def initial_sampling(self, params):
"""Wrapper for parallelized initial pool sampling
"""
i = params
theta_star = self.priors_sample()
model = self.simz( theta_star )
rho = test_dist(self.data, model)
while rho > self.eps0:
theta_star = self.priors_sample()
model = self.simz( theta_star )
rho = test_dist(self.data, model)
data_list = [np.int(i)]
for i_param in xrange(self.n_params):
data_list.append(theta_star[i_param])
data_list.append(1./np.float(self.N))
data_list.append(rho)
return np.array(data_list)
def importance_sampling(self, params):
""" Wrapper for parallelized importance sampling
"""
i_part = params
theta_star = weighted_sampling( self.theta_t_1, self.w_t_1 )
np.random.seed()
theta_starstar = multivariate_normal( theta_star, self.sig_t_1 ).rvs(size=1)
model_starstar = self.simz( theta_starstar )
rho = test_dist(self.data, model_starstar)
while rho > self.eps_t:
theta_star = weighted_sampling( self.theta_t_1, self.w_t_1 )
theta_starstar = multivariate_normal(theta_star, self.sig_t_1).rvs(size=1)
model_starstar = self.simz( theta_starstar )
rho = test_dist(self.data, model_starstar)
p_theta = self.prior_of_priors(theta_starstar)
pos_t = np.dstack(self.theta_t_1)
tmp_w_t = p_theta / np.sum(self.w_t_1 * multivariate_normal(self.theta_t[:,i_part], self.sig_t_1).pdf(pos_t))
data_list = [np.int(i_part)]
for i_param in xrange(self.n_params):
data_list.append(theta_starstar[i_param])
data_list.append(tmp_w_t)
data_list.append(rho)
return np.array(data_list)
def pmc_abc(data,
N = 1000,
eps0 = 0.01,
T = 20
):
start_time = time.time()
toolz = Params({
'mu': {'shape': 'gauss', 'mean': .0, 'stddev': 1.0},
'sigma': { 'shape': 'uniform', 'min': 0.0, 'max': 2.0}
})
t = 0
theta_t = np.zeros((2, N))
w_t = np.zeros((N))
for i in xrange(N):
theta_star = np.zeros(2)
theta_star[0] = toolz.prior()[0].rvs(size=1)[0]
theta_star[1] = toolz.prior()[1].rvs(size=1)[0]
#print theta_star
model = toolz.simulator( theta_star )
rho = test_dist(data[1], model(data[0]))
while rho > eps0:
theta_star[0] = toolz.prior()[0].rvs(size=1)[0]
theta_star[1] = toolz.prior()[1].rvs(size=1)[0]
model = toolz.simulator( theta_star )
rho = test_dist(data[1], model(data[0]))
theta_t[:,i] = theta_star
w_t[i] = 1.0/np.float(N)
sig_t = 2.0 * np.cov( theta_t ) # covariance matrix
print sig_t
# write out
np.savetxt(
''.join(['theta_w_t', str(t), '.dat']),
np.c_[theta_t[0,:], theta_t[1,:], w_t ]
)
print 'Initial Pool ', time.time() - start_time
fig = plt.figure(1)
sub = fig.add_subplot(111)
sub.scatter(
theta_t[0,:],
theta_t[1,:],
alpha = 1. ,
color = 'b'
)
#s = 10.**10.*w_t/w_t.sum() ,
sub.set_xlim([-2. , 2.])
sub.set_ylim([ 0. , 2.])
sub.set_xlabel(r'$\mu$')
sub.set_ylabel(r'$\sigma$')
plt.savefig("theta_scatter"+str(t)+".png")
plt.close()
start_time = time.time()
while t < T:
eps_t = np.percentile(rho, 75)
print 'Epsilon t', eps_t
theta_t_1 = theta_t.copy()
w_t_1 = w_t.copy()
sig_t_1 = sig_t.copy()
for i in xrange(N):
start_time = time.time()
theta_star = weighted_sampling( theta_t_1, w_t_1 )
theta_starstar = multivariate_normal( theta_star, sig_t_1 ).rvs(size=1)
while theta_starstar[1] < 0 :
theta_star = weighted_sampling( theta_t_1, w_t_1 )
theta_starstar = multivariate_normal(theta_star, sig_t_1).rvs(size=1)
#print theta_starstar
model_starstar = toolz.simulator( theta_starstar )
rho = test_dist(data[1], model_starstar(data[0]))
while rho > eps_t:
theta_star = weighted_sampling( theta_t_1, w_t_1 )
theta_starstar = multivariate_normal(theta_star, sig_t_1).rvs(size=1)
while theta_starstar[1] < 0 :
theta_star = weighted_sampling( theta_t_1, w_t_1 )
theta_starstar = multivariate_normal(theta_star, sig_t_1).rvs(size=1)
#print theta_starstar
model_starstar = toolz.simulator( theta_starstar )
rho = test_dist(data[1], model_starstar(data[0]))
#print theta_star, theta_starstar
theta_t[:,i] = theta_starstar
#print sig_t_1
p_theta = toolz.prior()[0].pdf(theta_t[0,i]) * toolz.prior()[1].pdf(theta_t[1,i])
#print p_theta
pos_t = np.dstack((theta_t_1[0,:],theta_t_1[1,:]))
#print multivariate_normal(theta_t[:,i], sig_t_1).pdf(pos_t).shape , w_t_1.shape
w_t[i] = p_theta / np.sum(w_t_1 * multivariate_normal(theta_t[:,i], sig_t_1).pdf(pos_t))
#print test_dist(data[1], model_starstar(data[0])), w_t[i]
#print 'For loop ', time.time() - start_time
sig_t = 2.0 * np.cov(theta_t)
t += 1
fig = plt.figure(1)
sub = fig.add_subplot(111)
sub.scatter(
theta_t[0,:],
theta_t[1,:],
alpha = 0.5
)
# s = w_t/w_t.sum() ,
sub.set_xlim([-2. , 2.])
sub.set_ylim([ 0. , 2.])
sub.set_xlabel(r'$\mu$')
sub.set_ylabel(r'$\sigma$')
plt.savefig("theta_scatter"+str(t)+".png")
plt.close()
np.savetxt(
''.join(['theta_w_t', str(t), '.dat']),
np.c_[theta_t[0,:], theta_t[1,:], w_t ]
)
print t, ' ;D'
