### @export 'negative-binomial_dispersion-alt_prior'
pi = mc.Uniform('pi', lower=0, upper=1, value=.5)
log_10_delta = mc.Normal('log_10_delta', mu=mu_log_10_delta, tau=.25**-2)
delta = mc.Lambda('delta', lambda x=log_10_delta: 5 + 10**x)
@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)
### @export 'negative-binomial_dispersion-fit_alt_prior'
mc.MCMC([pi, log_10_delta, delta, obs, pred]).sample(iter,
burn,
thin,
verbose=False,
progress_bar=False)
key = 'Neg. Binom., $\mu_{\log\delta}=%d$' % mu_log_10_delta
results[key] = dict(pred=pred.stats(), pi=pi.stats())
model_keys.append(key)
#mc.Matplot.plot(pi)
#mc.Matplot.plot(delta)
book_graphics.save_json('poisson_model.json', vars())
book_graphics.forest_plot(fname='neg_binom_priors.pdf', **vars())
pl.show()
pl.savefig('vzv_data.pdf')
### @export 'forest-plot-age-5'
df = pandas.read_csv('vzv.csv', index_col=None)
df = df[df['Region'] == 'Europe, Western']
df = df[(df['Year End'] >= 1997) & (df['Year End'] <= 2005)]
df5 = df[(df['Age Start'] <= 5) & (df['Age End'] >= 5)]
r = df5['Parameter Value']
n = df5['effective_sample_size']
l = [a.split(',')[0] + ' et al' for a in df5['authors']]
xmax = 1.0
book_graphics.forest_plot(r,
n,
data_labels=l,
xmax=xmax,
subplot_params=dict(bottom=.1,
right=.99,
top=.9,
left=.3))
pooled = (r * n).sum() / n.sum()
se = pl.sqrt(pooled * (1 - pooled) / n.sum())
# make diamond width of uncertainty
pl.fill([pooled - 1.96 * se, pooled, pooled + 1.96 * se, pooled],
[-.5, -.5 + .125 / 2, -.5, -.5 - .125 / 2],
color='k')
#pl.errorbar(pooled, -.5, xerr=[1.96*se], fmt='kd', mew=1, mec='white', ms=15)
pl.vlines([pooled], -.75, len(n), linewidth=1, linestyle='dashed', color='k')
pl.axis([-.01, 1.05, -.75, .25 + .5 * len(n)])
pl.text(-2 * xmax / 50, -.5, 'Pooled Estimate', ha='right', va='center')
pl.xlabel('Age (Years)')
pl.ylabel('VZV Seroprevalence (Per 1)')
pl.savefig('vzv_data.pdf')
### @export 'forest-plot-age-5'
df = pandas.read_csv('vzv.csv', index_col=None)
df = df[df['Region']=='Europe, Western']
df = df[(df['Year End']>=1997) & (df['Year End']<=2005)]
df5 = df[(df['Age Start'] <= 5) & (df['Age End'] >= 5)]
r = df5['Parameter Value']
n = df5['effective_sample_size']
l = [a.split(',')[0] + ' et al' for a in df5['authors']]
xmax=1.0
book_graphics.forest_plot(r, n, data_labels=l, xmax=xmax, subplot_params=dict(bottom=.1, right=.99, top=.9, left=.3))
pooled = (r*n).sum() / n.sum()
se = pl.sqrt(pooled*(1-pooled)/n.sum())
# make diamond width of uncertainty
pl.fill([pooled-1.96*se, pooled, pooled+1.96*se, pooled], [-.5, -.5 + .125/2, -.5, -.5 - .125/2], color='k')
#pl.errorbar(pooled, -.5, xerr=[1.96*se], fmt='kd', mew=1, mec='white', ms=15)
pl.vlines([pooled], -.75, len(n), linewidth=1, linestyle='dashed', color='k')
pl.axis([-.01, 1.05, -.75, .25+.5*len(n)])
pl.text(-2*xmax/50, -.5, 'Pooled Estimate', ha='right', va='center')
pl.title('Europe, Western')
pl.savefig('vzv_forest_europe.pdf')
df = pandas.read_csv('vzv.csv', index_col=None)
pi_median = []
pi_spread = []
for i, k in enumerate(results):
pi_median.append(results[k]['pi']['quantiles'][50])
pi_spread.append(results[k]['pi']['95% HPD interval'][1]-results[k]['pi']['95% HPD interval'][0])
min_est = min(pi_median).round(4)
max_est = max(pi_median).round(4)
min_spread = min(pi_spread).round(4)
max_spread = max(pi_spread).round(4)
book_graphics.save_json('schiz_forest.json', vars())
### data only plot, for computational infrastructure appendix
book_graphics.forest_plot(r, n, data_labels=cy,
xmax=.0115,
subplot_params=dict(bottom=.1, right=.99, top=.95, left=.15),
figparams=book_graphics.quarter_page_params,
fname='book/graphics/ci-prev_meta_analysis-schiz_data.png')
### master graphic of data and models, for rate model section of stats chapter
book_graphics.forest_plot(r, n, data_labels=cy,
xmax=.0115,
model_keys=['Binomial', 'Poisson', 'Beta binomial', 'Negative binomial', 'Normal', 'Lognormal', 'Offset lognormal'],
results=results,
#subplot_params=dict(bottom=.1, right=.99, top=.95, left=.15),
fig_params=dict(figsize=(11, 8.5), dpi=120),
fname='book/graphics/schiz_forest.pdf')
pl.show()
1./((s_pred/(pi+zeta))**2 + sigma**2))) \
- zeta
### @export 'offset-log-normal-fit-and-store'
mc.MCMC([pi, zeta, sigma, obs, pred]).sample(iter, burn, thin)
results['Offset lognormal'] = dict(pi=pi.stats(), pred=pred.stats())
### @export 'save'
pi_median = []
pi_spread = []
for i, k in enumerate(results):
pi_median.append(results[k]['pi']['quantiles'][50])
pi_spread.append(results[k]['pi']['95% HPD interval'][1]-results[k]['pi']['95% HPD interval'][0])
min_est = min(pi_median).round(4)
max_est = max(pi_median).round(4)
min_spread = min(pi_spread).round(4)
max_spread = max(pi_spread).round(4)
book_graphics.save_json('zero_forest.json', vars())
### master graphic of data and models, for zeros subsection of rate models section of stats chapter
book_graphics.forest_plot(r, n,
xmax=.0005,
model_keys=['Zero-inflated beta binomial', 'Beta binomial', 'Negative binomial', 'Lognormal', 'Offset lognormal'],
results=results,
pi_true=pi_true,
fname='zero_forest.pdf')
model_keys = ['Poisson', 'Negative Binomial']
### @export 'negative-binomial_dispersion-prior-exploration'
for mu_log_10_delta in [1,2,3]:
### @export 'negative-binomial_dispersion-alt_prior'
pi = mc.Uniform('pi', lower=0, upper=1, value=.5)
log_10_delta = mc.Normal('log_10_delta', mu=mu_log_10_delta, tau=.25**-2)
delta = mc.Lambda('delta', lambda x=log_10_delta: 5 + 10**x)
@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)
### @export 'negative-binomial_dispersion-fit_alt_prior'
mc.MCMC([pi, log_10_delta, delta, obs, pred]).sample(iter, burn, thin, verbose=False, progress_bar=False)
key = 'Neg. Binom., $\mu_{\log\delta}=%d$'%mu_log_10_delta
results[key] = dict(pred=pred.stats(), pi=pi.stats())
model_keys.append(key)
#mc.Matplot.plot(pi)
#mc.Matplot.plot(delta)
book_graphics.save_json('poisson_model.json', vars())
book_graphics.forest_plot(fname='neg_binom_priors.pdf', **vars())
pl.show()
mc.MCMC([pi, zeta, sigma, obs, pred]).sample(iter, burn, thin)
results['Offset lognormal'] = dict(pi=pi.stats(), pred=pred.stats())
### @export 'save'
pi_median = []
pi_spread = []
for i, k in enumerate(results):
pi_median.append(results[k]['pi']['quantiles'][50])
pi_spread.append(results[k]['pi']['95% HPD interval'][1] -
results[k]['pi']['95% HPD interval'][0])
min_est = min(pi_median).round(4)
max_est = max(pi_median).round(4)
min_spread = min(pi_spread).round(4)
max_spread = max(pi_spread).round(4)
book_graphics.save_json('zero_forest.json', vars())
### master graphic of data and models, for zeros subsection of rate models section of stats chapter
book_graphics.forest_plot(r,
n,
xmax=.0005,
model_keys=[
'Zero-inflated beta binomial', 'Beta binomial',
'Negative binomial', 'Lognormal',
'Offset lognormal'
],
results=results,
pi_true=pi_true,
fname='zero_forest.pdf')