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_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_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