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 resample(data):
if len(data) == 0:
return data
delta_true = .1
p = data['mu_pred']+1.e-6
# TODO: abstract this block of code into rate_model.py; it is also called in data_model.py
## ensure that all data has uncertainty quantified appropriately
# first replace all missing se from ci
missing_se = pl.isnan(data['standard_error']) | (data['standard_error'] <= 0)
data['standard_error'][missing_se] = (data['upper_ci'][missing_se] - data['lower_ci'][missing_se]) / (2*1.96)
# then replace all missing ess with se
missing_ess = pl.isnan(data['effective_sample_size'])
data['effective_sample_size'][missing_ess] = data['value'][missing_ess]*(1-data['value'][missing_ess])/data['standard_error'][missing_ess]**2
# warn and drop data that doesn't have effective sample size quantified, or is is non-positive
missing_ess = pl.isnan(data['effective_sample_size']) | (data['effective_sample_size'] < 0)
if sum(missing_ess) > 0:
print 'WARNING: %d rows of data has invalid quantification of uncertainty.' % sum(missing_ess)
data['effective_sample_size'][missing_ess] = 1.0
n = data['effective_sample_size']
data['true'] = p
data['value'] = (1.0 * mc.rnegative_binomial(n*p, delta_true*n*p)) / n
# uncomment below to test the effect of having very wrong data
#data['value'] = 0.
#data['effective_sample_size'] = 1.e6
return data
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 predictions(value=value,
N=N,
S=data_sample,
mu=rates,
delta=delta):
r_S = mc.rnegative_binomial(N[S]*mu, delta)/N[S]
r = pl.zeros(len(vars['data']))
r[S] = r_S
return r
def simulate_age_group_data(N=50, delta_true=150, pi_true=true_rate_function):
""" generate simulated data
"""
# start with a simple model with N rows of data
model = data_simulation.simple_model(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 = mc.runiform(1, 100, size=N)
age_mid = mc.runiform(age_width / 2, 100 - age_width / 2, size=N)
age_width[:10] = 10
age_mid[:10] = pl.arange(5, 105, 10)
#age_width[10:20] = 10
#age_mid[10:20] = pl.arange(5, 105, 10)
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
n = mc.runiform(100, 10000, size=N)
model.input_data['effective_sample_size'] = n
# integrate true age-specific rate across age groups to find true group rate
model.input_data['true'] = pl.nan
model.input_data['age_weights'] = ''
for i in range(N):
beta = mc.rnormal(0., .025**-2)
# TODO: clean this up, it is computing more than is necessary
age_weights = pl.exp(beta * model.ages)
sum_pi_wt = pl.cumsum(model.pi_age_true * age_weights)
sum_wt = pl.cumsum(age_weights)
p = (sum_pi_wt[age_end] - sum_pi_wt[age_start]) / (sum_wt[age_end] -
sum_wt[age_start])
model.input_data.ix[i, 'true'] = p[i]
model.input_data.ix[i, 'age_weights'] = ';'.join(
['%.4f' % w for w in age_weights[age_start[i]:(age_end[i] + 1)]])
# sample observed rate values from negative binomial distribution
model.input_data['value'] = mc.rnegative_binomial(
n * model.input_data['true'], delta_true) / n
print model.input_data.drop(['standard_error', 'upper_ci', 'lower_ci'],
axis=1)
return model
def simulate_age_group_data(N=50, delta_true=150, pi_true=true_rate_function):
""" generate simulated data
"""
# start with a simple model with N rows of data
model = data_simulation.simple_model(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 = mc.runiform(1, 100, size=N)
age_mid = mc.runiform(age_width/2, 100-age_width/2, size=N)
age_width[:10] = 10
age_mid[:10] = pl.arange(5, 105, 10)
#age_width[10:20] = 10
#age_mid[10:20] = pl.arange(5, 105, 10)
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
n = mc.runiform(100, 10000, size=N)
model.input_data['effective_sample_size'] = n
# integrate true age-specific rate across age groups to find true group rate
model.input_data['true'] = pl.nan
model.input_data['age_weights'] = ''
for i in range(N):
beta = mc.rnormal(0., .025**-2)
# TODO: clean this up, it is computing more than is necessary
age_weights = pl.exp(beta*model.ages)
sum_pi_wt = pl.cumsum(model.pi_age_true*age_weights)
sum_wt = pl.cumsum(age_weights)
p = (sum_pi_wt[age_end] - sum_pi_wt[age_start]) / (sum_wt[age_end] - sum_wt[age_start])
model.input_data.ix[i, 'true'] = p[i]
model.input_data.ix[i, 'age_weights'] = ';'.join(['%.4f'%w for w in age_weights[age_start[i]:(age_end[i]+1)]])
# sample observed rate values from negative binomial distribution
model.input_data['value'] = mc.rnegative_binomial(n*model.input_data['true'], delta_true) / n
print model.input_data.drop(['standard_error', 'upper_ci', 'lower_ci'], axis=1)
return model
def test_neg_binom_model_sim(N=16):
# simulate negative binomial data
pi_true = .01
delta_true = 50
n = pl.array(pl.exp(mc.rnormal(10, 1**-2, size=N)), dtype=int)
k = pl.array(mc.rnegative_binomial(n*pi_true, delta_true, size=N), dtype=float)
p = k/n
# create NB model and priors
vars = dict(mu_age=mc.Uniform('mu_age', 0., 1000., value=.01),
sigma=mc.Uniform('sigma', 0., 10000., value=1000.))
vars['mu_interval'] = mc.Lambda('mu_interval', lambda mu=vars['mu_age']: mu*pl.ones(N))
vars.update(rate_model.log_normal_model('sim', vars['mu_interval'], vars['sigma'], p, 1./pl.sqrt(n)))
# fit NB model
m = mc.MCMC(vars)
m.sample(1)
def resample(data):
if len(data) == 0:
return data
delta_true = .1
p = data['mu_pred'] + 1.e-6
# TODO: abstract this block of code into rate_model.py; it is also called in data_model.py
## ensure that all data has uncertainty quantified appropriately
# first replace all missing se from ci
missing_se = pl.isnan(
data['standard_error']) | (data['standard_error'] <= 0)
data['standard_error'][missing_se] = (
data['upper_ci'][missing_se] - data['lower_ci'][missing_se]) / (2 *
1.96)
# then replace all missing ess with se
missing_ess = pl.isnan(data['effective_sample_size'])
data['effective_sample_size'][missing_ess] = data['value'][missing_ess] * (
1 -
data['value'][missing_ess]) / data['standard_error'][missing_ess]**2
# warn and drop data that doesn't have effective sample size quantified, or is is non-positive
missing_ess = pl.isnan(
data['effective_sample_size']) | (data['effective_sample_size'] < 0)
if sum(missing_ess) > 0:
print 'WARNING: %d rows of data has invalid quantification of uncertainty.' % sum(
missing_ess)
data['effective_sample_size'][missing_ess] = 1.0
n = data['effective_sample_size']
data['true'] = p
data['value'] = (1.0 *
mc.rnegative_binomial(n * p, delta_true * n * p)) / n
# uncomment below to test the effect of having very wrong data
#data['value'] = 0.
#data['effective_sample_size'] = 1.e6
return data
def generate_data(N, delta_true, pi_true, heterogeneity, bias, sigma_prior):
a = pl.arange(0, 101, 1)
pi_age_true = pi_true(a)
model = data_simulation.simple_model(N)
model.parameters['p']['parameter_age_mesh'] = range(0, 101, 10)
model.parameters['p']['smoothness'] = dict(amount='Moderately')
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)
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]]
n = mc.runiform(10000, 100000, size=N)
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 * pl.exp(bias)
emp_priors = {}
emp_priors['p', 'mu'] = pi_age_true
emp_priors['p', 'sigma'] = sigma_prior*pi_age_true
model.emp_priors = emp_priors
model.a = a
model.pi_age_true = pi_age_true
model.delta_true = delta_true
return model
def p_pred(pi=pi, delta=delta, n=n_nonzero):
return mc.rnegative_binomial(pi * n + 1.0e-9, delta) / pl.array(n + 1.0e-9, dtype=float)
def p_pred(pi=pi, delta=delta, n=n_nonzero):
return mc.rnegative_binomial(pi * n + 1.e-9, delta) / pl.array(
n + 1.e-9, dtype=float)
def pred(pi=pi, delta=delta):
return mc.rnegative_binomial(pi * n_pred, delta) / float(n_pred)
import pylab as pl
import pymc as mc
import dismod3
import book_graphics
reload(book_graphics)
# set font
book_graphics.set_font()
n_small = 500
pi_true = .025
delta_true = 5.
n = pl.array(pl.exp(mc.rnormal(10, 1**-2, size=16)), dtype=int)
k = pl.array(mc.rnegative_binomial(n * pi_true, delta_true), dtype=float)
r = k / n
iter = 20000
burn = 10000
thin = 10
results = {}
xmax = .07
### @export 'distribution-comparison'
pl.figure(**book_graphics.quarter_page_params)
ax = pl.axes([.1, .3, .85, .65])
x = pl.arange(0, n_small * pi_true * 4, .1)
# plot binomial distribution
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 predictions(value=value, N=N,
mu_i=rates,
delta=delta,
Z=Z, eta=0.):
return mc.rnegative_binomial(N*mu_i, delta + eta*Z)/N
def validate_age_integrating_model_sim(N=500,
delta_true=.15,
pi_true=quadratic):
## generate simulated data
a = pl.arange(0, 101, 1)
pi_age_true = pi_true(a)
model = data_simulation.simple_model(N)
#model.parameters['p']['parameter_age_mesh'] = range(0, 101, 10)
#model.parameters['p']['smoothness'] = dict(amount='Very')
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)
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]]
n = mc.runiform(100, 10000, size=N)
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
## 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=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(a, 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)
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)
model.results = dict(param=[], bias=[], mare=[], mae=[], pc=[])
data_simulation.add_to_results(model, 'delta')
data_simulation.add_to_results(model, 'mu')
data_simulation.add_to_results(model, 'input_data')
model.results = pandas.DataFrame(model.results,
columns='param bias mae mare pc'.split())
print model.results
return model
def validate_covariate_model_dispersion(N=1000, delta_true=.15, pi_true=.01, zeta_true=[.5, -.5, 0.]):
## generate simulated data
a = pl.arange(0, 100, 1)
pi_age_true = pi_true * pl.ones_like(a)
model = data.ModelData()
model.parameters['p']['parameter_age_mesh'] = [0, 100]
model.input_data = pandas.DataFrame(index=range(N))
initialize_input_data(model.input_data)
Z = mc.rbernoulli(.5, size=(N, len(zeta_true))) * 1.0
delta = delta_true * pl.exp(pl.dot(Z, zeta_true))
for i in range(len(zeta_true)):
model.input_data['z_%d'%i] = Z[:,i]
model.input_data['true'] = pi_true
model.input_data['effective_sample_size'] = mc.runiform(100, 10000, N)
n = model.input_data['effective_sample_size']
p = model.input_data['true']
model.input_data['value'] = mc.rnegative_binomial(n*p, delta*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=10000, burn=5000, thin=5, 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.zeta = pandas.DataFrame(index=model.vars['p']['Z'].columns)
model.zeta['true'] = zeta_true
model.zeta['mu_pred'] = model.vars['p']['zeta'].stats()['mean']
model.zeta['sigma_pred'] = model.vars['p']['zeta'].stats()['standard deviation']
add_quality_metrics(model.zeta)
print '\nzeta'
print model.zeta
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
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.zeta['abs_err'].dropna())),
model.zeta.dropna()['covered?'].mean())
model.results = dict(param=[], bias=[], mare=[], mae=[], pc=[])
add_to_results(model, 'delta')
add_to_results(model, 'input_data')
add_to_results(model, 'zeta')
model.results = pandas.DataFrame(model.results, columns='param bias mae mare pc'.split())
return model
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
n = mc.runiform(100, 10000, size=N)
model.input_data['effective_sample_size'] = n
# find true rate, with covariate
p = model.pi_age_true[age_start] * pl.exp(
model.input_data['x_cov'] * beta_true)
# sample observed rate values from negative binomial distribution
model.input_data['true'] = p
model.input_data['value'] = mc.rnegative_binomial(n * p, delta_true) / n
# print model.input_data.drop(['standard_error', 'upper_ci', 'lower_ci'], axis=1)
# Create age-group model
## Spline model to represent age-specific rate
model.vars += dismod3.age_pattern.spline(name='sim',
ages=model.ages,
knots=pl.arange(0, 101, 20),
smoothing=pl.inf,
interpolation_method='linear')
## Midpoint model to represent age-group data
model.vars += dismod3.age_group.midpoint_approx(
name='sim',
ages=model.ages,
def validate_age_pattern_model_sim(N=500, delta_true=.15, pi_true=quadratic):
## generate simulated data
a = pl.arange(0, 101, 1)
pi_age_true = pi_true(a)
model = data_simulation.simple_model(N)
model.parameters['p']['parameter_age_mesh'] = range(0, 101, 10)
age_list = pl.array(mc.runiform(0, 100, size=N), dtype=int)
p = pi_age_true[age_list]
n = mc.runiform(100, 10000, size=N)
model.input_data['age_start'] = age_list
model.input_data['age_end'] = age_list
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
## 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=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(a, 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)
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)
model.results = dict(param=[], bias=[], mare=[], mae=[], pc=[])
data_simulation.add_to_results(model, 'delta')
data_simulation.add_to_results(model, 'mu')
data_simulation.add_to_results(model, 'input_data')
model.results = pandas.DataFrame(model.results, columns='param bias mae mare pc'.split())
print model.results
return model
def validate_covariate_model_fe(N=100,
delta_true=3,
pi_true=.01,
beta_true=[.5, -.5, 0.],
replicate=0):
# set random seed for reproducibility
mc.np.random.seed(1234567 + replicate)
## generate simulated data
a = pl.arange(0, 100, 1)
pi_age_true = pi_true * pl.ones_like(a)
model = data.ModelData()
model.parameters['p']['parameter_age_mesh'] = [0, 100]
model.input_data = pandas.DataFrame(index=range(N))
initialize_input_data(model.input_data)
# add fixed effect to simulated data
X = mc.rnormal(0., 1.**-2, size=(N, len(beta_true)))
Y_true = pl.dot(X, beta_true)
for i in range(len(beta_true)):
model.input_data['x_%d' % i] = X[:, i]
model.input_data['true'] = pi_true * pl.exp(Y_true)
model.input_data['effective_sample_size'] = mc.runiform(100, 10000, N)
n = model.input_data['effective_sample_size']
p = model.input_data['true']
model.input_data['value'] = mc.rnegative_binomial(n * p, delta_true) / 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=10000,
burn=5000,
thin=5,
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.beta = pandas.DataFrame(index=model.vars['p']['X'].columns)
model.beta['true'] = 0.
for i in range(len(beta_true)):
model.beta['true']['x_%d' % i] = beta_true[i]
model.beta['mu_pred'] = [
n.stats()['mean'] for n in model.vars['p']['beta']
]
model.beta['sigma_pred'] = [
n.stats()['standard deviation'] for n in model.vars['p']['beta']
]
add_quality_metrics(model.beta)
print '\nbeta'
print model.beta
model.results = dict(param=[], bias=[], mare=[], mae=[], pc=[])
add_to_results(model, 'beta')
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.beta['abs_err'].dropna())),
model.beta.dropna()['covered?'].mean())
add_to_results(model, 'input_data')
add_to_results(model, 'beta')
model.results = pandas.DataFrame(model.results)
return model
def validate_covariate_model_dispersion(N=1000,
delta_true=.15,
pi_true=.01,
zeta_true=[.5, -.5, 0.]):
## generate simulated data
a = pl.arange(0, 100, 1)
pi_age_true = pi_true * pl.ones_like(a)
model = data.ModelData()
model.parameters['p']['parameter_age_mesh'] = [0, 100]
model.input_data = pandas.DataFrame(index=range(N))
initialize_input_data(model.input_data)
Z = mc.rbernoulli(.5, size=(N, len(zeta_true))) * 1.0
delta = delta_true * pl.exp(pl.dot(Z, zeta_true))
for i in range(len(zeta_true)):
model.input_data['z_%d' % i] = Z[:, i]
model.input_data['true'] = pi_true
model.input_data['effective_sample_size'] = mc.runiform(100, 10000, N)
n = model.input_data['effective_sample_size']
p = model.input_data['true']
model.input_data['value'] = mc.rnegative_binomial(n * p, delta * 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=10000,
burn=5000,
thin=5,
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.zeta = pandas.DataFrame(index=model.vars['p']['Z'].columns)
model.zeta['true'] = zeta_true
model.zeta['mu_pred'] = model.vars['p']['zeta'].stats()['mean']
model.zeta['sigma_pred'] = model.vars['p']['zeta'].stats(
)['standard deviation']
add_quality_metrics(model.zeta)
print '\nzeta'
print model.zeta
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
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.zeta['abs_err'].dropna())),
model.zeta.dropna()['covered?'].mean())
model.results = dict(param=[], bias=[], mare=[], mae=[], pc=[])
add_to_results(model, 'delta')
add_to_results(model, 'input_data')
add_to_results(model, 'zeta')
model.results = pandas.DataFrame(model.results,
columns='param bias mae mare pc'.split())
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 validate_covariate_model_fe(N=100, delta_true=3, pi_true=.01, beta_true=[.5, -.5, 0.], replicate=0):
# set random seed for reproducibility
mc.np.random.seed(1234567 + replicate)
## generate simulated data
a = pl.arange(0, 100, 1)
pi_age_true = pi_true * pl.ones_like(a)
model = data.ModelData()
model.parameters['p']['parameter_age_mesh'] = [0, 100]
model.input_data = pandas.DataFrame(index=range(N))
initialize_input_data(model.input_data)
# add fixed effect to simulated data
X = mc.rnormal(0., 1.**-2, size=(N,len(beta_true)))
Y_true = pl.dot(X, beta_true)
for i in range(len(beta_true)):
model.input_data['x_%d'%i] = X[:,i]
model.input_data['true'] = pi_true * pl.exp(Y_true)
model.input_data['effective_sample_size'] = mc.runiform(100, 10000, N)
n = model.input_data['effective_sample_size']
p = model.input_data['true']
model.input_data['value'] = mc.rnegative_binomial(n*p, delta_true) / 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=10000, burn=5000, thin=5, 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.beta = pandas.DataFrame(index=model.vars['p']['X'].columns)
model.beta['true'] = 0.
for i in range(len(beta_true)):
model.beta['true']['x_%d'%i] = beta_true[i]
model.beta['mu_pred'] = [n.stats()['mean'] for n in model.vars['p']['beta']]
model.beta['sigma_pred'] = [n.stats()['standard deviation'] for n in model.vars['p']['beta']]
add_quality_metrics(model.beta)
print '\nbeta'
print model.beta
model.results = dict(param=[], bias=[], mare=[], mae=[], pc=[])
add_to_results(model, 'beta')
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.beta['abs_err'].dropna())),
model.beta.dropna()['covered?'].mean())
add_to_results(model, 'input_data')
add_to_results(model, 'beta')
model.results = pandas.DataFrame(model.results)
return model
replicates = 1000
residuals = [[], []]
coverage = [[], []]
### @export 'neg-binom-sim-study'
pi_true = .025
delta_true = 5.
n_pred = 1.e9
for i in range(replicates):
print '\nsimulation replicate %d' % i
## generate simulated data
n = pl.array(pl.exp(mc.rnormal(10, 1**-2, size=16)), dtype=int)
k = pl.array(mc.rnegative_binomial(n*pi_true, delta_true), dtype=float)
r = k/n
## setup negative binomial model
pi = mc.Uniform('pi', lower=0, upper=1, value=.5)
delta = mc.Uninformative('delta', value=100.)
@mc.potential
def obs(pi=pi, delta=delta):
return mc.negative_binomial_like(r*n, pi*n, delta)
@mc.deterministic
def pred(pi=pi, delta=delta):
return mc.rnegative_binomial(pi*n_pred, delta) / float(n_pred)
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 pred(pi=pi, delta=delta):
return mc.rnegative_binomial(pi*n_pred, delta) / float(n_pred)
model.input_data['age_start'] = age_start
model.input_data['age_end'] = age_end
# choose effective sample size uniformly at random
n = mc.runiform(100, 10000, size=N)
model.input_data['effective_sample_size'] = n
# find true rate, with covariate
p = model.pi_age_true[age_start] * pl.exp(model.input_data['x_cov']*beta_true)
# sample observed rate values from negative binomial distribution
model.input_data['true'] = p
model.input_data['value'] = mc.rnegative_binomial(n*p, delta_true) / n
# print model.input_data.drop(['standard_error', 'upper_ci', 'lower_ci'], axis=1)
# Create age-group model
## Spline model to represent age-specific rate
model.vars += dismod3.age_pattern.spline(name='sim', ages=model.ages,
knots=pl.arange(0,101,20),
smoothing=pl.inf,
interpolation_method='linear')
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_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