def log_prob_b2(b2, state, data):
# loglike
logit_p = state.b0 + state.b1 * data.x + b2 * data.x**2
p = mcmc.sigmoid(logit_p)
loglike = data.y * np.log(p) + (1 - data.y) * np.log1p(-p)
# logprior
logprior = b2_prior().lpdf(b2)
return loglike.sum() + logprior
# COMPILE
_ = fit(State(0, 0, 0), Data(x, y), burn=1, niter=1)
with Timer.Timer("MCMC", digits=3):
out = fit(State(0, 0, 0), Data(x, y), burn=1000)
print('Done')
b0 = np.array([s['b0'] for s in out])
b1 = np.array([s['b1'] for s in out])
b2 = np.array([s['b2'] for s in out])
B = len(out)
M = 200
xx = np.linspace(-4, 4, 100)
p = mcmc.sigmoid(b0[:, None] + b1[:, None] * xx[None, :] +
b2[:, None] * xx[None, :]**2)
# Plots
plt.plot(xx, p.mean(0), label='est')
plt.plot(xx, np.quantile(p, .975, axis=0), linestyle='--')
plt.plot(xx, np.quantile(p, .025, axis=0), linestyle='--')
plt.scatter(simdat['x'][::100], simdat['p'][::100], label='true', s=5)
plt.scatter(simdat['x'],
simdat['y'] + np.random.randn(len(simdat['y'])) * .01,
label='data',
s=5,
alpha=.1)
plt.legend()
plt.show()
def loglike(self, b0, b1, b2):
logit_p = b0 + self.data.x * b1 + (self.data.x**2) * b2
p = mcmc.sigmoid(logit_p)
ll = self.data.y * np.log(p) + (1 - self.data.y) * np.log1p(-p)
return ll.sum()