def fit_beta_by_pt(nsteps):
"""Fit a beta distribution by parallel tempering."""
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 = [10 ** 0.5]
opts.nsteps = nsteps
opts.anneal_length = 0
opts.T_init = 1
opts.use_hessian = False
opts.seed = 1
opts.norm_step_size = 0.5
opts.likelihood_fn = b.likelihood
opts.step_fn = step
# Create the MCMC object
num_temps = 8
pt = PT_MCMC(opts, num_temps, 10)
pt.estimate()
plt.ion()
for chain in pt.chains:
fig = plt.figure()
chain.prune(nsteps/10, 1)
(heights, points, lines) = plt.hist(chain.positions, bins=100,
normed=True)
plt.plot(points, beta.pdf(points, b.a, b.b), 'r')
plt.ylim((0,10))
plt.xlim((0, 1))
return pt
def fit_twod_gaussians_by_pt(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 = 0 # necessary so cooling does not occur
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
# Create the PT object
num_temps = 8
pt = PT_MCMC(opts, num_temps, 100)
pt.estimate()
plt.ion()
for chain in pt.chains:
fig = plt.figure()
chain.prune(nsteps/10, 1)
plt.scatter(chain.positions[:,0], chain.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.title('Temp = %.2f' % chain.options.T_init)
plt.show()
return pt
class NBD_MCMC_PT(object):
"""Fit mechanistic tBid/Bax models to NBD data.
Initialize internal MCMC object and then set additional fields.
Parameters
----------
options : MCMCOpts
Options for MCMC initialization.
nbd_avgs : numpy.array
data mean
nbd_stds : numpy.array
data SD
nbd_sites : list of strings
Sites from data to fit.
nbd_observables : list of strings
Observables from model to fit to the sites in nbd_sites.
builder : tbidbaxlipo.models.core.Builder
"""
def __init__(self, options, nbd_avgs, nbd_stds, nbd_sites, nbd_observables,
builder):
#self.mcmc = MCMC(options)
self.nbd_avgs = nbd_avgs
self.nbd_stds = nbd_stds
self.nbd_sites = nbd_sites
self.nbd_observables = nbd_observables
self.builder = builder
# Set the MCMC functions
options.likelihood_fn = self.get_likelihood_function()
options.prior_fn = self.builder.prior
options.step_fn = self.step
self.options = options
self.pt = PT_MCMC(options, 10, max_temp=1e7, min_temp=1, swap_period=5)
# Pickling functions for this class
#def __getstate__(self):
#self.pt = None
#self.options.likelihood_fn = None
#self.options.prior_fn = None
#self.options.step_fn = None
#mcmc_state = bayessb.MCMC.__getstate__(self)
#nbd_mcmc_state = self.__dict__.copy()
#return (mcmc_state, nbd_mcmc_state)
# May have to explicitly reset these in the chains of the PT
# return self.__dict__.copy()
#def __setstate__(self, state):
#(mcmc_state, nbd_mcmc_state) = state
#bayessb.MCMC.__setstate__(self, state)
#self.__dict__.update(nbd_mcmc_state)
#self.options.likelihood_fn = self.get_likelihood_function()
#self.options.prior_fn = self.builder.prior
#self.options.step_fn = self.step
# May have to explicitly reset these in the chains of the PT
# MCMC Functions
# ==============
def do_fit(self):
"""Runs MCMC on the given model."""
#self.mcmc.initialize()
# Print initial parameter values
"""
init_vals = zip([p.name for p in self.options.model.parameters],
self.mcmc.cur_params(position=self.mcmc.initial_position))
init_vals_str = 'Initial values:\n'
init_vals_str += '\n'.join(['%s: %g' % (init_vals[i][0],
init_vals[i][1])
for i in range(0, len(init_vals))])
print "------------------------"
print init_vals_str
print "------------------------"
"""
# Run it!
#self.mcmc.estimate()
self.pt.estimate()
def generate_figures(self, report_name='report', do_report=True,
mixed_start=None, num_samples=500):
"""Plots a series of useful visualizations of the walk, the
quality of the fit, etc."""
plt.ion()
if do_report:
rep = Report()
# Plot "Before" curves -------
before_fig = self.fit_plotting_function(self.mcmc.initial_position)
if do_report:
rep.add_figure(before_fig)
# Print initial parameter values
init_vals = zip([p.name for p in self.mcmc.options.model.parameters],
self.mcmc.cur_params(position=self.mcmc.initial_position))
init_vals_str = 'Initial values:\n'
init_vals_str += '\n'.join(['%s: %g' % (init_vals[i][0],
init_vals[i][1])
for i in range(0, len(init_vals))])
print init_vals_str
if do_report:
rep.add_text(init_vals_str)
# Plot "After" curves ------------
# Set to last fit position
if mixed_start is None:
mixed_start = self.mcmc.options.nsteps / 2
mixed_positions = self.mcmc.positions[mixed_start:,:]
mixed_accepted_positions = mixed_positions[
self.mcmc.accepts[mixed_start:]]
last_position = mixed_accepted_positions[-1,:]
after_fig = self.fit_plotting_function(last_position)
if do_report:
rep.add_figure(after_fig)
# Print final parameter values
last_fit_params = self.mcmc.cur_params(position=last_position)
last_vals = zip([p.name for p in self.mcmc.options.model.parameters],
last_fit_params)
last_vals_str = 'Final values:\n'
last_vals_str += '\n'.join(['%s: %g' % (last_vals[i][0],
last_vals[i][1])
for i in range(0, len(last_vals))])
print last_vals_str
if do_report:
rep.add_text(last_vals_str)
"""
# Plot sampling of fits # FIXME should be real sampling------
plt.figure()
plot_data(nbd_site)
max_position_index = len(mixed_accepted_positions) - 1
num_to_plot = min(num_samples, max_position_index)
for i in range(num_to_plot):
cur_position = mixed_accepted_positions[max_position_index - i,:]
x = nbd_timecourse(mcmc, cur_position, nbd_observable)
plt.plot(mcmc.options.tspan, x, 'b', label=nbd_site, alpha=0.02)
plt.title("Last %d accepted positions" % num_to_plot)
plt.show()
if do_report:
rep.add_current_figure()
# Plot marginal distributions of parameters ---------------
for i, cur_param in enumerate(mcmc.options.estimate_params):
plt.figure()
plt.hist(mixed_accepted_positions[:,i])
plt.title("%s, last %d accepts: initval %f" %
(cur_param.name, len(mixed_accepted_positions[:,i]),
cur_param.value))
plt.show()
if do_report:
rep.add_current_figure()
"""
# Plot convergence traces of all parameters
plt.figure()
plt.plot(self.mcmc.positions)
plt.title("Parameter traces")
plt.legend([p.name for p in self.mcmc.options.estimate_params],
loc='lower left', prop={'size':7})
plt.show()
if do_report:
rep.add_current_figure()
# Add code to report
if do_report:
# Add the code for the fitting (this file)
#rep.add_python_code('nbd_mcmc_pt.py')
# Add the code for the model
#rep.add_python_code('models/core.py')
#rep.add_python_code('models/one_cpt.py')
# Write the report
rep.write_report(report_name)
def plot_data(self, axis):
"""Plots the current data into the given axis."""
alpha = 0.5
if 'c3' in self.nbd_sites:
axis.plot(self.mcmc.options.tspan, self.nbd_avgs[0], 'r.',
label='c3 data', alpha=alpha)
if 'c62' in self.nbd_sites:
axis.plot(self.mcmc.options.tspan, self.nbd_avgs[1], 'g.',
label='c62 data', alpha=alpha)
#plt.plot(nbd.time_other, nbd_avgs[2], 'b.', label='c120 data',
# alpha=alpha)
#plt.plot(nbd.time_other, nbd_avgs[3], 'm.', label='c122 data',
# alpha=alpha)
#plt.plot(nbd.time_other, nbd_avgs[4], 'k.', label='c126 data',
# alpha=alpha)
def get_observable_timecourses(self, position):
"""Gets the timecourses associated with the experimental observables.
Parameters
----------
position : numpy.array
Values of parameters (in log10) at desired position.
Returns
-------
dict
Dict containing the a timecourse for every observable. Keys are
the observable names.
"""
# TODO Need to be able to get the indices for scaling parameters
# from the model so that they're not hardcoded
# Run the simulation and scale the simulated timecourses
yout = self.mcmc.simulate(position, observables=True)
params = self.mcmc.cur_params(position)
timecourses = {}
for obs in self.nbd_observables:
timecourses[obs] = ((yout[obs] /
self.mcmc.options.model.parameters['Bax_0'].value)
* params[3])
return timecourses
def fit_plotting_function(self, position):
"""Gets the observable timecourse and plots it against the data."""
# Run the simulation at the given position
timecourses = self.get_observable_timecourses(position)
# Make the plot
fig = Figure()
ax = fig.gca()
# Add the data to the plot
self.plot_data(ax)
# Add the simulations to the plot
for obs_name, timecourse in timecourses.iteritems():
ax.plot(self.mcmc.options.tspan, timecourse, label=obs_name)
# Label the plot
ax.set_xlabel('Time')
ax.set_ylabel('Concentration')
fontP = FontProperties()
fontP.set_size('small')
ax.legend(loc='upper center', prop=fontP, ncol=5,
bbox_to_anchor=(0.5, 1.1), fancybox=True, shadow=True)
canvas = FigureCanvasAgg(fig)
fig.set_canvas(canvas)
return fig
# A function to generate the likelihood function
def get_likelihood_function(self):
"""Returns a likelihood function for the specified NBD site."""
data_indices = []
if 'c3' in self.nbd_sites:
data_indices.append(0)
if 'c62' in self.nbd_sites:
data_indices.append(1)
# Make sure the list is not empty
if not data_indices:
raise Exception('Failed to initialize data_indices!')
# Make sure that there is a corresponding data trajectory for each
# observable
if len(data_indices) != len(self.nbd_observables):
raise Exception('Length of list of nbd_sites does not match the '
'list of nbd_observables!')
def likelihood(mcmc, position):
yout = mcmc.simulate(position, observables=True)
# TODO Need to be able to get the indices from the model so that
# they're not hardcoded
params = mcmc.cur_params(position)
err = 0
for data_index, obs_name in zip(data_indices, self.nbd_observables):
timecourse = ((yout[obs_name] /
mcmc.options.model.parameters['Bax_0'].value)
* params[3])
err += np.sum((self.nbd_avgs[data_index] - timecourse)**2 /
(2 * self.nbd_stds[data_index]**2))
return err
return likelihood
def get_basename(self):
"""A function for standardizing, in one place, the format for pickled
NBD_MCMC objects.
"""
return '%s_%s_%s_%d_s%d' % (self.options.model.name,
'-'.join(self.nbd_sites),
'-'.join(self.nbd_observables),
self.options.nsteps,
#self.mcmc.options.T_init,
#np.log10(self.options.thermo_temp),
self.options.seed)
@staticmethod
def step(mcmc):
"""The function to call at every iteration. Currently just prints
out a few progress indicators.
"""
window = mcmc.options.accept_window
local_acc = np.sum(mcmc.accepts[(mcmc.iter - window):mcmc.iter]) / \
float(window)
if mcmc.iter % 20 == 0:
print 'iter=%-5d sigma=%-.3f T=%-.3f loc_acc=%-.3f ' \
'glob_acc=%-.3f lkl=%g prior=%g post=%g' % \
(mcmc.iter, mcmc.sig_value, mcmc.T,
local_acc,
mcmc.acceptance/(mcmc.iter+1.), mcmc.accept_likelihood,
mcmc.accept_prior, mcmc.accept_posterior)