def _plot_ess(idata, plot_kws=None):
default_plot_kws = dict(figsize=(16, 8))
plot_kws = {} if plot_kws is None else plot_kws
plot_kws = {**default_plot_kws, **plot_kws}
axes = az.plot_ess(idata, **plot_kws)
if axes.ndim == 1:
axes = axes.reshape(1, -1)
n, m = axes.shape
for i in range(n):
for j in range(m):
label = axes[i, j].get_title().replace("\n", "[") + "]"
axes[i, j].set_title(label)
axes[i, j].xaxis.set_tick_params(labelsize=8)
axes[i, j].yaxis.set_tick_params(labelsize=8)
if j > 0:
axes[i, j].set_ylabel("")
else:
label = axes[i, j].get_ylabel()
axes[i, j].set_ylabel(label, size=12)
if (i + 1) < n:
axes[i, j].set_xlabel("")
else:
label = axes[i, j].get_xlabel()
axes[i, j].set_xlabel(label, size=12)
plt.subplots_adjust(left=0.08,
right=0.97,
top=0.97,
bottom=0.1,
wspace=0.15,
hspace=0.15)
return axes
def ess_plot(self, chain_id, num_points=10):
plts = az.plot_ess(self.chains, var_names=chain_id, kind='evolution', min_ess=0)
for i in range(len(plts)):
plot = plts[i]
plot.axes.lines[1].remove()
plot.axes.get_legend().remove()
y_data = plot.axes.lines[0].get_ydata()
y_max = np.nanmax(y_data)
plot.axes.set_ylim(0, y_max + 10.)
plts[i] = plot
return plts
def mcmc_diagnostic_plots(posterior, sample_stats, it):
az_trace = az.from_dict(posterior=posterior, sample_stats=sample_stats)
"""
# 2 parameters or more for these pair plots
if len(az_trace.posterior.data_vars) > 1:
ax = az.plot_pair(az_trace, kind="hexbin", gridsize=30, marginals=True)
fig = ax.ravel()[0].figure
plt.ylim((5000, 30000))
plt.xlim((1e-10, 1e-7))
fig.savefig(f"./results/pair_plot_it{it}.png")
plt.clf()
ax = az.plot_pair(
az_trace,
kind=["scatter", "kde"],
kde_kwargs={"fill_last": False},
point_estimate="mean",
marginals=True,
)
fig = ax.ravel()[0].figure
fig.savefig(f"./results/point_estimate_plot_it{it}.png")
plt.clf()
"""
ax = az.plot_trace(az_trace, divergences=False)
fig = ax.ravel()[0].figure
fig.savefig(f"./results/trace_plot_it{it}.png")
plt.clf()
ax = az.plot_posterior(az_trace)
fig = ax.ravel()[0].figure
fig.savefig(f"./results/posterior_plot_it{it}.png")
plt.clf()
lag = np.minimum(len(list(posterior.values())[0]), 100)
ax = az.plot_autocorr(az_trace, max_lag=lag)
fig = ax.ravel()[0].figure
fig.savefig(f"./results/autocorr_plot_it{it}.png")
plt.clf()
ax = az.plot_ess(az_trace, kind="evolution")
fig = ax.ravel()[0].figure
fig.savefig(f"./results/ess_evolution_plot_it{it}.png")
plt.clf()
plt.close()
"""
ESS Local Plot
==============
_thumb: .7, .5
"""
import arviz as az
az.style.use("arviz-darkgrid")
idata = az.load_arviz_data("centered_eight")
az.plot_ess(idata, var_names=["mu"], kind="local", marker="_", ms=20, mew=2)
"""
ESS Quantile Plot
=================
_thumb: .4, .5
"""
import matplotlib.pyplot as plt
import arviz as az
az.style.use("arviz-darkgrid")
idata = az.load_arviz_data("radon")
az.plot_ess(idata, var_names=["sigma_y"], kind="quantile", color="C4")
plt.show()
def run_model(month=7,
n_samples=1000,
interp_type='ncs',
binary=True,
spike=0.9,
hdi_prob=0.95,
zero_inf=0.7):
# preprocessing
binary_str = 'binary' if binary else 'nonbinary'
df = pd.read_csv('../data/' + interp_type + '-pop-deaths-and-' +
binary_str + '-mandates.csv',
index_col=0)
df = df.rename(columns={
"Age Group": "Age_Group",
"COVID-19 Deaths": "covid_19_deaths"
})
test_df = df[df["Month"] == month]
sex = np.array(test_df["Sex"])
mandates = test_df.iloc[:,
-4:] # takes all of the 4 mandate columns that currently exist
age = test_df["Age_Group"]
covid_deaths = test_df["covid_19_deaths"]
population = test_df[
"Population"] / 1000000 # makes the population in units of millions
n = len(test_df["Age_Group"].unique()
) # should decrease by 1 after proper age filtering
age_data = pd.get_dummies(test_df["Age_Group"]).drop("Under 1 year",
axis=1)
sex_data = pd.get_dummies(test_df["Sex"], drop_first=True)
# run the model
with pm.Model() as model:
# spike and slab prior
tau = pm.InverseGamma('tau', alpha=20, beta=20)
xi = pm.Bernoulli('xi', p=spike, shape=len(mandates.columns))
beta_mandates = pm.MvNormal('beta_mandate',
mu=0,
cov=tau * np.eye(len(mandates.columns)),
shape=len(mandates.columns))
# age prior
mu_age_mean = np.linspace(-5, 5, len(age_data.columns))
cov = pm.HalfNormal('cov', sigma=2)
mu_age = pm.MvNormal('mu_age',
mu=mu_age_mean,
cov=np.identity(len(age_data.columns)),
shape=(1, 10))
beta_age = pm.MvNormal('beta_age',
mu=mu_age,
cov=(cov**2) * np.identity(10),
shape=(1, 10))
# sex prior
mu_sex = pm.Normal('mu_sex', mu=0, sigma=1)
sigma_sex = pm.HalfNormal('simga_sex', sigma=2)
beta_sex = pm.Normal('beta_sex', mu=mu_sex, sigma=sigma_sex)
# intercept prior
mu_intercept = pm.Normal('mu_intercept', mu=0, sigma=1)
sigma_intercept = pm.HalfNormal('simga_intercept', sigma=2)
beta_intercept = pm.Normal('beta_intercept',
mu=mu_intercept,
sigma=sigma_intercept)
# mean setup for likelihood
mandates = np.array(mandates).astype(theano.config.floatX)
population = np.array(population).astype(theano.config.floatX)
sex = np.array(sex_data).astype(theano.config.floatX)
age = np.array(age_data).astype(theano.config.floatX)
w_mandates = theano.shared(mandates, 'w_mandate')
w_sex = theano.shared(sex, 'w_sex')
w_age = theano.shared(age, 'w_age')
mean = beta_intercept + pm.math.matrix_dot(w_mandates, xi*beta_mandates) \
+ pm.math.matrix_dot(w_sex, beta_sex).T \
+ pm.math.matrix_dot(w_age, beta_age.T).T
# likelihood
obs = pm.ZeroInflatedPoisson('y_obs',
psi=zero_inf,
theta=population * tt.exp(mean),
observed=covid_deaths)
# obs = pm.Normal('crap', mu=mean, sigma=3, observed=covid_deaths)
# sample from posterior
trace = pm.sample(n_samples,
tune=n_samples,
nuts={'target_accept': 0.98})
# posterior hdis
mandates = test_df.iloc[:, -4:]
x = az.summary(trace, var_names=["beta_mandate"], hdi_prob=hdi_prob)
x.index = mandates.columns
x.to_csv('../images/posteriors/mandate_' + interp_type + '_' + binary_str +
'_' + 'summary.csv')
x = az.summary(trace, var_names=["beta_sex"], hdi_prob=hdi_prob)
x.index = sex_data.columns
x.to_csv('../images/posteriors/sex_' + interp_type + '_' + binary_str +
'_' + 'summary.csv')
x = az.summary(trace, var_names=["beta_age"], hdi_prob=hdi_prob)
x.index = age_data.columns
x.to_csv('../images/posteriors/age_' + interp_type + '_' + binary_str +
'_' + 'summary.csv')
x = az.summary(trace, var_names=["beta_intercept"], hdi_prob=hdi_prob)
x.to_csv('../images/posteriors/intercept_' + interp_type + '_' +
binary_str + '_' + 'summary.csv')
# posterior distributions
ax = az.plot_forest(trace,
'ridgeplot',
var_names=["beta_intercept"],
combined=True,
hdi_prob=0.99999)
ax[0].set_title(r'Posterior Distribution of $\beta_0$')
plt.savefig('../images/posteriors/intercept_posteriors_' + interp_type +
'_' + binary_str + '.png')
ax = az.plot_forest(trace,
'ridgeplot',
var_names=["beta_age"],
combined=True,
hdi_prob=0.99999)
ax[0].set_yticklabels(reversed(age_data.columns))
ax[0].set_title(r'Posterior Distribution of $\beta_{age}$')
plt.savefig('../images/posteriors/age_posteriors_' + interp_type + '_' +
binary_str + '.png')
ax = az.plot_forest(trace,
'ridgeplot',
var_names=["beta_sex"],
combined=True,
hdi_prob=0.99999)
ax[0].set_yticklabels(reversed(sex_data.columns))
ax[0].set_title(r'Posterior Distribution of $\beta_{sex}$')
plt.savefig('../images/posteriors/sex_posteriors_' + interp_type + '_' +
binary_str + '.png')
ax = az.plot_forest(trace,
'ridgeplot',
var_names=["beta_mandate"],
combined=True,
hdi_prob=0.99999)
ax[0].set_yticklabels(reversed(mandates.columns))
ax[0].set_title(r'Posterior Distribution of $\beta_{mandate}$')
plt.savefig('../images/posteriors/mandate_posteriors_' + interp_type +
'_' + binary_str + '.png')
# ESS Plots
ax = az.plot_ess(trace, var_names=["beta_intercept"])
ax.set_title(r'$\beta_0$ ESS')
plt.savefig('../images/ess/' + interp_type + '_' + binary_str +
'_interceptESS.png')
ax = az.plot_ess(trace, var_names=["beta_age"])
ax[0, 0].set_title(r'$\beta_{age[1-4]}$ ESS', fontsize=18)
ax[0, 1].set_title(r'$\beta_{age[15-24]}$ ESS', fontsize=18)
ax[0, 2].set_title(r'$\beta_{age[25-34]}$ ESS', fontsize=18)
ax[1, 0].set_title(r'$\beta_{age[35-44]}$ ESS', fontsize=18)
ax[1, 1].set_title(r'$\beta_{age[45-54]}$ ESS', fontsize=18)
ax[1, 2].set_title(r'$\beta_{age[5-14]}$ ESS', fontsize=18)
ax[2, 0].set_title(r'$\beta_{age[55-64]}$ ESS', fontsize=18)
ax[2, 1].set_title(r'$\beta_{age[65-74]}$ ESS', fontsize=18)
ax[2, 2].set_title(r'$\beta_{age[75-84]}$ ESS', fontsize=18)
ax[3, 0].set_title(r'$\beta_{age[85+]}$ ESS', fontsize=18)
plt.savefig('../images/ess/' + interp_type + '_' + binary_str +
'_ageESS.png')
ax = az.plot_ess(trace, var_names=["beta_sex"])
ax.set_title(r'$\beta_{sex}$ ESS')
plt.savefig('../images/ess/' + interp_type + '_' + binary_str +
'_sexESS.png')
ax = az.plot_ess(trace, var_names=["beta_mandate"])
ax[0].set_title(r'$\beta_{mandate[April]}$ ESS', fontsize=18)
ax[1].set_title(r'$\beta_{mandate[May]}$ ESS', fontsize=18)
ax[2].set_title(r'$\beta_{mandate[June]}$ ESS', fontsize=18)
ax[3].set_title(r'$\beta_{mandate[July]}$ ESS', fontsize=18)
plt.savefig('../images/ess/' + interp_type + '_' + binary_str +
'_mandateESS.png')
# posterior predictive checking
with model:
ppc = pm.sample_posterior_predictive(trace, var_names=["y_obs"])
az.plot_ppc(az.from_pymc3(posterior_predictive=ppc, model=model))
plt.savefig('../images/posterior_predictive/' + interp_type + '_' +
binary_str + '.png')
# return trace so that user can work with posterior data directly
return trace
"""
ESS Quantile Plot
=================
_thumb: .4, .5
"""
import arviz as az
idata = az.load_arviz_data("radon")
ax = az.plot_ess(idata,
var_names=["sigma"],
kind="quantile",
color="red",
backend="bokeh")
def plot_ess(self, **kwargs):
"""Plot quantile, local or evolution of effective sample size (ESS)."""
return az.plot_ess(self.data, **kwargs)
# Infact, we will just the harmonic oscillator ansatz.
#We also compute the effective sample size using az.ess() from arviz package.
for sigma in numpy.linspace(0.01, 3, 30):
def normal_proposal(old_point):
symmetric
return Normal(old_point, sigma*torch.ones_like(old_point)).sample()
tf= HarmonicTrialFunction(torch.ones(1))
n_walkers = 2
init_config = torch.ones(n_walkers, 1)
results = metropolis_symmetric(tf, init_config, normal_proposal, num_walkers=n_walkers, num_steps=100000)
dataset1 = az.convert_to_dataset(results.numpy())
dataset2 = az.convert_to_inference_data(results.numpy())
az.plot_ess(dataset2, kind = "local")
plt.savefig("Local")
az.plot_ess(dataset2, kind = "quantile")
plt.savefig("quantile")
az.plot_ess(dataset2, kind = "evolution")
plt.savefig("Evolution")
print( az.ess(dataset1).data_vars)
# In the Output_of_run array we are using units of 1000.
#Output_of_run = numpy.array([0.02366, 1.087, 3.579, 7.21, 11.32, 15.9, 20.19, 25.2, 29.98, 32.94, 36.67, 39.41, 38.68, 42.96, 44.4, 45.35, 44.83, 45.94, 43.73, 46.34, 44.69, 45.15, 41.88,41.41, 41.33, 41, 38.46, 38.3, 37.49, 36.02])
#y_data = Output_of_run
#x_data = numpy.linspace(0.01, 3, 30)
#plt.scatter(x_data, y_data, c='r', label='ess scatter')
##plt.plot(x_data, y_data, label='ess fit')
#plt.xlabel('x')
#plt.ylabel('y')
#plt.title('ess vs sigma ')
"""
ESS Quantile Plot
=================
_thumb: .2, .8
"""
import matplotlib.pyplot as plt
import arviz as az
az.style.use("arviz-darkgrid")
idata = az.load_arviz_data("radon")
az.plot_ess(idata, var_names=["b"], kind="evolution")
plt.show()
std_stress_data_20 = np.loadtxt('std_stress_data_20.csv', delimiter=',')
std_stress_data_40 = np.loadtxt('std_stress_data_40.csv', delimiter=',')
std_stress_data_RS = np.loadtxt('std_stress_data_RS.csv', delimiter=',')
data = az.from_netcdf('save_arviz_data_stanwound')
az.style.use("default")
az.rhat(data, var_names=['kv', 'k0', 'kf', 'k2', 'b', 'mu', 'phif'])
extra_kwargs = {"color": "lightsteelblue"}
az.plot_ess(data,
kind="local",
var_names=['kv', 'k0', 'kf', 'k2', 'b', 'mu', 'phif'],
figsize=(18, 18),
color="royalblue",
extra_kwargs=extra_kwargs,
textsize=20)
az.plot_ess(data,
kind="quantile",
var_names=['kv', 'k0', 'kf', 'k2', 'b', 'mu', 'phif'],
figsize=(18, 18),
color="royalblue",
extra_kwargs=extra_kwargs,
textsize=20)
az.plot_ess(data,
kind="evolution",
var_names=['kv', 'k0', 'kf', 'k2', 'b', 'mu', 'phif'],
def param_validate_arviz(inferred, variables):
az.plot_mcse(inferred, var_names=variables)
az.plot_ess(inferred, var_names=variables)
az.plot_trace(inferred, var_names=variables)
"""
ESS Local Plot
==============
_thumb: .6, .5
"""
import arviz as az
idata = az.load_arviz_data("non_centered_eight")
ax = az.plot_ess(idata,
var_names=["mu"],
kind="local",
rug=True,
backend="bokeh")
"""
ESS Quantile Plot
=================
_thumb: .2, .8
"""
import arviz as az
idata = az.load_arviz_data("radon")
ax = az.plot_ess(idata, var_names=["b"], kind="evolution", backend="bokeh")
