def r2(trace):
"""
R squared
:param trace:
"""
y_true = trace.observed_data["y"].values
y_pred = trace.posterior_predictive.stack(sample=("chain",
"draw"))["y"].values.T
try:
print(az.r2_score(y_true, y_pred))
except (TypeError, ValueError) as e:
print(e)
plt.plot(x, y, 'b.')
plt.plot(x, alpha_m + beta_m * x, c='k',
label=f'y = {alpha_m:.2f} + {beta_m:.2f} * x')
az.plot_hpd(x, ppc['y_pred'], credible_interval=0.5, color='gray')
az.plot_hpd(x, ppc['y_pred'], color='gray')
plt.xlabel('x')
plt.ylabel('y', rotation=0)
plt.savefig('B11197_03_07.png', dpi=300)
# In[12]:
az.r2_score(y, ppc['y_pred'])
# ### The multivariate normal distribution
# Actually the bivariate
# In[13]:
sigma_x1 = 1
sigmas_x2 = [1, 2]
rhos = [-0.90, -0.5, 0, 0.5, 0.90]
k, l = np.mgrid[-5:5:.1, -5:5:.1]
pos = np.empty(k.shape + (2,))
pos[:, :, 0] = k
ax.set_ylabel("y",rotation = 0)
plt.legend()
plt.show()
# plot 2
fig, ax = plt.subplots(figsize = (8,4))
ax.scatter(x,y)
ax.plot(x, alpha_m + beta_m * x, c = "k",label=f'y = {alpha_m:.2f} + {beta_m:.2f} * x')
az.plot_hpd(x,trace["mu"],credible_interval = 0.98,color = "k")
ax.set_xlabel("x")
ax.set_ylabel("y",rotation = 0)
plt.legend()
plt.show()
# plot 3
# get the y from the posterior distribution
ppc = pm.sample_posterior_predictive(trace,samples = 2000,model = linear_model)
plt.figure()
plt.plot(x,y,"b.")
plt.plot(x,alpha_m + beta_m * x,c = "k",label=f'y = {alpha_m:.2f} + {beta_m:.2f} * x')
az.plot_hpd(x,ppc["obs"],credible_interval = 0.5, color = "gray")
az.plot_hpd(x,ppc["obs"],color = "gray")
plt.xlabel("x")
plt.ylabel("y")
plt.show()
# ------------------- get the R squared of our model ------------------------ #
r_squared = az.r2_score(y, ppc["obs"])
log.info("The r squared of the model is: %s", r_squared)
def bayesian_regression():
df_grocery = pd.read_csv('year_ward_grocery.csv')
df_grocery['female_perc'] = df_grocery.apply(lambda row: row['female'] / row['population'], axis=1)
df_diabetes = pd.read_csv('diabetes_estimates_osward_2016.csv', encoding='utf-8', header=0).dropna()
df_geo = pd.read_csv('london_pcd2geo_2015.csv', encoding='utf-8')
df_geo = df_geo[['osward','oslaua']]
df_geo = df_geo.drop_duplicates()
df = df_grocery.merge(df_diabetes, how='inner', left_on='area_id', right_on='osward')
df = df.merge(df_geo, how='inner', on='osward')
plt.figure(figsize=(8, 8))
plt.plot(df['energy_carb'], df['estimated_diabetes_prevalence'], 'bo')
plt.xlabel(f'energy_carb', size = 18)
plt.ylabel(f'estimated_diabetes_prevalence', size = 18)
X1=df['energy_carb'].values
X2=df['h_energy_nutrients_norm'].values
X3=df['avg_age'].values
X4=df['female_perc'].values
X5=df['num_transactions'].values
X6=df['people_per_sq_km'].values
X5 = np.array([np.log2(x) for x in X5])
X6 = np.array([np.log2(x) for x in X6])
Y=df['estimated_diabetes_prevalence'].values
oslaua2index = {}
i=0
for v in df['oslaua'].values:
if v not in oslaua2index:
oslaua2index[v]=i
i += 1
df['oslaua_idx'] = df.apply(lambda row : oslaua2index[row['oslaua']], axis=1)
n_oslauas = n_counties = len(df['oslaua_idx'].unique())
oslaua_idx = df['oslaua_idx'].values
hierarchical_model = pm.Model()
with hierarchical_model:
# Hyperpriors for group nodes
mu_a = pm.Normal('mu_a', mu=0., sigma=100)
sigma_a = pm.HalfNormal('sigma_a', 5.)
a = pm.Normal('a', mu=mu_a, sigma=sigma_a, shape=n_oslauas)
mu_b1 = pm.Normal('mu_b1', mu=0., sigma=100)
sigma_b1 = pm.HalfNormal('sigma_b1', 5.)
b1 = pm.Normal('b1', mu=mu_b1, sigma=sigma_b1, shape=n_oslauas)
mu_b2 = pm.Normal('mu_b2', mu=0., sigma=100)
sigma_b2 = pm.HalfNormal('sigma_b2', 5.)
b2 = pm.Normal('b2', mu=mu_b2, sigma=sigma_b2, shape=n_oslauas)
mu_b3 = pm.Normal('mu_b3', mu=0., sigma=100)
sigma_b3 = pm.HalfNormal('sigma_b3', 5.)
b3 = pm.Normal('b3', mu=mu_b3, sigma=sigma_b3, shape=n_oslauas)
mu_b4 = pm.Normal('mu_b4', mu=0., sigma=100)
sigma_b4 = pm.HalfNormal('sigma_b4', 5.)
b4 = pm.Normal('b4', mu=mu_b4, sigma=sigma_b4, shape=n_oslauas)
mu_b5 = pm.Normal('mu_b5', mu=0., sigma=100)
sigma_b5 = pm.HalfNormal('sigma_b5', 5.)
b5 = pm.Normal('b5', mu=mu_b5, sigma=sigma_b5, shape=n_oslauas)
mu_b6 = pm.Normal('mu_b6', mu=0., sigma=100)
sigma_b6 = pm.HalfNormal('sigma_b6', 5.)
b6 = pm.Normal('b6', mu=mu_b6, sigma=sigma_b6, shape=n_oslauas)
# Model error
eps = pm.HalfCauchy('eps', 5.)
estimate = a[oslaua_idx] + b1[oslaua_idx]*X1 + b2[oslaua_idx]*X2 + b3[oslaua_idx]*X3 + b4[oslaua_idx]*X4 + b5[oslaua_idx]*X5 + b6[oslaua_idx]*X6
# Likelihood (sampling distribution) of observations
likelihood = pm.Normal('likelihood', mu=estimate, sigma=eps, observed=Y)
hierarchical_trace = pm.sample(10000, tune=10000, target_accept=.9)
ppc = pm.sample_posterior_predictive(hierarchical_trace, samples=10000, model=hierarchical_model)
np.asarray(ppc['likelihood']).shape
print(az.r2_score(Y, ppc['likelihood']))