def generate_and_append_data(data,
data_type,
truth,
age_intervals,
gbd_region='Asia, Southeast',
country='Thailand',
year=2005,
sex='male'):
""" create simulated data"""
for a0, a1 in age_intervals:
d = {
'condition': 'type_2_diabetes',
'data_type': data_type,
'gbd_region': gbd_region,
'region': country,
'year_start': year,
'year_end': year,
'sex': sex,
'age_start': a0,
'age_end': a1,
'age_weights': list(np.ones(a1 + 1 - a0)),
'id': len(data)
}
p0 = dismod3.utils.rate_for_range(truth, range(a0, a1 + 1),
np.ones(a1 + 1 - a0))
p1 = mc.rbeta(p0 * dispersion, (1 - p0) * dispersion)
p2 = mc.rbinomial(n, p1) / n
d['value'] = p2
d['standard_error'] = np.sqrt(p2 * (1 - p2) / n)
data.append(d)
def simdata_postproc(sp_sub, survey_plan):
"""
This function should take a value for the Gaussian random field in the submodel
sp_sub, evaluated at the survey plan locations, and return a simulated dataset.
"""
p = pm.invlogit(sp_sub)
n = survey_plan.n
return pm.rbinomial(n, p)
def plot_beta_binomial_funnel(alpha, beta):
pi_true = alpha/(alpha+beta)
pi = mc.rbeta(alpha, beta, size=10000)
n = pl.exp(mc.rnormal(10, 2**-2, size=10000))
k = mc.rbinomial(pl.array(n, dtype=int), pi)
r = k/n
pl.vlines([pi_true], .1*n.min(), 10*n.max(),
linewidth=2, linestyle='-', color='w', zorder=9)
pl.vlines([pi_true], .1*n.min(), 10*n.max(),
linewidth=1, linestyle='--', color='black', zorder=10)
pl.plot(r, n, 'ko',
mew=0, alpha=.25)
pl.semilogy(schiz['r'], schiz['n'], 'ks', mew=1, mec='white', ms=4,
label='Observed values')
pl.xlabel('Rate (per PY)')
pl.ylabel('Study size (PY)')
pl.xticks([0, .005, .01])
pl.axis([-.0001, .0101, 50., 1500000])
pl.title(r'$\alpha=%d$, $\beta=%d$' % (alpha, beta))
def generate_and_append_data(data, data_type, truth, age_intervals,
gbd_region='Asia, Southeast', country='Thailand', year=2005, sex='male'):
""" create simulated data"""
for a0, a1 in age_intervals:
d = { 'condition': 'type_2_diabetes',
'data_type': data_type,
'gbd_region': gbd_region,
'region': country,
'year_start': year,
'year_end': year,
'sex': sex,
'age_start': a0,
'age_end': a1,
'age_weights': list(np.ones(a1 + 1 - a0)),
'id': len(data)}
p0 = dismod3.utils.rate_for_range(truth, range(a0, a1 + 1), np.ones(a1 + 1 - a0))
p1 = mc.rbeta(p0 * dispersion, (1 - p0) * dispersion)
p2 = mc.rbinomial(n, p1) / n
d['value'] = p2
d['standard_error'] = np.sqrt(p2 * (1 - p2) / n)
data.append(d)
def plot_beta_binomial_funnel(alpha, beta):
pi_true = alpha / (alpha + beta)
pi = mc.rbeta(alpha, beta, size=10000)
n = pl.exp(mc.rnormal(10, 2**-2, size=10000))
k = mc.rbinomial(pl.array(n, dtype=int), pi)
r = k / n
pl.vlines([pi_true],
.1 * n.min(),
10 * n.max(),
linewidth=2,
linestyle='-',
color='w',
zorder=9)
pl.vlines([pi_true],
.1 * n.min(),
10 * n.max(),
linewidth=1,
linestyle='--',
color='black',
zorder=10)
pl.plot(r, n, 'ko', mew=0, alpha=.25)
pl.semilogy(schiz['r'],
schiz['n'],
'ks',
mew=1,
mec='white',
ms=4,
label='Observed values')
pl.xlabel('Rate (per PY)')
pl.ylabel('Study size (PY)')
pl.xticks([0, .005, .01])
pl.axis([-.0001, .0101, 50., 1500000])
pl.title(r'$\alpha=%d$, $\beta=%d$' % (alpha, beta))
def pred(alpha=alpha, beta=beta):
return mc.rbinomial(n_pred, mc.rbeta(alpha, beta)) / float(n_pred)
def pred(pi=pi):
return mc.rbinomial(n_pred, pi) / float(n_pred)
def pred(pi=pi):
return mc.rbinomial(n, pi)
def simdata_postproc(sp_sub, survey_plan, a1, a2):
p = pm.stukel_invlogit(sp_sub, a1, a2)
n = survey_plan.n
return pm.rbinomial(n, p)
def p_pred(pi=pi, n=n_nonzero):
return mc.rbinomial(n, pi + 1.0e-9) / (1.0 * n)
def p_pred(pi=pi, n=n_nonzero):
return mc.rbinomial(n, pi + 1.e-9) / (1. * n)
def f(sp_sub, n=n):
return pm.rbinomial(n=n,p=pm.invlogit(sp_sub))
x = np.vstack((lon,lat,t)).T
cov1 = gencirc(x,r1)
cov2 = gencirc(x,r2)
M = c1*cov1+c2*cov2
S = pm.gp.FullRankCovariance(pm.gp.cov_funs.exponential.aniso_geo_rad, amp=.5, scale=.08, inc=.5, ecc=.5).cholesky(x[:,:2])
y = pm.rmv_normal_chol(M,S.T)+np.random.normal(N)*.1
z = pm.flib.invlogit(y)
lo_age = np.ones(N)*2
up_age = np.ones(N)*10
n = np.random.randint(10,500,size=N)
pos = pm.rbinomial(n, z)
neg = n-pos
data_file = np.rec.fromarrays([pos,neg,lo_age,up_age,lon,lat,t,cov1,cov2],names='pos,neg,lo_age,up_age,lon,lat,t,cov1,cov2')
# where_0 = np.where(M==0)
# where_1 = np.where(M==1)
# where_n1 = np.where(M==-1)
#
# pl.figure(1)
# pl.clf()
# pl.hist(z[where_0])
#
# pl.figure(2)
# pl.clf()
import numpy
import pymc
from pymc import rbinomial,Binomial,Normal,Gamma
import pylab
import scipy.stats
#numpy.random.seed(15)
Nsubj = 4
Ntrls = 100
# the data
signal_resp = rbinomial(n=Ntrls, p=0.80, size=Nsubj)
noise_resp = rbinomial(n=Ntrls, p=0.10, size=Nsubj)
# the model
prior_md = Normal('prior_md', mu=0.0, tau=0.001, value=0.0)
prior_mc = Normal('prior_mc', mu=0.0, tau=0.001, value=0.0)
prior_taud = Gamma('prior_taud', alpha=0.001, beta=0.001, value=0.01)
prior_tauc = Gamma('prior_tauc', alpha=0.001, beta=0.001, value=0.01)
dprm = Normal('dprm', mu=Pmd, tau=Ptaud, size=Nsubj, value=[0,0,0,0])
bias = Normal('bias', mu=Pmc, tau=Ptauc, size=Nsubj, value=[0,0,0,0])
Phi = scipy.stats.norm.cdf
@pymc.deterministic
def hi(d=dprm, c=bias):
return Phi(+0.5*d - c)
@pymc.deterministic
def pred(pi=pi):
return mc.rbinomial(n, pi)
import pylab as pl
import pymc as mc
import dismod3
import book_graphics
reload(book_graphics)
# set font
book_graphics.set_font()
### @export 'binomial-model-funnel'
pi_binomial_funnel = 0.004
n = pl.exp(mc.rnormal(10, 2 ** -2, size=10000))
k = mc.rbinomial(pl.array(n.round(), dtype=int), pi_binomial_funnel)
r = k / n
pl.figure(**book_graphics.half_page_params)
pl.vlines(
[pi_binomial_funnel],
0.1 * n.min(),
10 * n.max(),
linewidth=2,
linestyle="-",
color="w",
zorder=9,
label="_nolegend_",
)
pl.vlines(
[pi_binomial_funnel], 0.1 * n.min(), 10 * n.max(), linewidth=1, linestyle="--", color="k", zorder=10, label="$\pi$"
def pred(alpha=alpha, beta=beta, phi=phi):
if pl.rand() < phi:
return 0
else:
return mc.rbinomial(n_pred, mc.rbeta(alpha, beta)) / float(n_pred)
def validate_rate_model(rate_type='neg_binom', data_type='epilepsy', replicate=0):
# set random seed for reproducibility
mc.np.random.seed(1234567 + replicate)
# load data
model = dismod3.data.load('/home/j/Project/dismod/output/dm-32377/')
data = model.get_data('p')
#data = data.ix[:20, :]
# replace data with synthetic data if requested
if data_type == 'epilepsy':
# no replacement needed
pass
elif data_type == 'schiz':
import pandas as pd
data = pd.read_csv('/homes/abie/gbd_dev/gbd/tests/schiz.csv')
elif data_type == 'binom':
N = 1.e6
data['effective_sample_size'] = N
mu = data['value'].mean()
data['value'] = mc.rbinomial(N, mu, size=len(data.index)) / N
elif data_type == 'poisson':
N = 1.e6
data['effective_sample_size'] = N
mu = data['value'].mean()
data['value'] = mc.rpoisson(N*mu, size=len(data.index)) / N
elif data_type == 'normal':
mu = data['value'].mean()
sigma = .125*mu
data['standard_error'] = sigma
data['value'] = mc.rnormal(mu, sigma**-2, size=len(data.index))
elif data_type == 'log_normal':
mu = data['value'].mean()
sigma = .25
data['standard_error'] = sigma*mu
data['value'] = pl.exp(mc.rnormal(pl.log(mu), sigma**-2, size=len(data.index)))
else:
raise TypeError, 'Unknown data type "%s"' % data_type
# sample prevalence data
i_test = mc.rbernoulli(.25, size=len(data.index))
i_nan = pl.isnan(data['effective_sample_size'])
data['lower_ci'] = pl.nan
data['upper_ci'] = pl.nan
data.ix[i_nan, 'effective_sample_size'] = 0.
data['standard_error'] = pl.sqrt(data['value']*(1-data['value'])) / data['effective_sample_size']
data.ix[pl.isnan(data['standard_error']), 'standard_error'] = pl.inf
data['standard_error'][i_test] = pl.inf
data['effective_sample_size'][i_test] = 0.
data['value'] = pl.maximum(data['value'], 1.e-12)
model.input_data = data
# create model
# TODO: set parameters in model.parameters['p'] dict
# then have simple method to create age specific rate model
#model.parameters['p'] = ...
#model.vars += dismod3.ism.age_specific_rate(model, 'p')
model.parameters['p']['parameter_age_mesh'] = [0,100]
model.parameters['p']['heterogeneity'] = 'Very'
model.vars['p'] = dismod3.data_model.data_model(
'p', model, 'p',
'all', 'total', 'all',
None, None, None,
rate_type=rate_type,
interpolation_method='zero',
include_covariates=False)
# add upper bound on sigma in log normal model to help convergence
#if rate_type == 'log_normal':
# model.vars['p']['sigma'].parents['upper'] = 1.5
# add upper bound on sigma, zeta in offset log normal
#if rate_type == 'offset_log_normal':
# model.vars['p']['sigma'].parents['upper'] = .1
# model.vars['p']['p_zeta'].value = 5.e-9
# model.vars['p']['p_zeta'].parents['upper'] = 1.e-8
# fit model
dismod3.fit.fit_asr(model, 'p', iter=20000, thin=10, burn=10000)
#dismod3.fit.fit_asr(model, 'p', iter=100, thin=1, burn=0)
# compare estimate to hold-out
data['mu_pred'] = model.vars['p']['p_pred'].stats()['mean']
data['lb_pred'] = model.vars['p']['p_pred'].stats()['95% HPD interval'][:,0]
data['ub_pred'] = model.vars['p']['p_pred'].stats()['95% HPD interval'][:,1]
import data_simulation
model.test = data[i_test]
data = model.test
data['true'] = data['value']
data_simulation.add_quality_metrics(data)
data_simulation.initialize_results(model)
data_simulation.add_to_results(model, 'test')
data_simulation.finalize_results(model)
return model
def f(sp_sub, n=n):
return pm.rbinomial(n=n, p=pm.invlogit(sp_sub))
def validate_rate_model(rate_type='neg_binom',
data_type='epilepsy',
replicate=0):
# set random seed for reproducibility
mc.np.random.seed(1234567 + replicate)
# load data
model = dismod3.data.load('/home/j/Project/dismod/output/dm-32377/')
data = model.get_data('p')
#data = data.ix[:20, :]
# replace data with synthetic data if requested
if data_type == 'epilepsy':
# no replacement needed
pass
elif data_type == 'schiz':
import pandas as pd
data = pd.read_csv('/homes/abie/gbd_dev/gbd/tests/schiz.csv')
elif data_type == 'binom':
N = 1.e6
data['effective_sample_size'] = N
mu = data['value'].mean()
data['value'] = mc.rbinomial(N, mu, size=len(data.index)) / N
elif data_type == 'poisson':
N = 1.e6
data['effective_sample_size'] = N
mu = data['value'].mean()
data['value'] = mc.rpoisson(N * mu, size=len(data.index)) / N
elif data_type == 'normal':
mu = data['value'].mean()
sigma = .125 * mu
data['standard_error'] = sigma
data['value'] = mc.rnormal(mu, sigma**-2, size=len(data.index))
elif data_type == 'log_normal':
mu = data['value'].mean()
sigma = .25
data['standard_error'] = sigma * mu
data['value'] = pl.exp(
mc.rnormal(pl.log(mu), sigma**-2, size=len(data.index)))
else:
raise TypeError, 'Unknown data type "%s"' % data_type
# sample prevalence data
i_test = mc.rbernoulli(.25, size=len(data.index))
i_nan = pl.isnan(data['effective_sample_size'])
data['lower_ci'] = pl.nan
data['upper_ci'] = pl.nan
data.ix[i_nan, 'effective_sample_size'] = 0.
data['standard_error'] = pl.sqrt(
data['value'] * (1 - data['value'])) / data['effective_sample_size']
data.ix[pl.isnan(data['standard_error']), 'standard_error'] = pl.inf
data['standard_error'][i_test] = pl.inf
data['effective_sample_size'][i_test] = 0.
data['value'] = pl.maximum(data['value'], 1.e-12)
model.input_data = data
# create model
# TODO: set parameters in model.parameters['p'] dict
# then have simple method to create age specific rate model
#model.parameters['p'] = ...
#model.vars += dismod3.ism.age_specific_rate(model, 'p')
model.parameters['p']['parameter_age_mesh'] = [0, 100]
model.parameters['p']['heterogeneity'] = 'Very'
model.vars['p'] = dismod3.data_model.data_model(
'p',
model,
'p',
'all',
'total',
'all',
None,
None,
None,
rate_type=rate_type,
interpolation_method='zero',
include_covariates=False)
# add upper bound on sigma in log normal model to help convergence
#if rate_type == 'log_normal':
# model.vars['p']['sigma'].parents['upper'] = 1.5
# add upper bound on sigma, zeta in offset log normal
#if rate_type == 'offset_log_normal':
# model.vars['p']['sigma'].parents['upper'] = .1
# model.vars['p']['p_zeta'].value = 5.e-9
# model.vars['p']['p_zeta'].parents['upper'] = 1.e-8
# fit model
dismod3.fit.fit_asr(model, 'p', iter=20000, thin=10, burn=10000)
#dismod3.fit.fit_asr(model, 'p', iter=100, thin=1, burn=0)
# compare estimate to hold-out
data['mu_pred'] = model.vars['p']['p_pred'].stats()['mean']
data['lb_pred'] = model.vars['p']['p_pred'].stats()['95% HPD interval'][:,
0]
data['ub_pred'] = model.vars['p']['p_pred'].stats()['95% HPD interval'][:,
1]
import data_simulation
model.test = data[i_test]
data = model.test
data['true'] = data['value']
data_simulation.add_quality_metrics(data)
data_simulation.initialize_results(model)
data_simulation.add_to_results(model, 'test')
data_simulation.finalize_results(model)
return model
def f(sp_sub, a, b, n=n):
p = pm.invlogit(sp_sub)
h = pm.rbeta(a, b, size=len(sp_sub))
p_def = g6pd.p_fem_def(p, h)
return pm.rbinomial(n=n, p=p)
def simdata_postproc(sp_sub, survey_plan):
p = pm.invlogit(sp_sub)
n = survey_plan.n
return pm.rbinomial(n, p)
def f(sp_sub, a, b, n=n):
p = pm.invlogit(sp_sub)
h = pm.rbeta(a,b,size=len(sp_sub))
p_def = g6pd.p_fem_def(p,h)
return pm.rbinomial(n=n, p=p)
if len(names)>2:
for name in names[:-2]:
cv[name] = np.random.normal(size=n_data+n_pred)*on#np.ones(n_data)
cv['m'] = np.ones(n_data+n_pred)*on
cv['t'] = t*on
C = pm.gp.FullRankCovariance(my_st, amp=1, scale=1, inc=np.pi/4, ecc=.3,st=.1, sd=.5, tlc=.2, sf = .1)
dm = np.vstack((lon,lat,t)).T
C_eval = C(dm,dm)
f = pm.rmv_normal_cov(np.sum([cv[name]*vals[name] for name in names],axis=0), C_eval) + np.random.normal(size=n_data+n_pred)*np.sqrt(V)
p = pm.flib.invlogit(f)
ns = 100
pos = pm.rbinomial(ns, p)
neg = ns - pos
print p
ra_data = np.rec.fromarrays((pos[:n_data], neg[:n_data], lon[:n_data], lat[:n_data]) + tuple([cv[name][:n_data] for name in names]), names=['pos','neg','lon','lat']+names)
pl.rec2csv(ra_data,'test_data.csv')
ra_pred = np.rec.fromarrays((pos[n_data:], neg[n_data:], lon[n_data:], lat[n_data:]) + tuple([cv[name][n_data:] for name in names]), names=['pos','neg','lon','lat']+names)
pl.rec2csv(ra_pred,'test_pred.csv')
os.system('infer cov_test test_db test_data.csv -t 10 -n 8 -i 100000')
# os.system('cov-test-predict test test_pred.csv 1000 100')
#
# # ra_data = pl.csv2rec('test_data.csv')
# # ra_pred = pl.csv2rec('test_pred.csv')
def p_pred(pi=pi_latent, n=n_nonzero):
return mc.rbinomial(n, pi) / (1. * n)
import pylab as pl
import pymc as mc
import dismod3
import book_graphics
reload(book_graphics)
# set font
book_graphics.set_font()
### @export 'binomial-model-funnel'
pi_binomial_funnel = .004
n = pl.exp(mc.rnormal(10, 2**-2, size=10000))
k = mc.rbinomial(pl.array(n.round(), dtype=int), pi_binomial_funnel)
r = k / n
pl.figure(**book_graphics.half_page_params)
pl.vlines([pi_binomial_funnel],
.1 * n.min(),
10 * n.max(),
linewidth=2,
linestyle='-',
color='w',
zorder=9,
label='_nolegend_')
pl.vlines([pi_binomial_funnel],
.1 * n.min(),
10 * n.max(),
linewidth=1,
def p_pred(pi=pi_latent, n=n_nonzero):
return mc.rbinomial(n, pi) / (1.0 * n)
def pred(alpha=alpha, beta=beta, phi=phi):
if pl.rand() < phi:
return 0
else:
return mc.rbinomial(n_pred, mc.rbeta(alpha, beta)) / float(n_pred)
###############################
# Simulate data.
###############################
# How many datapoints?
n = 250
# Put down a random scattering of data locations on the unit sphere.
X = spherical.well_spaced_mesh(n)
# Generate some binomial data. Prevalence is going to be high at the equator, low at the poles.
p_true = np.exp(-X[:,2]**2*5)
# Number sampled and number positive.
N = 100
k = pm.rbinomial(N, p_true)
################################
# Fit the model.
################################
M = pm.MCMC(make_model(N,k,X,cholmod,spherical),db='hdf5')
scalar_variables = filter(lambda x:not x.observed, [M.m, M.amp, M.kappa])
if len(scalar_variables)>0:
M.use_step_method(pm.AdaptiveMetropolis, scalar_variables)
# Comment to use the default AdaptiveMetropolis step method.
# GMRFMetropolis kind of scales better to high dimensions, but may mix worse in low.
M.use_step_method(pymc_objects.GMRFMetropolis, M.S, M.likelihood_string, M.M, M.Q, M.likelihood_variables, n_sweeps=100)
M.isample(1000,0,10)
################################
def f(sp_sub, a, n=n):
return pm.rbinomial(n=n, p=pm.stukel_invlogit(sp_sub, *a))
def deaths_sim(n=n, p=theta):
"""deaths_sim = rbinomial(n, p)"""
return pm.rbinomial(n, p)
def create_test_rates(rate_function_str='(age/100.0)**2', rate_type='prevalence data',
age_list=None, num_subjects=1000):
import dismod3.models as models
if not age_list:
#age_list = range(0,101,10)
age_list = np.random.random_integers(0,90,20)
params = {}
params['disease'], flag = models.Disease.objects.get_or_create(name='Test Disease')
params['region'], flag = models.Region.objects.get_or_create(name='World')
params['rate_type'] = rate_type
params['sex'] = 'total'
params['country'] = 'Canada'
params['epoch_start'] = 2000
params['epoch_end'] = 2000
rate_list = []
# TODO: make this safe and robust
if isinstance(rate_function_str, str):
rate_function = eval('lambda age: %s'%rate_function_str)
else:
from scipy.interpolate import interp1d
rf_vals = np.array(rate_function_str) # it is actually an Nx2 array
rate_function = interp1d(rf_vals[:,0], rf_vals[:,1], kind='cubic')
rate_vec = np.array([rate_function(a) for a in range(101)])
for a in age_list:
#params['age_start'] = a-5
params['age_start'] = a
#params['age_end'] = params['age_start']
#params['age_end'] = a+5
params['age_end'] = np.random.random_integers(a, 100)
params['denominator'] = num_subjects
params['numerator'] = 0
new_rate = models.Rate(**params)
new_rate.params['Notes'] = 'Simulated data, created using function %s' % rate_function_str
new_rate.params['Urbanicity'] = (np.random.randn() > 0) and 'Urban' or 'Rural'
new_rate.save()
p = probabilistic_utils.rate_for_range(rate_vec, new_rate.age_start, new_rate.age_end, new_rate.population())
# adjust p to make data heterogeneous according to 'Urbanicity' covariate
if new_rate.params['Urbanicity'] == 'Urban':
p *= 1.5
#multiplicative_noise = 1.
#multiplicative_noise = 1 + 0.1*np.random.randn()
#new_rate.numerator = multiplicative_noise * \
# new_rate.denominator * probabilistic_utils.rate_for_range(rate_vec, new_rate.age_start, new_rate.age_end, new_rate.population())
new_rate.numerator = mc.rbinomial(new_rate.denominator, p)
new_rate.save()
rate_list.append(new_rate)
return rate_list, rate_function
