def sample_bimodal_gauss(mcmc_algo, comm):
mu_gold_a, std_dev_gold_a = -8.0, 1.0
mu_gold_b, std_dev_gold_b = 10.0, 1.0
def log_like_fn(theta, data=None):
return np.log(
(1 / 6.) * stats.norm.pdf(theta[0],
loc=mu_gold_a,
scale=std_dev_gold_a) +
(5 / 6.) * stats.norm.pdf(theta[0],
loc=mu_gold_b,
scale=std_dev_gold_b)) \
- log_prior(theta)
def log_prior(theta):
if (-100 < theta[0] < 100):
return 0
else:
return -np.inf
if comm.rank == 0: print("========== SAMPLE BIMODAL GAUSSI ===========")
theta_0 = np.array([1.0])
n_chains = comm.size*6
my_mcmc = DreamMpi(log_like_fn, theta_0, n_chains=n_chains, varepsilon=1e-7, mpi_comm=comm, burnin_gen=0)
my_mcmc.run_mcmc(1000 * n_chains)
# my_mcmc = DeMcMpi(log_like_fn, theta_0, n_chains=comm.size*n_chains, varepsilon=1e-7, mpi_comm=comm, burnin_gen=0)
#my_mcmc = DeMc(log_like_fn, n_chains=comm.size*n_chains, inflate=1e1, mpi_comm=comm, burnin_gen=0)
#my_mcmc.run_mcmc(5000 * n_chains, theta_0)
# view results
theta_est, sig_est, chain = my_mcmc.param_est(n_burn=1000)
theta_est_, sig_est_, full_chain = my_mcmc.param_est(n_burn=0)
if comm.rank == 0:
print("Esimated mu: %s" % str(theta_est))
print("Estimated sigma: %s " % str(sig_est))
print("Acceptance fraction: %f" % my_mcmc.acceptance_fraction)
print("Expected Acceptance fraction: %f" % (0.36))
sys.stdout.flush()
# vis the parameter estimates
mc_plot.plot_mcmc_params(chain, ["$\mu_b$"], savefig='gauss_bi_mu_mcmc_ex.png', truths=[(1/6.)*(-8.)+(5/6.)*(10.)])
# vis the full chain
mc_plot.plot_mcmc_indep_chains(full_chain, n_chains, ["$\mu_b$"],
savefig='gauss_bi_mu_chain_ex.png',
truths=[(1/6.)*(-8.)+(5/6.)*(10.)], scatter=True)
else:
pass
def sample_gauss(mcmc_algo, comm):
"""! @brief Sample from a gaussian distribution """
mu_gold, std_dev_gold = 5.0, 0.5
def log_like_fn(theta, data=None):
return np.log(stats.norm.pdf(theta[0],
loc=mu_gold,
scale=std_dev_gold)) - log_prior(theta)
def log_prior(theta):
if -100 < theta[0] < 100:
return 0
else:
return -np.inf
if comm.rank == 0: print("========== SAMPLE GAUSSI ===========")
theta_0 = np.array([1.0])
n_chains = comm.size*6
my_mcmc = DreamMpi(log_like_fn, theta_0, n_chains=n_chains, mpi_comm=comm)
my_mcmc.run_mcmc(4000)
# view results
theta_est, sig_est, chain = my_mcmc.param_est(n_burn=1000)
theta_est_, sig_est_, full_chain = my_mcmc.param_est(n_burn=0)
if comm.rank == 0:
print("Esimated mu: %s" % str(theta_est))
print("Estimated sigma: %s " % str(sig_est))
print("Acceptance fraction: %f" % my_mcmc.acceptance_fraction)
sys.stdout.flush()
# vis the parameter estimates
mc_plot.plot_mcmc_params(chain, ["$\mu$"], savefig='gauss_mu_mcmc_ex.png', truths=[5.0])
# vis the full chain
mc_plot.plot_mcmc_indep_chains(full_chain, n_chains, ["$\mu$"], savefig='gauss_mu_chain_ex.png',
truths=[5.0], scatter=True)
else:
pass
def fit_line(mcmc_algo, comm):
"""!
@brief Example data from http://dfm.io/emcee/current/user/line/
For example/testing only.
"""
# Choose the "true" parameters.
m_true = -0.9594
b_true = 4.294
f_true = 0.534
# Generate some synthetic data from the model.
N = 50
x = np.sort(10 * np.random.rand(N))
yerr = 0.1 + 0.5 * np.random.rand(N)
y = m_true * x + b_true
y += np.abs(f_true * y) * np.random.randn(N)
y += yerr * np.random.randn(N)
# from http://dfm.io/emcee/current/user/line/
def lnlike(theta, x, y, yerr):
m, b, lnf = theta
model = m * x + b
inv_sigma2 = 1.0/(yerr**2 + model**2*np.exp(2*lnf))
return -0.5*(np.sum((y-model)**2*inv_sigma2 - np.log(inv_sigma2)))
def lnprior(theta):
m, b, lnf = theta
if -5.0 < m < 0.5 and 0.0 < b < 10.0 and -10.0 < lnf < 1.0:
return 0.0
return -np.inf
def lnprob(theta, x, y, yerr):
lp = lnprior(theta)
if not np.isfinite(lp):
return -np.inf
return lp + lnlike(theta, x, y, yerr)
# custom prior (ignore the unknown var term)
def log_prior(theta):
if (-50 < theta[0] < 50) and (-50 < theta[1] < 50):
return 0.
else:
return -np.inf
def model_fn(theta):
return theta[0] + theta[1] * x
def log_like_fn(theta, data):
sigma = 1.0
log_like = -0.5 * (np.sum((data - model_fn(theta)) ** 2 / sigma \
- np.log(1./sigma)) + log_prior(theta))
return log_like
# === EXAMPLE 1 ===
if comm.rank == 0: print("========== FIT LIN MODEL 1 ===========")
theta_0 = np.array([4.0, -0.5])
n_chains = comm.size*6
my_mcmc = DreamMpi(log_like_fn, theta_0, n_chains=n_chains, mpi_comm=comm,
inflate=1e1, ln_kwargs={'data': y})
my_mcmc.run_mcmc(500 * 100)
# view results
theta_est, sig_est, chain = my_mcmc.param_est(n_burn=10000)
theta_est_, sig_est_, full_chain = my_mcmc.param_est(n_burn=0)
if comm.rank == 0:
print("Esimated params: %s" % str(theta_est))
print("Estimated params sigma: %s " % str(sig_est))
print("Acceptance fraction: %f" % my_mcmc.acceptance_fraction)
# vis the parameter estimates
mc_plot.plot_mcmc_params(chain,
labels=["$y_0$", "m"],
savefig='line_mcmc_ex.png',
truths=[4.294, -0.9594])
# vis the full chain
mc_plot.plot_mcmc_indep_chains(full_chain, n_chains,
labels=["$y_0$", "m"],
savefig='lin_chain_ex.png',
truths=[4.294, -0.9594], scatter=True)
# === EXAMPLE 2 ===
comm.Barrier()
if comm.rank == 0: print("========== FIT LIN MODEL 2 ===========")
theta_0 = np.array([-0.8, 4.5, 0.2])
n_chains = comm.size*6
my_mcmc = DreamMpi(lnprob, theta_0, n_chains=n_chains, mpi_comm=comm,
ln_kwargs={'x': x, 'y': y, 'yerr': yerr}, inflate=1e1)
my_mcmc.run_mcmc(500 * 100)
theta_est, sig_est, chain = my_mcmc.param_est(n_burn=10000)
theta_est_, sig_est_, full_chain = my_mcmc.param_est(n_burn=0)
if comm.rank == 0:
print("Esimated params: %s" % str(theta_est))
print("Estimated params sigma: %s " % str(sig_est))
print("Acceptance fraction: %f" % my_mcmc.acceptance_fraction)
# vis the parameter estimates
mc_plot.plot_mcmc_params(chain,
labels=["m", "$y_0$", "$\mathrm{ln}(f)$"],
savefig='line_mcmc_ex_2.png',
truths=[-0.9594, 4.294, np.log(f_true)])
# vis the full chain
mc_plot.plot_mcmc_indep_chains(full_chain, n_chains,
labels=["m", "$y_0$", "$\mathrm{ln}(f)$"],
savefig='lin_chain_ex_2.png',
truths=[-0.9594, 4.294, np.log(f_true)],
scatter=True)
def fit_exp_data(theta_0, mcmc_algo="DE-MC"):
"""!
@brief Fit an exponential model to some data
"""
# get data
t_data, y_data = read_data()
sigma_0 = 1e-4
theta_0 = np.array(list(theta_0) + [sigma_0])
varepsilon = np.asarray([1e-2, 1e-2, 1e-3, 1e-8, 1e-9]) * 1e-2
# Run MCMC
n_chains = 6
my_mcmc = DreamMpi(lnprob,
theta_0,
n_chains=n_chains,
mpi_comm=comm,
n_cr_gen=200,
burnin_gen=4000,
varepsilon=varepsilon,
ln_kwargs={
'y_data': y_data,
't': t_data
})
my_mcmc.run_mcmc(1000 * 100, suffle=True, flip=0.5)
# Run Emcee MCMC
if comm.rank == 0:
ndim, nwalkers = 5, 100
pos = [theta_0 + 1e-6 * np.random.randn(ndim) for i in range(nwalkers)]
sampler = EnsembleSampler(nwalkers,
ndim,
lnprob,
args=(t_data, y_data))
sampler.run_mcmc(pos, 1000) # 100 * 1000 tot samples
samples = sampler.chain[:, 400:, :].reshape((-1, ndim))
fig = corner.corner(
samples,
labels=["$\tau$", "$c_\infty$", "$c_0$", "l", r"$\sigma$"])
fig.savefig("exp_emcee_out.png")
print("=== EMCEE ===")
print("Emcee mean acceptance fraction: {0:.3f}".format(
np.mean(sampler.acceptance_fraction)))
# view results
print("=== Opti values by Bipymc MCMC ===")
print("[tau, c_inf, c_0, leakage]:")
theta_est, sig_est, chain = my_mcmc.param_est(n_burn=400 * 100)
theta_est_, sig_est_, full_chain = my_mcmc.param_est(n_burn=0)
if comm.rank == 0:
print("MCMC Esimated params: %s" % str(theta_est))
print("MCMC Estimated params sigma: %s " % str(sig_est))
print("Acceptance fraction: %f" % my_mcmc.acceptance_fraction)
print("P_cr: %s" % str(my_mcmc.p_cr))
# vis the parameter estimates
mc_plot.plot_mcmc_params(
chain,
labels=[r"$\tau$", "$c_\infty$", "$c_0$", "leak", r"$\sigma$"],
savefig='exp_mcmc_out.png',
)
# vis the full chain
mc_plot.plot_mcmc_indep_chains(
full_chain,
n_chains,
labels=[r"$\tau$", "$c_\infty$", "$c_0$", "leak", r"$\sigma$"],
savefig='exp_chain_out.png',
)
# plot trajectories
xdata, ydata = read_data()
plt.close()
i = 0
reduced_model = lambda t, tau, c_inf, c_0, set_leak, sigma: exp_c1_model_full(
tau, c_inf, c_0, set_leak, t)
for sample in chain:
i += 1
plt.plot(xdata,
np.abs(reduced_model(xdata, *sample) - sample[1]) /
sample[1],
lw=0.2,
alpha=0.02,
c='b')
if i > 1000:
break
plt.title("MCMC Fit")
plt.plot(xdata,
np.abs(reduced_model(xdata, *theta_est) - theta_est[1]) /
theta_est[1],
lw=1.0,
alpha=0.8,
label="MCMC",
c='b')
plt.scatter(xdata,
np.abs(ydata - theta_est[1]) / theta_est[1],
s=2,
alpha=0.9,
c='r',
label="data")
plt.ylabel("$|C_t - c_\infty| /C_\infty$")
plt.xlabel("time")
plt.legend()
plt.savefig("mcmc_trajectories.png", dpi=160)
# plot the slopes at the end
pass
# compute and plot c_o/c_inf
c_inf_samples = chain[:, 1]
c_0_samples = chain[:, 2]
c_ratio = c_0_samples / c_inf_samples
c_ratio_avg, c_ratio_sd = np.mean(c_ratio), np.std(c_ratio)
print("c_0/c_inf estimate: %0.3e +/- %0.3e" %
(c_ratio_avg, c_ratio_sd))
def test_samplers(self):
"""
Test ability of each mcmc method to draw samples
from the 2d bimodal_gauss distribution.
"""
n_samples = 100000
n_burn = 40000
for sampler_name, (my_mcmc, n_chains) in iteritems(self.sampler_dict):
t0 = time.time()
try:
my_mcmc.run_mcmc(n_samples)
except:
my_mcmc.run_mcmc(n_samples, [0.0, 0.0])
t1 = time.time()
theta_est, sig_est, chain = my_mcmc.param_est(n_burn=n_burn)
theta_est_, sig_est_, full_chain = my_mcmc.param_est(n_burn=0)
if self.comm.rank == 0:
print("=== " + str(sampler_name) + " ===")
print("Sampler walltime: %d (s)" % int(t1 - t0))
print("Esimated params: %s" % str(theta_est))
print("Estimated params sigma: %s " % str(sig_est))
print("Acceptance fraction: %f" % my_mcmc.acceptance_fraction)
try:
print("P_cr: %s" % str(my_mcmc.p_cr))
except:
pass
y1, y2 = chain[:, 0], chain[:, 1]
if sampler_name == 'demc' or sampler_name == 'dream':
self.assertAlmostEqual(1.5, theta_est[0], delta=0.1)
self.assertAlmostEqual(1.5, theta_est[1], delta=0.1)
elif sampler_name == 'dram':
self.assertNotAlmostEqual(1.5, theta_est[0], delta=0.1)
self.assertNotAlmostEqual(1.5, theta_est[1], delta=0.1)
else:
pass
# plot mcmc samples
plt.figure()
plt.scatter(y1, y2, s=2, alpha=0.10)
plt.grid(ls='--', alpha=0.5)
plt.xlim(-2, 4)
plt.ylim(-2, 4)
plt.axvline(theta_est[0], -10, 10, c='r')
plt.axhline(theta_est[1], -10, 10, c='r')
plt.xlabel("x1")
plt.ylabel("x2")
plt.title(sampler_name + " " + r"$ \mu=(%0.2f,%0.2f)$" %
(theta_est[0], theta_est[1]))
plt.savefig(str(sampler_name) + "_bimodal_gauss_sample.png")
plt.close()
# plot mcmc chains
mc_plot.plot_mcmc_indep_chains(full_chain,
n_chains,
labels=["x1", "x2"],
savefig=str(sampler_name) +
"_chains.png",
scatter=True,
nburn=int(n_burn))