def fit_beta(nsteps):
"""Fit a beta distribution by MCMC."""
num_dimensions = 1
# Create the dummy model
b = BetaFit(0.5, 0.5)
# Create the options
opts = MCMCOpts()
opts.model = b
opts.estimate_params = b.parameters
opts.initial_values = [1.001]
opts.nsteps = nsteps
opts.anneal_length = nsteps/10
opts.T_init = 100
opts.use_hessian = False
opts.seed = 1
opts.norm_step_size = 0.01
opts.likelihood_fn = b.likelihood
opts.step_fn = step
# Create the MCMC object
mcmc = MCMC(opts)
mcmc.initialize()
mcmc.estimate()
mcmc.prune(nsteps/10, 1)
plt.ion()
for i in range(mcmc.num_estimate):
plt.figure()
(heights, points, lines) = plt.hist(mcmc.positions[:,i], bins=100,
normed=True)
plt.plot(points, beta.pdf(points, b.a, b.b), 'r')
return mcmc
def fit_gaussian(nsteps):
num_dimensions = 1
# Create the dummy model
means = 10 ** np.random.rand(num_dimensions)
variances = np.random.rand(num_dimensions)
g = GaussianFit(means, variances)
# Create the options
opts = MCMCOpts()
opts.model = g
opts.estimate_params = g.parameters
opts.initial_values = [1]
opts.nsteps = nsteps
opts.anneal_length = nsteps/10
opts.T_init = 1
opts.use_hessian = False
opts.seed = 1
opts.norm_step_size = 1
opts.likelihood_fn = g.likelihood
opts.step_fn = step
# Create the MCMC object
mcmc = MCMC(opts)
mcmc.initialize()
mcmc.estimate()
mcmc.prune(nsteps/10, 1)
plt.ion()
for i in range(mcmc.num_estimate):
mean_i = np.mean(mcmc.positions[:,i])
var_i = np.var(mcmc.positions[:, i])
print "True mean: %f" % means[i]
print "Sampled mean: %f" % mean_i
print "True variance: %f" % variances[i]
print "Sampled variance: %f" % var_i
plt.figure()
(heights, points, lines) = plt.hist(mcmc.positions[:,i], bins=50,
normed=True)
plt.plot(points, norm.pdf(points, loc=means[i],
scale=np.sqrt(variances[i])), 'r')
mean_err = np.zeros(len(mcmc.positions))
var_err = np.zeros(len(mcmc.positions))
for i in range(len(mcmc.positions)):
mean_err[i] = (means[0] - np.mean(mcmc.positions[:i+1,0]))
var_err[i] = (variances[0] - np.var(mcmc.positions[:i+1,0]))
plt.figure()
plt.plot(mean_err)
plt.plot(var_err)
return mcmc
def __init__(self, opts, num_chains, max_temp, min_temp=1, swap_period=20):
self.options = opts
self.max_temp = max_temp
self.min_temp = min_temp
self.swap_period = swap_period
self.iter = 0
"""Current step iteration (runs to ``nsteps``)."""
self.chains = []
"""The set of chains in the temperature series."""
# Calculate the temperature series
temps = np.logspace(np.log10(min_temp), np.log10(max_temp),
num_chains)
# Initialize each of the chains
for i, temp in enumerate(temps):
chain = MCMC(opts)
chain.options.T_init = temp
chain.initialize()
chain.iter = chain.start_iter
self.chains.append(chain)
# Initialize arrays for storing swap info
num_swaps = self.options.nsteps / swap_period
self.swap_proposals = np.zeros((num_swaps, 2))
"""Each swap proposal is stored as [i, j] row in this array."""
self.pi_xi = np.zeros(num_swaps)
"""The posterior of chain i at the position of i."""
self.pi_xj = np.zeros(num_swaps)
"""The posterior of chain i at the position of j."""
self.pj_xi = np.zeros(num_swaps)
"""The posterior of chain j at the position of i."""
self.pj_xj = np.zeros(num_swaps)
"""The posterior of chain j at the position of j."""
self.delta_test_posteriors = np.zeros(num_swaps)
"""The posterior probability ratio for swap/noswap."""
self.swap_alphas = np.zeros(num_swaps)
"""The random number used to accept/reject the swap."""
self.swap_accepts = np.zeros(num_swaps, dtype=bool)
"""Booleans indicating accepted swaps."""
self.swap_rejects = np.zeros(num_swaps, dtype=bool)
"""Booleans indicating rejected swaps."""
self.swap_iter = 0
"""Current swap iteration (runs to ``nsteps / swap_period``)"""
def __init__(self, opts, num_chains, max_temp, min_temp=1, swap_period=20):
self.options = opts
self.max_temp = max_temp
self.min_temp = min_temp
self.swap_period = swap_period
self.iter = 0
"""Current step iteration (runs to ``nsteps``)."""
self.chains = []
"""The set of chains in the temperature series."""
# Calculate the temperature series
temps = np.logspace(np.log10(min_temp), np.log10(max_temp), num_chains)
# Initialize each of the chains
for i, temp in enumerate(temps):
chain = MCMC(opts)
chain.options.T_init = temp
chain.initialize()
chain.iter = chain.start_iter
self.chains.append(chain)
# Initialize arrays for storing swap info
num_swaps = self.options.nsteps / swap_period
self.swap_proposals = np.zeros((num_swaps, 2))
"""Each swap proposal is stored as [i, j] row in this array."""
self.pi_xi = np.zeros(num_swaps)
"""The posterior of chain i at the position of i."""
self.pi_xj = np.zeros(num_swaps)
"""The posterior of chain i at the position of j."""
self.pj_xi = np.zeros(num_swaps)
"""The posterior of chain j at the position of i."""
self.pj_xj = np.zeros(num_swaps)
"""The posterior of chain j at the position of j."""
self.delta_test_posteriors = np.zeros(num_swaps)
"""The posterior probability ratio for swap/noswap."""
self.swap_alphas = np.zeros(num_swaps)
"""The random number used to accept/reject the swap."""
self.swap_accepts = np.zeros(num_swaps, dtype=bool)
"""Booleans indicating accepted swaps."""
self.swap_rejects = np.zeros(num_swaps, dtype=bool)
"""Booleans indicating rejected swaps."""
self.swap_iter = 0
"""Current swap iteration (runs to ``nsteps / swap_period``)"""
def fit_twod_gaussians(nsteps):
means_x = [ 0.1, 0.5, 0.9,
0.1, 0.5, 0.9,
0.1, 0.5, 0.9]
means_y = [0.1, 0.1, 0.1,
0.5, 0.5, 0.5,
0.9, 0.9, 0.9]
sd = 0.01
tdg = TwoDGaussianFit(means_x, means_y, sd ** 2)
# Create the options
opts = MCMCOpts()
opts.model = tdg
opts.estimate_params = tdg.parameters
opts.initial_values = [1.001, 1.001]
opts.nsteps = nsteps
opts.anneal_length = nsteps/10
opts.T_init = 1
opts.use_hessian = False
opts.seed = 1
opts.norm_step_size = 0.1
opts.likelihood_fn = tdg.likelihood
opts.step_fn = step
mcmc = MCMC(opts)
mcmc.initialize()
mcmc.estimate()
plt.ion()
fig = plt.figure()
mcmc.prune(0, 20)
plt.scatter(mcmc.positions[:,0], mcmc.positions[:,1])
ax = fig.gca()
for x, y in zip(means_x, means_y):
circ = plt.Circle((x, y), radius=2*sd, color='r', fill=False)
ax.add_patch(circ)
plt.xlim((-0.5, 1.5))
plt.ylim((-0.5, 1.5))
plt.show()
return mcmc
# Create temperature array based on number of workers (excluding master)
temps = np.logspace(np.log10(min_temp), np.log10(max_temp), num_chains-1)
# Create the options
opts = MCMCOpts()
opts.model = tdg
opts.estimate_params = tdg.parameters
opts.initial_values = [1.001, 1.001]
opts.nsteps = nsteps
opts.anneal_length = 0 # necessary so cooling does not occur
opts.T_init = temps[rank - 1] # Use the temperature for this worker
opts.use_hessian = False
opts.seed = 1
opts.norm_step_size = 0.1
opts.likelihood_fn = tdg.likelihood
mcmc = MCMC(opts)
mcmc.initialize()
# The master coordinates when swaps occur ---------
if rank == 0:
pt = PT_MPI_Master(comm, rank, opts, swap_period, num_chains)
pt.run()
# Everyone else runs MCMC steps and swaps when told -----------
else:
pt = PT_MPI_Worker(comm, rank, mcmc, swap_period)
pt.run()
sd = 0.01
tdg = TwoDGaussianFit(means_x, means_y, sd**2)
# Create temperature array based on number of workers (excluding master)
temps = np.logspace(np.log10(min_temp), np.log10(max_temp), num_chains - 1)
# Create the options
opts = MCMCOpts()
opts.model = tdg
opts.estimate_params = tdg.parameters
opts.initial_values = [1.001, 1.001]
opts.nsteps = nsteps
opts.anneal_length = 0 # necessary so cooling does not occur
opts.T_init = temps[rank - 1] # Use the temperature for this worker
opts.use_hessian = False
opts.seed = 1
opts.norm_step_size = 0.1
opts.likelihood_fn = tdg.likelihood
mcmc = MCMC(opts)
mcmc.initialize()
# The master coordinates when swaps occur ---------
if rank == 0:
pt = PT_MPI_Master(comm, rank, opts, swap_period, num_chains)
pt.run()
# Everyone else runs MCMC steps and swaps when told -----------
else:
pt = PT_MPI_Worker(comm, rank, mcmc, swap_period)
pt.run()