def logG(self, t, xp, x):
ESSmin = self.ESSrmin * x.N
f = lambda e: rs.essl(e * x.llik) - ESSmin
epn = x.exponents[-1]
if f(1. - epn) > 0: # we're done (last iteration)
delta = 1. - epn
new_epn = 1.
# put 1. manually so that we can safely test == 1.
else:
delta = optimize.brentq(f, 1.e-12, 1. - epn) # secant search
# left endpoint is >0, since f(0.) = nan if any likelihood = -inf
new_epn = epn + delta
x.exponents.append(new_epn)
return self.logG_tempering(x, delta)
sigmas = sigma0 + np.linspace(-.199, .2, 401)
thetas = [[mu0, rho0, sig] for sig in sigmas]
# range of T's
Ts = [10, 100, 1000]
colors = {10: 'lightgray', 100: 'gray', 1000: 'black'}
plt.style.use('ggplot')
plt.figure()
for T in Ts:
print('FFBS for T=%i' % T)
alg = particles.SMC(fk=fkmod(theta0, T), N=100, store_history=True)
alg.run()
trajs = alg.hist.backward_sampling(M=100)
ll0 = log_joint_density(theta0, trajs)
ess_ls = []
for theta in thetas:
ll = log_joint_density(theta, trajs)
ess = rs.essl(ll - ll0)
ess_ls.append(ess)
plt.plot(sigmas, ess_ls, label='T=%i' % T, color=colors[T])
plt.xlabel('sigma')
plt.ylabel('ESS')
plt.legend(loc=2)
savefigs = True # False if you don't want to save plots as pdfs
if savefigs:
plt.savefig('hurzeler_kunsch.pdf')
plt.show()