp):
l = age_lims[i]
age_distribution.append(S_trace[np.random.randint(S_trace.shape[0]), 0,
l[0]:l[1] + 1])
age_distribution[-1] /= np.sum(age_distribution[-1])
# Draw age for each individual, draw an age-correction profile for each location,
# compute probability of positive for each individual, see how many individuals are
# positive.
A = []
pos = []
for s in xrange(N_samp):
A.append(
np.array(pm.rcategorical(age_distribution[s], size=N_exam[s]),
dtype=int) + age_lims[s][0])
P_samp = pm.invlogit(f_samp[s].ravel(
)) * correction_factor_array[:, np.random.randint(N_age_samps)][A[-1]]
pos.append(pm.rbernoulli(P_samp))
return A, pos, age_distribution
def test_fixed_effect_priors():
model = data.ModelData()
# set prior on sex
parameters = dict(fixed_effects={'x_sex': dict(dist='TruncatedNormal', mu=1., sigma=.5, lower=-10, upper=10)})
# simulate normal data
n = 32.
sex_list = pl.array(['male', 'female', 'total'])
sex = sex_list[mc.rcategorical([.3, .3, .4], n)]
beta_true = dict(male=-1., total=0., female=1.)
pi_true = pl.exp([beta_true[s] for s in sex])
sigma_true = .05
p = mc.rnormal(pi_true, 1./sigma_true**2.)
model.input_data = pandas.DataFrame(dict(value=p, sex=sex))
model.input_data['area'] = 'all'
model.input_data['year_start'] = 2010
model.input_data['year_start'] = 2010
# create model and priors
vars = {}
vars.update(covariate_model.mean_covariate_model('test', 1, model.input_data, parameters, model,
'all', 'total', 'all'))
print vars['beta']
assert vars['beta'][0].parents['mu'] == 1.
def test_covariate_model_dispersion():
# simulate normal data
n = 100
model = data.ModelData()
model.hierarchy, model.output_template = data_simulation.small_output()
Z = mc.rcategorical([.5, 5.], n)
zeta_true = -.2
pi_true = .1
ess = 10000.*pl.ones(n)
eta_true = pl.log(50)
delta_true = 50 + pl.exp(eta_true)
p = mc.rnegative_binomial(pi_true*ess, delta_true*pl.exp(Z*zeta_true)) / ess
model.input_data = pandas.DataFrame(dict(value=p, z_0=Z))
model.input_data['area'] = 'all'
model.input_data['sex'] = 'total'
model.input_data['year_start'] = 2000
model.input_data['year_end'] = 2000
# create model and priors
vars = dict(mu=mc.Uninformative('mu_test', value=pi_true))
vars.update(covariate_model.mean_covariate_model('test', vars['mu'], model.input_data, {}, model, 'all', 'total', 'all'))
vars.update(covariate_model.dispersion_covariate_model('test', model.input_data, .1, 10.))
vars.update(rate_model.neg_binom_model('test', vars['pi'], vars['delta'], p, ess))
# fit model
m = mc.MCMC(vars)
m.sample(2)
def step(self):
# The right-hand sides for the linear constraints
self.rhs = dict(zip(self.constraint_offdiags,
[np.asarray(np.dot(pm.utils.value(od), self.g.value)).squeeze() for od in self.constraint_offdiags]))
for i in xrange(self.n):
try:
lb, ub, rhs = self.get_bounds(i)
except ConstraintError:
warnings.warn('Bounds could not be set, this element is very highly constrained')
continue
newgs = np.hstack((self.g.value[i], pm.rtruncnorm(0,1,lb,ub,size=self.n_draws)))
lpls = np.hstack((self.get_likelihood_only(), np.empty(self.n_draws)))
for j, newg in enumerate(newgs[1:]):
self.set_g_value(newg, i)
# The newgs are drawn from the prior, taking the canstraints into account, so
# accept them based on the 'likelihood children' only.
try:
lpls[j+1] = self.get_likelihood_only()
except pm.ZeroProbability:
lpls[j+1] = -np.inf
lpls -= pm.flib.logsum(lpls)
newg = newgs[pm.rcategorical(np.exp(lpls))]
self.set_g_value(newg, i)
for od in self.constraint_offdiags:
rhs[od] += np.asarray(pm.utils.value(od))[:,i].squeeze() * newg
self.rhs = rhs
def test_fixed_effect_priors():
model = dismod_mr.data.ModelData()
# set prior on sex
parameters = dict(
fixed_effects={
'x_sex':
dict(dist='TruncatedNormal', mu=1., sigma=.5, lower=-10, upper=10)
})
# simulate normal data
n = 32
sex_list = np.array(['male', 'female', 'total'])
sex = sex_list[mc.rcategorical([.3, .3, .4], n)]
beta_true = dict(male=-1., total=0., female=1.)
pi_true = np.exp([beta_true[s] for s in sex])
sigma_true = .05
p = mc.rnormal(pi_true, 1. / sigma_true**2.)
model.input_data = pd.DataFrame(dict(value=p, sex=sex))
model.input_data['area'] = 'all'
model.input_data['year_start'] = 2010
model.input_data['year_start'] = 2010
# create model and priors
vars = {}
vars.update(
dismod_mr.model.covariates.mean_covariate_model(
'test', 1, model.input_data, parameters, model, 'all', 'total',
'all'))
print(vars['beta'])
assert vars['beta'][0].parents['mu'] == 1.
def step(self):
x0 = np.copy(self.stochastic.value)
dx = pymc.rnormal(np.zeros(np.shape(x0)), self.proposal_tau)
logp = [self.logp_plus_loglike]
x_prime = [x0]
for direction in [-1, 1]:
for i in xrange(25):
delta = direction * np.exp(.1 * i) * dx
try:
self.stochastic.value = x0 + delta
logp.append(self.logp_plus_loglike)
x_prime.append(x0 + delta)
except pymc.ZeroProbability:
self.stochastic.value = x0
i = pymc.rcategorical(np.exp(np.array(logp) - pymc.flib.logsum(logp)))
self.stochastic.value = x_prime[i]
if i == 0:
self.rejected += 1
if self.verbose > 2:
print self._id + ' rejecting'
else:
self.accepted += 1
if self.verbose > 2:
print self._id + ' accepting'
def test_random_effect_priors():
model = dismod_mr.data.ModelData()
# set prior on sex
parameters = dict(random_effects={
'USA':
dict(dist='TruncatedNormal', mu=.1, sigma=.5, lower=-10, upper=10)
})
# simulate normal data
n = 32
area_list = np.array(['all', 'USA', 'CAN'])
area = area_list[mc.rcategorical([.3, .3, .4], n)]
alpha_true = dict(all=0., USA=.1, CAN=-.2)
pi_true = np.exp([alpha_true[a] for a in area])
sigma_true = .05
p = mc.rnormal(pi_true, 1. / sigma_true**2.)
model.input_data = pd.DataFrame(dict(value=p, area=area))
model.input_data['sex'] = 'male'
model.input_data['year_start'] = 2010
model.input_data['year_end'] = 2010
model.hierarchy.add_edge('all', 'USA')
model.hierarchy.add_edge('all', 'CAN')
# create model and priors
vars = {}
vars.update(
dismod_mr.model.covariates.mean_covariate_model(
'test', 1, model.input_data, parameters, model, 'all', 'total',
'all'))
print(vars['alpha'])
print(vars['alpha'][1].parents['mu'])
def step(self):
x0 = np.copy(self.stochastic.value)
dx = pymc.rnormal(np.zeros(np.shape(x0)), self.proposal_tau)
logp = [self.logp_plus_loglike]
x_prime = [x0]
for direction in [-1, 1]:
for i in xrange(25):
delta = direction*np.exp(.1*i)*dx
try:
self.stochastic.value = x0 + delta
logp.append(self.logp_plus_loglike)
x_prime.append(x0 + delta)
except pymc.ZeroProbability:
self.stochastic.value = x0
i = pymc.rcategorical(np.exp(np.array(logp) - pymc.flib.logsum(logp)))
self.stochastic.value = x_prime[i]
if i == 0:
self.rejected += 1
if self.verbose > 2:
print self._id + ' rejecting'
else:
self.accepted += 1
if self.verbose > 2:
print self._id + ' accepting'
def step(self):
x0 = self.value[self.n]
u = pymc.rnormal(np.zeros(self.N), 1.)
dx = np.dot(u, self.value)
self.stochastic.value = x0
logp = [self.logp_plus_loglike]
x_prime = [x0]
for direction in [-1, 1]:
for i in xrange(25):
delta = direction * np.exp(.1 * i) * dx
try:
self.stochastic.value = x0 + delta
logp.append(self.logp_plus_loglike)
x_prime.append(x0 + delta)
except pymc.ZeroProbability:
self.stochastic.value = x0
i = pymc.rcategorical(np.exp(np.array(logp) - pymc.flib.logsum(logp)))
self.value[self.n] = x_prime[i]
self.stochastic.value = x_prime[i]
if i == 0:
self.rejected += 1
if self.verbose > 2:
print self._id + ' rejecting'
else:
self.accepted += 1
if self.verbose > 2:
print self._id + ' accepting'
self.n += 1
if self.n == self.N:
self.n = 0
def test_random_effect_priors():
model = data.ModelData()
# set prior on sex
parameters = dict(random_effects={'USA': dict(dist='TruncatedNormal', mu=.1, sigma=.5, lower=-10, upper=10)})
# simulate normal data
n = 32.
area_list = pl.array(['all', 'USA', 'CAN'])
area = area_list[mc.rcategorical([.3, .3, .4], n)]
alpha_true = dict(all=0., USA=.1, CAN=-.2)
pi_true = pl.exp([alpha_true[a] for a in area])
sigma_true = .05
p = mc.rnormal(pi_true, 1./sigma_true**2.)
model.input_data = pandas.DataFrame(dict(value=p, area=area))
model.input_data['sex'] = 'male'
model.input_data['year_start'] = 2010
model.input_data['year_end'] = 2010
model.hierarchy.add_edge('all', 'USA')
model.hierarchy.add_edge('all', 'CAN')
# create model and priors
vars = {}
vars.update(covariate_model.mean_covariate_model('test', 1, model.input_data, parameters, model,
'all', 'total', 'all'))
print vars['alpha']
print vars['alpha'][1].parents['mu']
assert vars['alpha'][1].parents['mu'] == .1
def step(self):
x0 = self.value[self.n]
u = pm.rnormal(np.zeros(self.N), 1.)
dx = np.dot(u, self.value)
self.stochastic.value = x0
logp = [self.logp_plus_loglike]
x_prime = [x0]
for direction in [-1, 1]:
for i in xrange(25):
delta = direction*np.exp(.1*i)*dx
try:
self.stochastic.value = x0 + delta
logp.append(self.logp_plus_loglike)
x_prime.append(x0 + delta)
except pm.ZeroProbability:
self.stochastic.value = x0
i = pm.rcategorical(np.exp(np.array(logp) - pm.flib.logsum(logp)))
self.value[self.n] = x_prime[i]
self.stochastic.value = x_prime[i]
if i == 0:
self.rejected += 1
else:
self.accepted += 1
self.n += 1
if self.n == self.N:
self.n = 0
def test_covariate_model_dispersion():
# simulate normal data
n = 100
model = dismod_mr.data.ModelData()
model.hierarchy, model.output_template = dismod_mr.testing.data_simulation.small_output()
Z = mc.rcategorical([.5, 5.], n)
zeta_true = -.2
pi_true = .1
ess = 10000.*np.ones(n)
eta_true = np.log(50)
delta_true = 50 + np.exp(eta_true)
p = mc.rnegative_binomial(pi_true*ess, delta_true*np.exp(Z*zeta_true)) / ess
model.input_data = pd.DataFrame(dict(value=p, z_0=Z))
model.input_data['area'] = 'all'
model.input_data['sex'] = 'total'
model.input_data['year_start'] = 2000
model.input_data['year_end'] = 2000
# create model and priors
variables = dict(mu=mc.Uninformative('mu_test', value=pi_true))
variables.update(dismod_mr.model.covariates.mean_covariate_model('test', variables['mu'], model.input_data, {},
model, 'all', 'total', 'all'))
variables.update(dismod_mr.model.covariates.dispersion_covariate_model('test', model.input_data, .1, 10.))
variables.update(dismod_mr.model.likelihood.neg_binom('test', variables['pi'], variables['delta'], p, ess))
# fit model
m = mc.MCMC(variables)
m.sample(2)
def sim_ordinal(I, J, K, alpha=None, beta=None):
# test input params here
Is = range(I)
Js = range(J)
Ks = range(K)
N = I * J
Ns = range(N)
if alpha == None:
alpha = alloc_mat(K, K)
for k1 in Ks:
for k2 in Ks:
alpha[k1][k2] = max(1,(K + (0.5 if k1 == k2 else 0) \
- abs(k1 - k2))**4)
if beta == None:
beta = alloc_vec(K, 2.0)
# simulated params
beta = alloc_vec(K, 2.0)
prevalence = pymc.rdirichlet(beta).tolist()
prevalence.append(1.0 - sum(prevalence)) # complete
category = []
for i in Is:
category.append(pymc.rcategorical(prevalence).tolist())
accuracy = alloc_tens(J, K, K)
for j in Js:
for k in Ks:
accuracy[j][k] = pymc.rdirichlet(alpha[k]).tolist()
accuracy[j][k].append(1.0 - sum(accuracy[j][k]))
# simulated data
item = []
anno = []
label = []
for i in Is:
for j in Js:
item.append(i)
anno.append(j)
label.append(pymc.rcategorical(accuracy[j][category[i]]).tolist())
N = len(item)
return (prevalence, category, accuracy, item, anno, label)
def step(self):
self._index += 1
if self._index % self.sleep_interval == 0:
v = pm.value(self.v)
m = pm.value(self.m)
val = self.stochastic.value
lp = pm.logp_of_set(self.other_children)
# Choose a direction along which to step.
dirvec = np.random.normal(size=self.n)
dirvec /= np.sqrt(np.sum(dirvec**2))
# Orthogonalize
orthoproj = gramschmidt(dirvec)
scaled_orthoproj = v*orthoproj.T
pck = np.dot(dirvec, scaled_orthoproj.T)
kck = np.linalg.inv(np.dot(scaled_orthoproj,orthoproj))
pckkck = np.dot(pck,kck)
# Figure out conditional variance
condvar = np.dot(dirvec, dirvec*v) - np.dot(pck, pckkck)
# condmean = np.dot(dirvec, m) + np.dot(pckkck, np.dot(orthoproj.T, (val-m)))
# Compute slice of log-probability surface
tries = np.linspace(-4*np.sqrt(condvar), 4*np.sqrt(condvar), 501)
lps = 0*tries
for i in xrange(len(tries)):
new_val = val + tries[i]*dirvec
self.stochastic.value = new_val
try:
lps[i] = self.f_fr.logp + self.stochastic.logp
except:
lps[i] = -np.inf
if np.all(np.isinf(lps)):
raise ValueError, 'All -inf.'
lps -= pm.flib.logsum(lps[True-np.isinf(lps)])
ps = np.exp(lps)
index = pm.rcategorical(ps)
new_val = val + tries[index]*dirvec
self.stochastic.value = new_val
try:
lpp = pm.logp_of_set(self.other_children)
if np.log(np.random.random()) < lpp - lp:
self.accepted += 1
else:
self.stochastic.value = val
self.rejected += 1
except pm.ZeroProbability:
self.stochastic.value = val
self.rejected += 1
self.logp_plus_loglike
def test_covariate_model_sim_w_hierarchy():
n = 50
# setup hierarchy
hierarchy, output_template = data_simulation.small_output()
# simulate normal data
area_list = np.array(['all', 'USA', 'CAN'])
area = area_list[mc.rcategorical([.3, .3, .4], n)]
sex_list = np.array(['male', 'female', 'total'])
sex = sex_list[mc.rcategorical([.3, .3, .4], n)]
year = np.array(mc.runiform(1990, 2010, n), dtype=int)
alpha_true = dict(all=0., USA=.1, CAN=-.2)
pi_true = np.exp([alpha_true[a] for a in area])
sigma_true = .05 * np.ones_like(pi_true)
p = mc.rnormal(pi_true, 1. / sigma_true**2.)
model = dismod_mr.data.ModelData()
model.input_data = pd.DataFrame(
dict(value=p, area=area, sex=sex, year_start=year, year_end=year))
model.hierarchy, model.output_template = hierarchy, output_template
# create model and priors
vars = {}
vars.update(
dismod_mr.model.covariates.mean_covariate_model(
'test', 1, model.input_data, {}, model, 'all', 'total', 'all'))
vars.update(
dismod_mr.model.likelihood.normal('test', vars['pi'], 0., p,
sigma_true))
# fit model
m = mc.MCMC(vars)
m.sample(2)
assert 'sex' not in vars['U']
assert 'x_sex' in vars['X']
assert len(vars['beta']) == 1
def step(self):
direction = self.choose_direction(norm=False)
current_value = self.get_current_value()
x_prime = np.vstack((current_value, np.outer(np.linspace(-self.xprime_sds,self.xprime_sds,self.xprime_n),direction) + current_value))
lps = np.empty(self.xprime_n+1)
lps[0] = self.logp_plus_loglike
for i in xrange(self.xprime_n):
self.set_current_value(x_prime[i+1])
lps[i+1] = self.logp_plus_loglike
next_value = x_prime[pm.rcategorical(np.exp(lps-pm.flib.logsum(lps)))]
self.set_current_value(next_value)
self.store(next_value)
def test_covariate_model_sim_w_hierarchy():
n = 50
# setup hierarchy
hierarchy, output_template = data_simulation.small_output()
# simulate normal data
area_list = pl.array(['all', 'USA', 'CAN'])
area = area_list[mc.rcategorical([.3, .3, .4], n)]
sex_list = pl.array(['male', 'female', 'total'])
sex = sex_list[mc.rcategorical([.3, .3, .4], n)]
year = pl.array(mc.runiform(1990, 2010, n), dtype=int)
alpha_true = dict(all=0., USA=.1, CAN=-.2)
pi_true = pl.exp([alpha_true[a] for a in area])
sigma_true = .05*pl.ones_like(pi_true)
p = mc.rnormal(pi_true, 1./sigma_true**2.)
model = data.ModelData()
model.input_data = pandas.DataFrame(dict(value=p, area=area, sex=sex, year_start=year, year_end=year))
model.hierarchy, model.output_template = hierarchy, output_template
# create model and priors
vars = {}
vars.update(covariate_model.mean_covariate_model('test', 1, model.input_data, {}, model,
'all', 'total', 'all'))
vars.update(rate_model.normal_model('test', vars['pi'], 0., p, sigma_true))
# fit model
m = mc.MCMC(vars)
m.sample(2)
assert 'sex' not in vars['U']
assert 'x_sex' in vars['X']
assert len(vars['beta']) == 1
def states_random(trans_mat, N_obs, p0, size=None):
""" Samples states from an HMM.
Parameters
==========
trans_mat: ndarray
A transition probability matrix for K-many states with
shape (K, K-1).
N_obs: int
Number of observations.
p0: ndarray
Initial state probabilities. If `None`, the steady state
is computed and used.
size: int
Not used.
Returns
=======
A ndarray of length N_obs containing sampled state numbers/indices/labels.
"""
P = np.column_stack((trans_mat, 1. - trans_mat.sum(axis=1)))
p = p0
if p is None:
p = compute_steady_state(trans_mat)
states = np.empty(N_obs, dtype=np.uint8)
states[0] = pymc.rcategorical(p)
for i in range(1, N_obs):
states[i] = pymc.rcategorical(P[int(states[i - 1])])
return states
def step(self):
direction = self.choose_direction(norm=False)
current_value = self.get_current_value()
x_prime = np.vstack(
(current_value,
np.outer(
np.linspace(-self.xprime_sds, self.xprime_sds, self.xprime_n),
direction) + current_value))
lps = np.empty(self.xprime_n + 1)
lps[0] = self.logp_plus_loglike
for i in xrange(self.xprime_n):
self.set_current_value(x_prime[i + 1])
lps[i + 1] = self.logp_plus_loglike
next_value = x_prime[pm.rcategorical(np.exp(lps -
pm.flib.logsum(lps)))]
self.set_current_value(next_value)
self.store(next_value)
def SIR_simplex_sample(mu, tau, cutoff, sum_val, N, N_proposals=1000, N_samps=1000):
"""
Returns raw log-weights, indices chosen and SIR samples for sets of N draws
from a truncated lognormal distribution, conditioned so that their sum is
equal to sum_val.
This SIR algorithm will fail miserably unless sum_val is relatively likely
given N and the parameters of the lognormal distribution.
:Parameters:
- mu : float
The mean parameter.
- tau : float
The precision parameter.
- cutoff : float
The truncation value.
- sum_val : float
The sum that is being conditioned on.
- N : integer
The number of variates in each vector
- N_proposals : integer
The number of vectors to propose.
- N_samps : integer
The number of vectors to return.
"""
# Draw samples, compute missing values, evaluate log-weights.
samps = np.exp(geto_truncnorm(mu, tau, log(cutoff), (N-1,N_proposals)))
last_vals = sum_val - np.sum(samps,axis=0)
weights = np.array([pm.lognormal_like(last_val_now, mu, tau) for last_val_now in last_vals])
# Check that there are at least some positive weights.
where_pos = np.where(weights>-1e308)
if len(where_pos[0])==0:
raise RuntimeError, 'No weights are positive. You have used a shitty value for N.'
# Normalize and exponentiate log-weights.
weights[where(last_vals>cutoff)]=-np.Inf
weights -= log_sum(weights)
# Append missing values to samples.
samps = np.vstack((samps,last_vals))
# Slice and return.
ind=np.array(pm.rcategorical(p=np.exp(weights),size=N_samps),dtype=int)
return weights, ind, samps[:,ind]
def gmm_model(data, K, mu_0=0.0, alpha_0=0.1, beta_0=0.1, alpha=1.0):
"""
K: number of component
n_samples: number of n_samples
n_features: number of features
mu_0: prior mean of mu_k
alpha_0: alpha of Inverse Gamma tau_k
beta_0: beta of Inverse Gamma tau_k
alpha = prior of dirichlet distribution phi_0
latent variable:
phi_0: shape = (K-1, ), dirichlet distribution
phi: shape = (K, ), add K-th value back to phi_0
z: shape = (n_samples, ), Categorical distribution, z[k] is component indicator
mu_k: shape = (K, n_features), normal distribution, mu_k[k] is mean of k-th component
tau_k : shape = (K, n_features), inverse-gamma distribution, tau_k[k] is variance of k-th component
"""
n_samples, n_features = data.shape
# latent variables
tau_k = pm.InverseGamma('tau_k',
alpha_0 * np.ones((K, n_features)),
beta_0 * np.ones((K, n_features)),
value=beta_0 * np.ones((K, n_features)))
mu_k = pm.Normal('mu_k',
np.ones((K, n_features)) * mu_0,
tau_k,
value=np.ones((K, n_features)) * mu_0)
phi_0 = pm.Dirichlet('phi_0', theta=np.ones(K) * alpha)
@pm.deterministic(dtype=float)
def phi(value=np.ones(K) / K, phi_0=phi_0):
val = np.hstack((phi_0, (1 - np.sum(phi_0))))
return val
z = pm.Categorical('z',
p=phi,
value=pm.rcategorical(np.ones(K) / K, size=n_samples))
# observed variables
x = pm.Normal('x', mu=mu_k[z], tau=tau_k[z], value=data, observed=True)
return pm.Model([mu_k, tau_k, phi_0, phi, z, x])
def gmm_model(data, K, mu_0=0.0, alpha_0=0.1, beta_0=0.1, alpha=1.0):
"""
K: number of component
n_samples: number of n_samples
n_features: number of features
mu_0: prior mean of mu_k
alpha_0: alpha of Inverse Gamma tau_k
beta_0: beta of Inverse Gamma tau_k
alpha = prior of dirichlet distribution phi_0
latent variable:
phi_0: shape = (K-1, ), dirichlet distribution
phi: shape = (K, ), add K-th value back to phi_0
z: shape = (n_samples, ), Categorical distribution, z[k] is component indicator
mu_k: shape = (K, n_features), normal distribution, mu_k[k] is mean of k-th component
tau_k : shape = (K, n_features), inverse-gamma distribution, tau_k[k] is variance of k-th component
"""
n_samples, n_features = data.shape
# latent variables
tau_k = pm.InverseGamma(
"tau_k",
alpha_0 * np.ones((K, n_features)),
beta_0 * np.ones((K, n_features)),
value=beta_0 * np.ones((K, n_features)),
)
mu_k = pm.Normal("mu_k", np.ones((K, n_features)) * mu_0, tau_k, value=np.ones((K, n_features)) * mu_0)
phi_0 = pm.Dirichlet("phi_0", theta=np.ones(K) * alpha)
@pm.deterministic(dtype=float)
def phi(value=np.ones(K) / K, phi_0=phi_0):
val = np.hstack((phi_0, (1 - np.sum(phi_0))))
return val
z = pm.Categorical("z", p=phi, value=pm.rcategorical(np.ones(K) / K, size=n_samples))
# observed variables
x = pm.Normal("x", mu=mu_k[z], tau=tau_k[z], value=data, observed=True)
return pm.Model([mu_k, tau_k, phi_0, phi, z, x])
def ages_and_data(N_exam, f_samp, correction_factor_array, age_lims):
"""Called by pred_samps. Simulates ages of survey participants and data given f."""
N_samp = len(f_samp)
N_age_samps = correction_factor_array.shape[1]
# Get samples for the age distribution at the observation points.
age_distribution = []
for i in xrange(N_samp):
l = age_lims[i]
age_distribution.append(S_trace[np.random.randint(S_trace.shape[0]),0,l[0]:l[1]+1])
age_distribution[-1] /= np.sum(age_distribution[-1])
# Draw age for each individual, draw an age-correction profile for each location,
# compute probability of positive for each individual, see how many individuals are
# positive.
A = []
pos = []
for s in xrange(N_samp):
A.append(np.array(pm.rcategorical(age_distribution[s], size=N_exam[s]),dtype=int) + age_lims[s][0])
P_samp = pm.invlogit(f_samp[s].ravel())*correction_factor_array[:,np.random.randint(N_age_samps)][A[-1]]
pos.append(pm.rbernoulli(P_samp))
return A, pos, age_distribution
reload(dismod3) # set font book_graphics.set_font() pi_true = scipy.interpolate.interp1d([0, 20, 40, 60, 100], [.4, .425, .6, .5, .4]) beta_true = .3 delta_true = 50. N = 30 # start with a simple model with N rows of data model = data_simulation.simple_model(N) # set covariate to 0/1 values randomly model.input_data['x_cov'] = 1. * mc.rcategorical([.5, .5], size=N) # record the true age-specific rates model.ages = pl.arange(0, 101, 1) model.pi_age_true = pi_true(model.ages) # choose age groups randomly age_width = pl.zeros(N) age_mid = mc.runiform(age_width/2, 100-age_width/2, size=N) age_start = pl.array(age_mid - age_width/2, dtype=int) age_end = pl.array(age_mid + age_width/2, dtype=int) model.input_data['age_start'] = age_start model.input_data['age_end'] = age_end
def validate_covariate_model_re(N=500, delta_true=.15, pi_true=.01, sigma_true = [.1,.1,.1,.1,.1], ess=1000):
## set simulation parameters
import dismod3
import simplejson as json
model = data.ModelData.from_gbd_jsons(json.loads(dismod3.disease_json.DiseaseJson().to_json()))
model.parameters['p']['parameter_age_mesh'] = [0, 100]
model.parameters['p']['heterogeneity'] = 'Slightly' # ensure heterogeneity is slightly
area_list = []
for sr in sorted(model.hierarchy.successors('all')):
area_list.append(sr)
for r in sorted(model.hierarchy.successors(sr)):
area_list.append(r)
area_list += sorted(model.hierarchy.successors(r))[:5]
area_list = pl.array(area_list)
## generate simulation data
model.input_data = pandas.DataFrame(index=range(N))
initialize_input_data(model.input_data)
alpha = alpha_true_sim(model, area_list, sigma_true)
# choose observed prevalence values
model.input_data['effective_sample_size'] = ess
model.input_data['area'] = area_list[mc.rcategorical(pl.ones(len(area_list)) / float(len(area_list)), N)]
model.input_data['true'] = pl.nan
for i, a in model.input_data['area'].iteritems():
model.input_data['true'][i] = pi_true * pl.exp(pl.sum([alpha[n] for n in nx.shortest_path(model.hierarchy, 'all', a) if n in alpha]))
n = model.input_data['effective_sample_size']
p = model.input_data['true']
model.input_data['value'] = mc.rnegative_binomial(n*p, delta_true*n*p) / n
## Then fit the model and compare the estimates to the truth
model.vars = {}
model.vars['p'] = data_model.data_model('p', model, 'p', 'all', 'total', 'all', None, None, None)
model.map, model.mcmc = fit_model.fit_data_model(model.vars['p'], iter=20000, burn=10000, thin=10, tune_interval=100)
graphics.plot_one_ppc(model.vars['p'], 'p')
graphics.plot_convergence_diag(model.vars)
pl.show()
model.input_data['mu_pred'] = model.vars['p']['p_pred'].stats()['mean']
model.input_data['sigma_pred'] = model.vars['p']['p_pred'].stats()['standard deviation']
add_quality_metrics(model.input_data)
model.alpha = pandas.DataFrame(index=[n for n in nx.traversal.dfs_preorder_nodes(model.hierarchy)])
model.alpha['true'] = pandas.Series(dict(alpha))
model.alpha['mu_pred'] = pandas.Series([n.stats()['mean'] for n in model.vars['p']['alpha']], index=model.vars['p']['U'].columns)
model.alpha['sigma_pred'] = pandas.Series([n.stats()['standard deviation'] for n in model.vars['p']['alpha']], index=model.vars['p']['U'].columns)
add_quality_metrics(model.alpha)
print '\nalpha'
print model.alpha.dropna()
model.sigma = pandas.DataFrame(dict(true=sigma_true))
model.sigma['mu_pred'] = [n.stats()['mean'] for n in model.vars['p']['sigma_alpha']]
model.sigma['sigma_pred']=[n.stats()['standard deviation'] for n in model.vars['p']['sigma_alpha']]
add_quality_metrics(model.sigma)
print 'sigma_alpha'
print model.sigma
model.results = dict(param=[], bias=[], mare=[], mae=[], pc=[])
add_to_results(model, 'sigma')
model.delta = pandas.DataFrame(dict(true=[delta_true]))
model.delta['mu_pred'] = pl.exp(model.vars['p']['eta'].trace()).mean()
model.delta['sigma_pred'] = pl.exp(model.vars['p']['eta'].trace()).std()
add_quality_metrics(model.delta)
print 'delta'
print model.delta
add_to_results(model, 'delta')
print '\ndata prediction bias: %.5f, MARE: %.3f, coverage: %.2f' % (model.input_data['abs_err'].mean(),
pl.median(pl.absolute(model.input_data['rel_err'].dropna())),
model.input_data['covered?'].mean())
print 'effect prediction MAE: %.3f, coverage: %.2f' % (pl.median(pl.absolute(model.alpha['abs_err'].dropna())),
model.alpha.dropna()['covered?'].mean())
add_to_results(model, 'input_data')
add_to_results(model, 'alpha')
model.results = pandas.DataFrame(model.results)
return model
def validate_ai_re(N=500, delta_true=.15, sigma_true=[.1,.1,.1,.1,.1], pi_true=quadratic, smoothness='Moderately', heterogeneity='Slightly'):
## generate simulated data
a = pl.arange(0, 101, 1)
pi_age_true = pi_true(a)
import dismod3
import simplejson as json
model = data.ModelData.from_gbd_jsons(json.loads(dismod3.disease_json.DiseaseJson().to_json()))
gbd_hierarchy = model.hierarchy
model = data_simulation.simple_model(N)
model.hierarchy = gbd_hierarchy
model.parameters['p']['parameter_age_mesh'] = range(0, 101, 10)
model.parameters['p']['smoothness'] = dict(amount=smoothness)
model.parameters['p']['heterogeneity'] = heterogeneity
age_start = pl.array(mc.runiform(0, 100, size=N), dtype=int)
age_end = pl.array(mc.runiform(age_start, 100, size=N), dtype=int)
age_weights = pl.ones_like(a)
sum_pi_wt = pl.cumsum(pi_age_true*age_weights)
sum_wt = pl.cumsum(age_weights*1.)
p = (sum_pi_wt[age_end] - sum_pi_wt[age_start]) / (sum_wt[age_end] - sum_wt[age_start])
# correct cases where age_start == age_end
i = age_start == age_end
if pl.any(i):
p[i] = pi_age_true[age_start[i]]
model.input_data['age_start'] = age_start
model.input_data['age_end'] = age_end
model.input_data['effective_sample_size'] = mc.runiform(100, 10000, size=N)
from validate_covariates import alpha_true_sim
area_list = pl.array(['all', 'super-region_3', 'north_africa_middle_east', 'EGY', 'KWT', 'IRN', 'IRQ', 'JOR', 'SYR'])
alpha = alpha_true_sim(model, area_list, sigma_true)
print alpha
model.input_data['true'] = pl.nan
model.input_data['area'] = area_list[mc.rcategorical(pl.ones(len(area_list)) / float(len(area_list)), N)]
for i, a in model.input_data['area'].iteritems():
model.input_data['true'][i] = p[i] * pl.exp(pl.sum([alpha[n] for n in nx.shortest_path(model.hierarchy, 'all', a) if n in alpha]))
p = model.input_data['true']
n = model.input_data['effective_sample_size']
model.input_data['value'] = mc.rnegative_binomial(n*p, delta_true*n*p) / n
## Then fit the model and compare the estimates to the truth
model.vars = {}
model.vars['p'] = data_model.data_model('p', model, 'p', 'north_africa_middle_east', 'total', 'all', None, None, None)
#model.map, model.mcmc = fit_model.fit_data_model(model.vars['p'], iter=1005, burn=500, thin=5, tune_interval=100)
model.map, model.mcmc = fit_model.fit_data_model(model.vars['p'], iter=10000, burn=5000, thin=25, tune_interval=100)
graphics.plot_one_ppc(model.vars['p'], 'p')
graphics.plot_convergence_diag(model.vars)
graphics.plot_one_type(model, model.vars['p'], {}, 'p')
pl.plot(range(101), pi_age_true, 'r:', label='Truth')
pl.legend(fancybox=True, shadow=True, loc='upper left')
pl.show()
model.input_data['mu_pred'] = model.vars['p']['p_pred'].stats()['mean']
model.input_data['sigma_pred'] = model.vars['p']['p_pred'].stats()['standard deviation']
data_simulation.add_quality_metrics(model.input_data)
model.delta = pandas.DataFrame(dict(true=[delta_true]))
model.delta['mu_pred'] = pl.exp(model.vars['p']['eta'].trace()).mean()
model.delta['sigma_pred'] = pl.exp(model.vars['p']['eta'].trace()).std()
data_simulation.add_quality_metrics(model.delta)
model.alpha = pandas.DataFrame(index=[n for n in nx.traversal.dfs_preorder_nodes(model.hierarchy)])
model.alpha['true'] = pandas.Series(dict(alpha))
model.alpha['mu_pred'] = pandas.Series([n.stats()['mean'] for n in model.vars['p']['alpha']], index=model.vars['p']['U'].columns)
model.alpha['sigma_pred'] = pandas.Series([n.stats()['standard deviation'] for n in model.vars['p']['alpha']], index=model.vars['p']['U'].columns)
model.alpha = model.alpha.dropna()
data_simulation.add_quality_metrics(model.alpha)
model.sigma = pandas.DataFrame(dict(true=sigma_true))
model.sigma['mu_pred'] = [n.stats()['mean'] for n in model.vars['p']['sigma_alpha']]
model.sigma['sigma_pred']=[n.stats()['standard deviation'] for n in model.vars['p']['sigma_alpha']]
data_simulation.add_quality_metrics(model.sigma)
print 'delta'
print model.delta
print '\ndata prediction bias: %.5f, MARE: %.3f, coverage: %.2f' % (model.input_data['abs_err'].mean(),
pl.median(pl.absolute(model.input_data['rel_err'].dropna())),
model.input_data['covered?'].mean())
model.mu = pandas.DataFrame(dict(true=pi_age_true,
mu_pred=model.vars['p']['mu_age'].stats()['mean'],
sigma_pred=model.vars['p']['mu_age'].stats()['standard deviation']))
data_simulation.add_quality_metrics(model.mu)
data_simulation.initialize_results(model)
data_simulation.add_to_results(model, 'delta')
data_simulation.add_to_results(model, 'mu')
data_simulation.add_to_results(model, 'input_data')
data_simulation.add_to_results(model, 'alpha')
data_simulation.add_to_results(model, 'sigma')
data_simulation.finalize_results(model)
print model.results
return model
def validate_consistent_model_sim(N=500,
delta_true=.5,
true=dict(i=quadratic,
f=constant,
r=constant)):
types = pl.array(['i', 'r', 'f', 'p'])
## generate simulated data
model = data_simulation.simple_model(N)
model.input_data['effective_sample_size'] = 1.
model.input_data['value'] = 0.
for t in types:
model.parameters[t]['parameter_age_mesh'] = range(0, 101, 20)
sim = consistent_model.consistent_model(model, 'all', 'total', 'all', {})
for t in 'irf':
for i, k_i in enumerate(sim[t]['knots']):
sim[t]['gamma'][i].value = pl.log(true[t](k_i))
age_start = pl.array(mc.runiform(0, 100, size=N), dtype=int)
age_end = pl.array(mc.runiform(age_start, 100, size=N), dtype=int)
data_type = types[mc.rcategorical(pl.ones(len(types), dtype=float) /
float(len(types)),
size=N)]
a = pl.arange(101)
age_weights = pl.ones_like(a)
sum_wt = pl.cumsum(age_weights)
p = pl.zeros(N)
for t in types:
mu_t = sim[t]['mu_age'].value
sum_mu_wt = pl.cumsum(mu_t * age_weights)
p_t = (sum_mu_wt[age_end] - sum_mu_wt[age_start]) / (sum_wt[age_end] -
sum_wt[age_start])
# correct cases where age_start == age_end
i = age_start == age_end
if pl.any(i):
p_t[i] = mu_t[age_start[i]]
# copy part into p
p[data_type == t] = p_t[data_type == t]
n = mc.runiform(100, 10000, size=N)
model.input_data['data_type'] = data_type
model.input_data['age_start'] = age_start
model.input_data['age_end'] = age_end
model.input_data['effective_sample_size'] = n
model.input_data['true'] = p
model.input_data['value'] = mc.rnegative_binomial(n * p,
delta_true * n * p) / n
# coarse knot spacing for fast testing
for t in types:
model.parameters[t]['parameter_age_mesh'] = range(0, 101, 20)
## Then fit the model and compare the estimates to the truth
model.vars = {}
model.vars = consistent_model.consistent_model(model, 'all', 'total',
'all', {})
model.map, model.mcmc = fit_model.fit_consistent_model(model.vars,
iter=10000,
burn=5000,
thin=25,
tune_interval=100)
graphics.plot_convergence_diag(model.vars)
graphics.plot_fit(model, model.vars, {}, {})
for i, t in enumerate('i r f p rr pf'.split()):
pl.subplot(2, 3, i + 1)
pl.plot(a, sim[t]['mu_age'].value, 'w-', label='Truth', linewidth=2)
pl.plot(a, sim[t]['mu_age'].value, 'r-', label='Truth', linewidth=1)
#graphics.plot_one_type(model, model.vars['p'], {}, 'p')
#pl.legend(fancybox=True, shadow=True, loc='upper left')
pl.show()
model.input_data['mu_pred'] = 0.
model.input_data['sigma_pred'] = 0.
for t in types:
model.input_data['mu_pred'][
data_type == t] = model.vars[t]['p_pred'].stats()['mean']
model.input_data['sigma_pred'][data_type == t] = model.vars['p'][
'p_pred'].stats()['standard deviation']
data_simulation.add_quality_metrics(model.input_data)
model.delta = pandas.DataFrame(
dict(true=[delta_true for t in types if t != 'rr']))
model.delta['mu_pred'] = [
pl.exp(model.vars[t]['eta'].trace()).mean() for t in types if t != 'rr'
]
model.delta['sigma_pred'] = [
pl.exp(model.vars[t]['eta'].trace()).std() for t in types if t != 'rr'
]
data_simulation.add_quality_metrics(model.delta)
print 'delta'
print model.delta
print '\ndata prediction bias: %.5f, MARE: %.3f, coverage: %.2f' % (
model.input_data['abs_err'].mean(),
pl.median(pl.absolute(model.input_data['rel_err'].dropna())),
model.input_data['covered?'].mean())
model.mu = pandas.DataFrame()
for t in types:
model.mu = model.mu.append(pandas.DataFrame(
dict(true=sim[t]['mu_age'].value,
mu_pred=model.vars[t]['mu_age'].stats()['mean'],
sigma_pred=model.vars[t]['mu_age'].stats()
['standard deviation'])),
ignore_index=True)
data_simulation.add_quality_metrics(model.mu)
print '\nparam prediction bias: %.5f, MARE: %.3f, coverage: %.2f' % (
model.mu['abs_err'].mean(),
pl.median(pl.absolute(
model.mu['rel_err'].dropna())), model.mu['covered?'].mean())
print
data_simulation.initialize_results(model)
data_simulation.add_to_results(model, 'delta')
data_simulation.add_to_results(model, 'mu')
data_simulation.add_to_results(model, 'input_data')
data_simulation.finalize_results(model)
print model.results
return model
def validate_consistent_re(N=500, delta_true=.15, sigma_true=[.1,.1,.1,.1,.1],
true=dict(i=quadratic, f=constant, r=constant)):
types = pl.array(['i', 'r', 'f', 'p'])
## generate simulated data
model = data_simulation.simple_model(N)
model.input_data['effective_sample_size'] = 1.
model.input_data['value'] = 0.
# coarse knot spacing for fast testing
for t in types:
model.parameters[t]['parameter_age_mesh'] = range(0, 101, 20)
sim = consistent_model.consistent_model(model, 'all', 'total', 'all', {})
for t in 'irf':
for i, k_i in enumerate(sim[t]['knots']):
sim[t]['gamma'][i].value = pl.log(true[t](k_i))
age_start = pl.array(mc.runiform(0, 100, size=N), dtype=int)
age_end = pl.array(mc.runiform(age_start, 100, size=N), dtype=int)
data_type = types[mc.rcategorical(pl.ones(len(types), dtype=float) / float(len(types)), size=N)]
a = pl.arange(101)
age_weights = pl.ones_like(a)
sum_wt = pl.cumsum(age_weights)
p = pl.zeros(N)
for t in types:
mu_t = sim[t]['mu_age'].value
sum_mu_wt = pl.cumsum(mu_t*age_weights)
p_t = (sum_mu_wt[age_end] - sum_mu_wt[age_start]) / (sum_wt[age_end] - sum_wt[age_start])
# correct cases where age_start == age_end
i = age_start == age_end
if pl.any(i):
p_t[i] = mu_t[age_start[i]]
# copy part into p
p[data_type==t] = p_t[data_type==t]
# add covariate shifts
import dismod3
import simplejson as json
gbd_model = data.ModelData.from_gbd_jsons(json.loads(dismod3.disease_json.DiseaseJson().to_json()))
model.hierarchy = gbd_model.hierarchy
from validate_covariates import alpha_true_sim
area_list = pl.array(['all', 'super-region_3', 'north_africa_middle_east', 'EGY', 'KWT', 'IRN', 'IRQ', 'JOR', 'SYR'])
alpha = {}
for t in types:
alpha[t] = alpha_true_sim(model, area_list, sigma_true)
print json.dumps(alpha, indent=2)
model.input_data['area'] = area_list[mc.rcategorical(pl.ones(len(area_list)) / float(len(area_list)), N)]
for i, a in model.input_data['area'].iteritems():
t = data_type[i]
p[i] = p[i] * pl.exp(pl.sum([alpha[t][n] for n in nx.shortest_path(model.hierarchy, 'all', a) if n in alpha]))
n = mc.runiform(100, 10000, size=N)
model.input_data['data_type'] = data_type
model.input_data['age_start'] = age_start
model.input_data['age_end'] = age_end
model.input_data['effective_sample_size'] = n
model.input_data['true'] = p
model.input_data['value'] = mc.rnegative_binomial(n*p, delta_true) / n
# coarse knot spacing for fast testing
for t in types:
model.parameters[t]['parameter_age_mesh'] = range(0, 101, 20)
## Then fit the model and compare the estimates to the truth
model.vars = {}
model.vars = consistent_model.consistent_model(model, 'all', 'total', 'all', {})
#model.map, model.mcmc = fit_model.fit_consistent_model(model.vars, iter=101, burn=0, thin=1, tune_interval=100)
model.map, model.mcmc = fit_model.fit_consistent_model(model.vars, iter=10000, burn=5000, thin=25, tune_interval=100)
graphics.plot_convergence_diag(model.vars)
graphics.plot_fit(model, model.vars, {}, {})
for i, t in enumerate('i r f p rr pf'.split()):
pl.subplot(2, 3, i+1)
pl.plot(range(101), sim[t]['mu_age'].value, 'w-', label='Truth', linewidth=2)
pl.plot(range(101), sim[t]['mu_age'].value, 'r-', label='Truth', linewidth=1)
pl.show()
model.input_data['mu_pred'] = 0.
model.input_data['sigma_pred'] = 0.
for t in types:
model.input_data['mu_pred'][data_type==t] = model.vars[t]['p_pred'].stats()['mean']
model.input_data['sigma_pred'][data_type==t] = model.vars[t]['p_pred'].stats()['standard deviation']
data_simulation.add_quality_metrics(model.input_data)
model.delta = pandas.DataFrame(dict(true=[delta_true for t in types if t != 'rr']))
model.delta['mu_pred'] = [pl.exp(model.vars[t]['eta'].trace()).mean() for t in types if t != 'rr']
model.delta['sigma_pred'] = [pl.exp(model.vars[t]['eta'].trace()).std() for t in types if t != 'rr']
data_simulation.add_quality_metrics(model.delta)
model.alpha = pandas.DataFrame()
model.sigma = pandas.DataFrame()
for t in types:
alpha_t = pandas.DataFrame(index=[n for n in nx.traversal.dfs_preorder_nodes(model.hierarchy)])
alpha_t['true'] = pandas.Series(dict(alpha[t]))
alpha_t['mu_pred'] = pandas.Series([n.stats()['mean'] for n in model.vars[t]['alpha']], index=model.vars[t]['U'].columns)
alpha_t['sigma_pred'] = pandas.Series([n.stats()['standard deviation'] for n in model.vars[t]['alpha']], index=model.vars[t]['U'].columns)
alpha_t['type'] = t
model.alpha = model.alpha.append(alpha_t.dropna(), ignore_index=True)
sigma_t = pandas.DataFrame(dict(true=sigma_true))
sigma_t['mu_pred'] = [n.stats()['mean'] for n in model.vars[t]['sigma_alpha']]
sigma_t['sigma_pred'] = [n.stats()['standard deviation'] for n in model.vars[t]['sigma_alpha']]
model.sigma = model.sigma.append(sigma_t.dropna(), ignore_index=True)
data_simulation.add_quality_metrics(model.alpha)
data_simulation.add_quality_metrics(model.sigma)
print 'delta'
print model.delta
print '\ndata prediction bias: %.5f, MARE: %.3f, coverage: %.2f' % (model.input_data['abs_err'].mean(),
pl.median(pl.absolute(model.input_data['rel_err'].dropna())),
model.input_data['covered?'].mean())
model.mu = pandas.DataFrame()
for t in types:
model.mu = model.mu.append(pandas.DataFrame(dict(true=sim[t]['mu_age'].value,
mu_pred=model.vars[t]['mu_age'].stats()['mean'],
sigma_pred=model.vars[t]['mu_age'].stats()['standard deviation'])),
ignore_index=True)
data_simulation.add_quality_metrics(model.mu)
print '\nparam prediction bias: %.5f, MARE: %.3f, coverage: %.2f' % (model.mu['abs_err'].mean(),
pl.median(pl.absolute(model.mu['rel_err'].dropna())),
model.mu['covered?'].mean())
print
data_simulation.initialize_results(model)
data_simulation.add_to_results(model, 'delta')
data_simulation.add_to_results(model, 'mu')
data_simulation.add_to_results(model, 'input_data')
data_simulation.add_to_results(model, 'alpha')
data_simulation.add_to_results(model, 'sigma')
data_simulation.finalize_results(model)
print model.results
return model
def validate_ai_re(N=500,
delta_true=.15,
sigma_true=[.1, .1, .1, .1, .1],
pi_true=quadratic,
smoothness='Moderately',
heterogeneity='Slightly'):
## generate simulated data
a = pl.arange(0, 101, 1)
pi_age_true = pi_true(a)
import dismod3
import simplejson as json
model = data.ModelData.from_gbd_jsons(
json.loads(dismod3.disease_json.DiseaseJson().to_json()))
gbd_hierarchy = model.hierarchy
model = data_simulation.simple_model(N)
model.hierarchy = gbd_hierarchy
model.parameters['p']['parameter_age_mesh'] = range(0, 101, 10)
model.parameters['p']['smoothness'] = dict(amount=smoothness)
model.parameters['p']['heterogeneity'] = heterogeneity
age_start = pl.array(mc.runiform(0, 100, size=N), dtype=int)
age_end = pl.array(mc.runiform(age_start, 100, size=N), dtype=int)
age_weights = pl.ones_like(a)
sum_pi_wt = pl.cumsum(pi_age_true * age_weights)
sum_wt = pl.cumsum(age_weights * 1.)
p = (sum_pi_wt[age_end] - sum_pi_wt[age_start]) / (sum_wt[age_end] -
sum_wt[age_start])
# correct cases where age_start == age_end
i = age_start == age_end
if pl.any(i):
p[i] = pi_age_true[age_start[i]]
model.input_data['age_start'] = age_start
model.input_data['age_end'] = age_end
model.input_data['effective_sample_size'] = mc.runiform(100, 10000, size=N)
from validate_covariates import alpha_true_sim
area_list = pl.array([
'all', 'super-region_3', 'north_africa_middle_east', 'EGY', 'KWT',
'IRN', 'IRQ', 'JOR', 'SYR'
])
alpha = alpha_true_sim(model, area_list, sigma_true)
print alpha
model.input_data['true'] = pl.nan
model.input_data['area'] = area_list[mc.rcategorical(
pl.ones(len(area_list)) / float(len(area_list)), N)]
for i, a in model.input_data['area'].iteritems():
model.input_data['true'][i] = p[i] * pl.exp(
pl.sum([
alpha[n] for n in nx.shortest_path(model.hierarchy, 'all', a)
if n in alpha
]))
p = model.input_data['true']
n = model.input_data['effective_sample_size']
model.input_data['value'] = mc.rnegative_binomial(n * p,
delta_true * n * p) / n
## Then fit the model and compare the estimates to the truth
model.vars = {}
model.vars['p'] = data_model.data_model('p', model, 'p',
'north_africa_middle_east',
'total', 'all', None, None, None)
#model.map, model.mcmc = fit_model.fit_data_model(model.vars['p'], iter=1005, burn=500, thin=5, tune_interval=100)
model.map, model.mcmc = fit_model.fit_data_model(model.vars['p'],
iter=10000,
burn=5000,
thin=25,
tune_interval=100)
graphics.plot_one_ppc(model.vars['p'], 'p')
graphics.plot_convergence_diag(model.vars)
graphics.plot_one_type(model, model.vars['p'], {}, 'p')
pl.plot(range(101), pi_age_true, 'r:', label='Truth')
pl.legend(fancybox=True, shadow=True, loc='upper left')
pl.show()
model.input_data['mu_pred'] = model.vars['p']['p_pred'].stats()['mean']
model.input_data['sigma_pred'] = model.vars['p']['p_pred'].stats(
)['standard deviation']
data_simulation.add_quality_metrics(model.input_data)
model.delta = pandas.DataFrame(dict(true=[delta_true]))
model.delta['mu_pred'] = pl.exp(model.vars['p']['eta'].trace()).mean()
model.delta['sigma_pred'] = pl.exp(model.vars['p']['eta'].trace()).std()
data_simulation.add_quality_metrics(model.delta)
model.alpha = pandas.DataFrame(
index=[n for n in nx.traversal.dfs_preorder_nodes(model.hierarchy)])
model.alpha['true'] = pandas.Series(dict(alpha))
model.alpha['mu_pred'] = pandas.Series(
[n.stats()['mean'] for n in model.vars['p']['alpha']],
index=model.vars['p']['U'].columns)
model.alpha['sigma_pred'] = pandas.Series(
[n.stats()['standard deviation'] for n in model.vars['p']['alpha']],
index=model.vars['p']['U'].columns)
model.alpha = model.alpha.dropna()
data_simulation.add_quality_metrics(model.alpha)
model.sigma = pandas.DataFrame(dict(true=sigma_true))
model.sigma['mu_pred'] = [
n.stats()['mean'] for n in model.vars['p']['sigma_alpha']
]
model.sigma['sigma_pred'] = [
n.stats()['standard deviation'] for n in model.vars['p']['sigma_alpha']
]
data_simulation.add_quality_metrics(model.sigma)
print 'delta'
print model.delta
print '\ndata prediction bias: %.5f, MARE: %.3f, coverage: %.2f' % (
model.input_data['abs_err'].mean(),
pl.median(pl.absolute(model.input_data['rel_err'].dropna())),
model.input_data['covered?'].mean())
model.mu = pandas.DataFrame(
dict(true=pi_age_true,
mu_pred=model.vars['p']['mu_age'].stats()['mean'],
sigma_pred=model.vars['p']['mu_age'].stats()
['standard deviation']))
data_simulation.add_quality_metrics(model.mu)
data_simulation.initialize_results(model)
data_simulation.add_to_results(model, 'delta')
data_simulation.add_to_results(model, 'mu')
data_simulation.add_to_results(model, 'input_data')
data_simulation.add_to_results(model, 'alpha')
data_simulation.add_to_results(model, 'sigma')
data_simulation.finalize_results(model)
print model.results
return model
def validate_covariate_model_re(N=500,
delta_true=.15,
pi_true=.01,
sigma_true=[.1, .1, .1, .1, .1],
ess=1000):
## set simulation parameters
import dismod3
import simplejson as json
model = data.ModelData.from_gbd_jsons(
json.loads(dismod3.disease_json.DiseaseJson().to_json()))
model.parameters['p']['parameter_age_mesh'] = [0, 100]
model.parameters['p'][
'heterogeneity'] = 'Slightly' # ensure heterogeneity is slightly
area_list = []
for sr in sorted(model.hierarchy.successors('all')):
area_list.append(sr)
for r in sorted(model.hierarchy.successors(sr)):
area_list.append(r)
area_list += sorted(model.hierarchy.successors(r))[:5]
area_list = pl.array(area_list)
## generate simulation data
model.input_data = pandas.DataFrame(index=range(N))
initialize_input_data(model.input_data)
alpha = alpha_true_sim(model, area_list, sigma_true)
# choose observed prevalence values
model.input_data['effective_sample_size'] = ess
model.input_data['area'] = area_list[mc.rcategorical(
pl.ones(len(area_list)) / float(len(area_list)), N)]
model.input_data['true'] = pl.nan
for i, a in model.input_data['area'].iteritems():
model.input_data['true'][i] = pi_true * pl.exp(
pl.sum([
alpha[n] for n in nx.shortest_path(model.hierarchy, 'all', a)
if n in alpha
]))
n = model.input_data['effective_sample_size']
p = model.input_data['true']
model.input_data['value'] = mc.rnegative_binomial(n * p,
delta_true * n * p) / n
## Then fit the model and compare the estimates to the truth
model.vars = {}
model.vars['p'] = data_model.data_model('p', model, 'p', 'all', 'total',
'all', None, None, None)
model.map, model.mcmc = fit_model.fit_data_model(model.vars['p'],
iter=20000,
burn=10000,
thin=10,
tune_interval=100)
graphics.plot_one_ppc(model.vars['p'], 'p')
graphics.plot_convergence_diag(model.vars)
pl.show()
model.input_data['mu_pred'] = model.vars['p']['p_pred'].stats()['mean']
model.input_data['sigma_pred'] = model.vars['p']['p_pred'].stats(
)['standard deviation']
add_quality_metrics(model.input_data)
model.alpha = pandas.DataFrame(
index=[n for n in nx.traversal.dfs_preorder_nodes(model.hierarchy)])
model.alpha['true'] = pandas.Series(dict(alpha))
model.alpha['mu_pred'] = pandas.Series(
[n.stats()['mean'] for n in model.vars['p']['alpha']],
index=model.vars['p']['U'].columns)
model.alpha['sigma_pred'] = pandas.Series(
[n.stats()['standard deviation'] for n in model.vars['p']['alpha']],
index=model.vars['p']['U'].columns)
add_quality_metrics(model.alpha)
print '\nalpha'
print model.alpha.dropna()
model.sigma = pandas.DataFrame(dict(true=sigma_true))
model.sigma['mu_pred'] = [
n.stats()['mean'] for n in model.vars['p']['sigma_alpha']
]
model.sigma['sigma_pred'] = [
n.stats()['standard deviation'] for n in model.vars['p']['sigma_alpha']
]
add_quality_metrics(model.sigma)
print 'sigma_alpha'
print model.sigma
model.results = dict(param=[], bias=[], mare=[], mae=[], pc=[])
add_to_results(model, 'sigma')
model.delta = pandas.DataFrame(dict(true=[delta_true]))
model.delta['mu_pred'] = pl.exp(model.vars['p']['eta'].trace()).mean()
model.delta['sigma_pred'] = pl.exp(model.vars['p']['eta'].trace()).std()
add_quality_metrics(model.delta)
print 'delta'
print model.delta
add_to_results(model, 'delta')
print '\ndata prediction bias: %.5f, MARE: %.3f, coverage: %.2f' % (
model.input_data['abs_err'].mean(),
pl.median(pl.absolute(model.input_data['rel_err'].dropna())),
model.input_data['covered?'].mean())
print 'effect prediction MAE: %.3f, coverage: %.2f' % (
pl.median(pl.absolute(model.alpha['abs_err'].dropna())),
model.alpha.dropna()['covered?'].mean())
add_to_results(model, 'input_data')
add_to_results(model, 'alpha')
model.results = pandas.DataFrame(model.results)
return model
def _untilt_sample(x,i,s,a):
if isinstance(i, int): # make random sample here (this might be a bad idea)
i = pm.rcategorical(np.ones(x.shape[0])/x.shape[0],size=i)
return ba.untilt(x[i,:],s,a)
def bic_norm_hmm_init_params(y, X_matrices):
""" Initialize a normal HMM regression mixture with a GMM mixture
of a BIC determined number of states. Starting with an initial
set of design matrices, this function searches for the best number
of additional constant states to add to the model.
Parameters
==========
y: pandas.DataFrame or pandas.Series
Time-indexed vector of observations.
X_matrices: list of pandas.DataFrame
Collection of design matrices for each initial state.
Returns
=======
init_params:
A `NormalHMMInitialParams` object.
"""
N_states = len(X_matrices)
from sklearn import mixture
lowest_bic = np.infty
bic = []
for n_components in range(N_states, 10):
gmm = mixture.GMM(n_components=n_components, covariance_type="diag")
_ = gmm.fit(y.dropna())
bic.append(gmm.bic(y.dropna()))
if bic[-1] < lowest_bic:
lowest_bic = bic[-1]
best_gmm = gmm
from operator import itemgetter
gmm_order = sorted(enumerate(best_gmm.means_), key=itemgetter(1))
gmm_order = np.asarray(map(itemgetter(0), gmm_order))
gmm_order_map = dict(zip(gmm_order, range(len(gmm_order))))
gmm_states = pd.DataFrame(None,
index=y.index,
columns=['state'],
dtype=np.int)
gmm_raw_predicted = best_gmm.predict(y.dropna()).astype(np.int)
gmm_states[~y.isnull().values.ravel()] = gmm_raw_predicted[:, None]
from functools import partial
gmm_lam = partial(lambda x: gmm_order_map.get(x, np.nan))
states_ordered = gmm_states['state'].map(gmm_lam)
# When best_gmm.n_components > N_states we need to map multiple
# GMM estimated states to a single state (the last, really) in
# the model. Below we create the map that says which states
# in GMM map to which states in the model.
from itertools import izip_longest
from collections import defaultdict
gmm_to_state_map = dict(
izip_longest(range(best_gmm.n_components),
range(N_states),
fillvalue=N_states - 1))
state_to_gmm_map = defaultdict(list)
for i, v in zip(gmm_to_state_map.values(), gmm_to_state_map.keys()):
state_to_gmm_map[i].append(v)
gmm_to_state_lam = partial(lambda x: gmm_to_state_map.get(x, np.nan))
states_initial = states_ordered.map(gmm_to_state_lam)
trans_freqs = compute_trans_freqs(states_initial, N_states)
alpha_trans_0 = calc_alpha_prior(states_initial,
N_states,
trans_freqs=trans_freqs)
if any(y.isnull()):
# Now, let's sample values for the missing observations.
# TODO: Would be better if we did this according to the
# initial transition probabilities, no?
for t in np.arange(y.size)[y.isnull().values.ravel()]:
if t == 0:
p0 = compute_steady_state(trans_freqs[:, :-1])
state = pymc.rcategorical(p0)
else:
state = pymc.rcategorical(trans_freqs[int(states_initial[t -
1])])
states_initial[t] = state
beta_prior_means = []
beta_prior_covars = []
obs_prior_vars = np.empty(N_states)
for i, gmm_states in state_to_gmm_map.items():
this_order = gmm_order[gmm_states]
these_weights = best_gmm.weights_[this_order]
these_weights /= these_weights.sum()
these_means = best_gmm.means_[this_order]
these_covars = best_gmm.covars_[this_order]
# Use the exact mixture variance when we have two
# states to combine; otherwise, use a crude estimate.
# TODO: We can get an expression for len(gmm_states) > 2.
if len(gmm_states) == 2:
pi_, pi_n = these_weights
sigma_1, sigma_2 = these_covars
mu_diff = np.ediff1d(these_means)
this_cov = pi_ * (sigma_1**2 + mu_diff**2 * pi_n**2) +\
pi_n * (sigma_2**2 + mu_diff**2 * pi_**2)
this_cov = float(this_cov)
else:
this_cov = these_covars.sum()
# TODO: How should/could we use this?
# this_mean = np.dot(these_weights, best_gmm.means_[this_order])
# Get the data conditional on this [estimated] state.
states_cond = np.asarray(
map(lambda x: True if x in gmm_states else False, states_ordered))
from sklearn import linear_model
reg_model = linear_model.ElasticNetCV(fit_intercept=False)
N_beta = X_matrices[i].shape[1]
X_cond = X_matrices[i][states_cond]
y_cond = y[states_cond].get_values().ravel()
if not X_cond.empty:
# TODO: Could ask how this compares to the intercept-only model above.
reg_model_fit = reg_model.fit(X_cond, y_cond)
reg_model_err = np.atleast_1d(
np.var(reg_model_fit.predict(X_cond) - y_cond))
beta_prior_means += [np.atleast_1d(reg_model_fit.coef_)]
beta_prior_covars += [np.repeat(reg_model_err, N_beta)]
else:
beta_prior_means += [np.zeros(N_beta)]
# TODO: A better default for an "uninformed" initial value?
# This is really a job for a prior distribution.
beta_prior_covars += [100. * np.ones(N_beta)]
obs_prior_vars[i] = this_cov
init_params = NormalHMMInitialParams(alpha_trans_0, None, states_initial,
beta_prior_means, beta_prior_covars,
obs_prior_vars, None)
return init_params
def gmm_norm_hmm_init_params(y, X_matrices):
""" Generates initial parameters for the univariate normal-emissions HMM
with normal mean priors.
Parameters
==========
y: pandas.DataFrame or pandas.Series
Time-indexed vector of observations.
X_matrices: list of pandas.DataFrame
Collection of design matrices for each hidden state's mean.
Returns
=======
init_params:
A `NormalHMMInitialParams` object.
"""
# initialize with simple gaussian mixture
from sklearn.mixture import GMM
N_states = len(X_matrices)
gmm_model = GMM(N_states, covariance_type='diag')
gmm_model_fit = gmm_model.fit(y.dropna())
from operator import itemgetter
gmm_order = sorted(enumerate(gmm_model_fit.means_), key=itemgetter(1))
gmm_order = map(itemgetter(0), gmm_order)
gmm_order_map = dict(zip(gmm_order, range(len(gmm_order))))
# gmm_ord_weights = np.asarray([gmm_model_fit.weights_[x] for x in
# gmm_order])
# TODO: attempt conditional regression when X matrices tell us
# that we'll be fitting regression terms?
# For now we just set those terms to zero.
gmm_ord_means = np.asarray([
np.append(gmm_model_fit.means_[x], [0.] * (X_matrices[i].shape[1] - 1))
for i, x in enumerate(gmm_order)
])
gmm_ord_obs_covars = np.asarray(
[gmm_model_fit.covars_[x, 0] for x in gmm_order])
gmm_states = pd.DataFrame(None,
index=y.index,
columns=['state'],
dtype=np.int)
gmm_raw_predicted = gmm_model_fit.predict(y.dropna()).astype(np.int)
gmm_states[~y.isnull().values] = gmm_raw_predicted[:, None]
from functools import partial
gmm_lam = partial(lambda x: gmm_order_map.get(x, np.nan))
gmm_ord_states = gmm_states['state'].map(gmm_lam)
beta_prior_covars = [
np.ones(X_matrices[i].shape[1]) * 10 for i in range(len(X_matrices))
]
trans_freqs = compute_trans_freqs(gmm_ord_states, N_states)
alpha_trans_0 = calc_alpha_prior(gmm_ord_states,
N_states,
trans_freqs=trans_freqs)
if any(y.isnull()):
# Now, let's sample values for the missing observations.
# TODO: Would be better if we did this according to the
# initial transition probabilities, no?
for t in np.arange(y.size)[y.isnull().values.ravel()]:
if t == 0:
p0 = compute_steady_state(trans_freqs[:, :-1])
state = pymc.rcategorical(p0)
else:
state = pymc.rcategorical(trans_freqs[int(gmm_ord_states[t -
1])])
gmm_ord_states[t] = state
init_params = NormalHMMInitialParams(alpha_trans_0, None, gmm_ord_states,
gmm_ord_means, beta_prior_covars,
gmm_ord_obs_covars, None)
return init_params
reload(dismod3)
# set font
book_graphics.set_font()
pi_true = scipy.interpolate.interp1d([0, 20, 40, 60, 100],
[.4, .425, .6, .5, .4])
beta_true = .3
delta_true = 50.
N = 30
# start with a simple model with N rows of data
model = data_simulation.simple_model(N)
# set covariate to 0/1 values randomly
model.input_data['x_cov'] = 1. * mc.rcategorical([.5, .5], size=N)
# record the true age-specific rates
model.ages = pl.arange(0, 101, 1)
model.pi_age_true = pi_true(model.ages)
# choose age groups randomly
age_width = pl.zeros(N)
age_mid = mc.runiform(age_width / 2, 100 - age_width / 2, size=N)
age_start = pl.array(age_mid - age_width / 2, dtype=int)
age_end = pl.array(age_mid + age_width / 2, dtype=int)
model.input_data['age_start'] = age_start
model.input_data['age_end'] = age_end
# choose effective sample size uniformly at random
def settlement_size_samples(mu, tau, cutoff, sum_mu, sum_tau, pop_accounted, N):
"""
Returns N samples from the distribution of unsampled settlement sizes.
Settlement sizes are drawn from a truncated lognormal distribution
conditional on their sum being equal to sum_val.
At the SIR stage, 100 samples are proposed and 10 are retained.
:Parameters:
- mu : float
The mean parameter.
- tau : float
The precision parameter.
- cutoff : float
The truncation value.
- sum_mu : float
The mean of the lognormal distribution of total population.
- sum_tau : float
The precision parameter of the lognormal distribution of total population.
- pop_accounted : integer
The total population accounted for by the GRUMP urban extents.
- N : integer
The number of samples to return.
"""
N_sum_vals = N/10
# Compute moments and characteristic function for single population size,
# to be used in all posterior evaluations.
lnorms = np.exp(geto_truncnorm(mu, tau, log(cutoff), 10000))
sum_moments = np.mean(lnorms), np.var(lnorms)
oFT = robust_CF(mu, tau, cutoff)
# Generate values for total population in region not accounted for by
# GRUMP urban extents.
sum_vals = pm.rlognormal(sum_mu, sum_tau, size=N_sum_vals)-pop_accounted
where_not_OK = np.where(sum_vals < 0)
while len(where_not_OK[0]) > 0:
sum_vals[where_not_OK] = pm.rlognormal(sum_mu, sum_tau, size=len(where_not_OK[0]))-pop_accounted
where_not_OK = np.where(sum_vals < 0)
# Create 10 samples using SIR for each sum.
samps = []
for sum_val in sum_vals:
tries = 0
while tries < 10:
try:
# Find posterior of N given this sum, and draw a single sample from it.
Nmesh, p = robust_posterior(mu, tau, cutoff, sum_val, prior_fun=None, sum_moments=sum_moments, oFT=oFT)
N = Nmesh[int(pm.rcategorical(p))]
# Draw 10 samples for the sizes of the constituent populations given their number and
# the total population size.
w,i,s = SIR_simplex_sample(mu, tau, cutoff, sum_val, N, N_proposals=1000, N_samps=10)
break
except RuntimeError:
print 'Failed at N=%f, Nmesh=%s, p=%s. Trying again'%(N,Nmesh,p)
tries += 1
if tries==10:
import sys
a,b,c = sys.exc_info()
raise a,b,c
samps.extend(list(s.T))
# Return, you're done!
return samps
