def main():
seed = 2
random = numpy.random.RandomState(seed)
sigma = 0.1
ntimes = 20
tspan = numpy.linspace(0, 40, ntimes)
solver = pysb.integrate.Solver(model, tspan)
solver.run()
ydata = solver.y * (random.randn(*solver.y.shape) * sigma + 1)
ysim_max = solver.y.max(0)
ydata_norm = ydata / ysim_max
opts = bayessb.MCMCOpts()
opts.model = model
opts.tspan = tspan
# estimate rates only (not initial conditions) from wild guesses
opts.estimate_params = [
p for p in model.parameters if p.name.startswith('k')
]
opts.initial_values = [1e-4, 1e3, 1e6]
opts.nsteps = 10000
opts.likelihood_fn = functools.partial(likelihood,
data=ydata_norm,
scale_factor=ysim_max,
sigma=sigma)
opts.prior_fn = prior
opts.step_fn = step
opts.use_hessian = True
opts.hessian_period = opts.nsteps / 10
opts.seed = seed
mcmc = bayessb.MCMC(opts)
mcmc.run()
mixed_nsteps = opts.nsteps / 2
mixed_positions = mcmc.positions[-mixed_nsteps:]
mixed_accepts = mcmc.accepts[-mixed_nsteps:]
mixed_accept_positions = mixed_positions[mixed_accepts]
marginal_mean_pos = numpy.mean(mixed_accept_positions, 0)
# position is far from marginal mean, but posterior is good (determined by
# trial and error and some interactive plotting)
interesting_step = 8830
print "\nGenerating figures..."
# show scatter plot
scatter(mcmc, opts.nsteps / 2, mcmc.positions[interesting_step],
marginal_mean_pos)
# show prediction for C trajectory, which was not fit to
prediction(mcmc, opts.nsteps / 2, 2, ysim_max[2], sigma, plot_samples=True)
plt.title("Prediction for C")
# show "true" trajectories and noisy data
data(mcmc, ydata_norm, ysim_max, [0, 1])
plt.title("True trajectories and noisy data")
# show all plots at once
plt.show()
def do_fit(iteration):
"""Runs MCMC on the globally defined model."""
def likelihood(mcmc, position):
yout = mcmc.simulate(position, observables=True)
err = np.sum((synthetic_data['A_'] - yout['A_'])**2 / (2 * sigma**2))
return err
# Initialize the MCMC arguments
opts = bayessb.MCMCOpts()
opts.model = model
opts.tspan = tspan
# Because there is a degradation reaction, there is a __source_0
# parameter in the model that we need to ignore
opts.estimate_params = [
p for p in model.parameters if p.name != '__source_0'
]
# Choose MCMC start values randomly from [0, 10)
opts.initial_values = np.random.uniform(0, 10, 2)
opts.nsteps = nsteps
opts.likelihood_fn = likelihood
opts.step_fn = step
opts.use_hessian = True
opts.hessian_period = opts.nsteps / 10
opts.seed = random_seed
mcmc = bayessb.MCMC(opts)
mcmc.run()
# Pickle it!
basename = 'convergence_test'
output_basename = '%s_%d_steps_seed_%d_iter_%d' % \
(basename, opts.nsteps, random_seed, iteration)
mcmc.options.likelihood_fn = None
output_file = open('%s.pck' % output_basename, 'w')
pickle.dump(mcmc, output_file)
output_file.close()
# Show best fit params
mcmc.position = mcmc.positions[np.argmin(mcmc.likelihoods)]
best_fit_params = mcmc.cur_params(position=mcmc.position)
p_name_vals = zip([p.name for p in model.parameters], best_fit_params)
print('\n'.join([
'%s: %g' % (p_name_vals[i][0], p_name_vals[i][1])
for i in range(0, len(p_name_vals))
]))
return mcmc
ydata = numpy.load(data_filename1)
yvar = numpy.load(data_filename2)
print ydata[:,1:4]
ydata_norm = normalize(ydata[:,1:4])
print ydata_norm
exp_var = normalize_var(ydata[:,1:4], yvar[:,0:3]) #Zinkel's data is averaged with n=3.
# There are too few time points. Therefore, the solver will be inaccurate.
# Instead, I will allow the model to run 4320 time points per every 36 hours (1000 per 30000s).
timepoints = ydata[:,0]*3600 #[hrs]
t_end = timepoints.max(0)
tspan = numpy.linspace(0, t_end, 3000)
obs_names = ['Obs_pC3']
opts = bayessb.MCMCOpts()
opts.model = model
opts.tspan = tspan
opts.protien_conctrations = initial_concentrations
opts.experim_conditions = {'WT':[], 'BIDKO':['Bid_0'], 'DKO':['Bax_0', 'Bak_0'], 'TKO':['Bid_0', 'Bak_0', 'Bax_0']}
# values for prior calculation
opts.nsteps = 10000
opts.likelihood_fn = likelihood
opts.prior_fn = prior
opts.step_fn = step
opts.seed = 1
opts.atol=1e-6
opts.rtol=1e-3
def build_opts():
global parp_initial, exp_ecrp, cparp_sim_norm, exp_ecrp_var, plateau_idx
global prior_mean, prior_var
# instantiate an instance of our model
model = Model()
# EC-RP trajectory (experimental data, arbitrary units)
exp_ecrp = np.array([
0.4820, 0.4540, 0.4500, 0.4430, 0.4440, 0.4420, 0.4430, 0.4470, 0.4390,
0.4490, 0.4450, 0.4450, 0.4390, 0.4410, 0.4370, 0.4450, 0.4470, 0.4390,
0.4430, 0.4410, 0.4390, 0.4410, 0.4420, 0.4430, 0.4490, 0.4420, 0.4460,
0.4480, 0.4500, 0.4420, 0.4460, 0.4450, 0.4520, 0.4480, 0.4520, 0.4460,
0.4470, 0.4500, 0.4500, 0.4470, 0.4490, 0.4570, 0.4500, 0.4530, 0.4550,
0.4510, 0.4560, 0.4560, 0.4600, 0.4530, 0.4540, 0.4510, 0.4590, 0.4570,
0.4490, 0.4510, 0.4640, 0.4580, 0.4560, 0.4610, 0.4620, 0.4600, 0.4590,
0.4640, 0.4640, 0.4650, 0.4750, 0.4760, 0.4760, 0.4780, 0.4760, 0.4810,
0.4830, 0.4930, 0.4870, 0.4890, 0.4890, 0.5180, 0.6120, 0.7280, 0.8050,
0.9120, 0.9570, 0.9980, 1.025, 1.025, 1.068, 1.074, 1.061, 1.056,
1.049, 1.064, 1.092, 1.086, 1.044, 1.023, 1.062, 1.058, 1.077, 1.081,
1.068, 1.066, 1.078, 1.103, 1.116, 1.099, 1.118, 1.087, 1.086, 1.066,
1.076, 1.075, 1.069, 1.080, 1.077, 1.086, 1.079, 1.088, 1.084, 1.092,
1.088, 1.099, 1.093, 1.108, 1.101, 1.104, 1.106, 1.099, 1.110, 1.102,
1.104, 1.111, 1.113, 1.118, 1.117, 1.118, 1.114, 1.131, 1.140, 1.131,
1.135, 1.143, 1.144, 1.146, 1.145, 1.146, 1.137, 1.149, 1.164, 1.157,
1.150, 1.148, 1.151, 1.164, 1.148, 1.157, 1.163, 1.141, 1.152, 1.151,
1.159, 1.164, 1.154, 1.152, 1.141, 1.143, 1.163, 1.158, 1.152, 1.144,
1.151, 1.156, 1.154, 1.151, 1.150, 1.148, 1.150, 1.150, 1.147, 1.148,
1.161, 1.154, 1.160, 1.158, 1.160, 1.140, 1.149, 1.152, 1.161, 1.152,
1.158, 1.156, 1.154, 1.156, 1.157, 1.148, 1.156, 1.159, 1.160, 1.160,
1.150, 1.153, 1.163, 1.156, 1.171, 1.147, 1.166, 1.155, 1.159, 1.163,
1.157, 1.154, 1.154, 1.159, 1.151, 1.162, 1.167, 1.166, 1.159, 1.160,
1.170, 1.165, 1.171, 1.179, 1.164, 1.176, 1.175, 1.178, 1.175, 1.170,
1.178, 1.173, 1.168, 1.168, 1.169, 1.174, 1.177, 1.178, 1.179, 1.181,
1.182
])
# index for beginning and end of MOMP (where the EC-RP signal spikes)
momp_start_idx = 75
momp_end_idx = 86
# data was collected at evenly-spaced points over 12 hours
tspan = np.linspace(0, 12 * 3600, len(exp_ecrp))
# select the forward/reverse/catalytic parameters for estimation
kf = filter_params(model, 'kf')
kr = filter_params(model, 'kr')
kc = filter_params(model, 'kc')
estimate_params = sort_params(model, kf + kr + kc)
# grab the initial amount of parp, for normalizing CPARP trajectories
parp_initial = [p.value for p in model.parameters if p.name == 'PARP_0'][0]
prior_mean, prior_var = calculate_prior_stats(estimate_params, kf, kr, kc)
# clean up the noise in the latter part of the EC-RP signal and rescale to 0-1
# ----------
# shift the range down to begin at 0
exp_ecrp -= exp_ecrp.min()
# take discrete difference
ecrp_dd = np.diff(exp_ecrp)
# get first index after momp start where the signal drops (i.e. dd is negative)
plateau_idx = [
i for i in range(momp_start_idx, len(ecrp_dd)) if ecrp_dd[i] < 0
][0]
# rescale the portion before that index to a max of 1
exp_ecrp[:plateau_idx] /= exp_ecrp[plateau_idx]
# clamp the latter portion directly to 1
exp_ecrp[plateau_idx:] = 1.0
# set up a vector of variance values for the ecrp signal
exp_ecrp_var = np.empty_like(tspan)
# start with a single value for the variance at all time points
exp_ecrp_var[:] = 0.0272
# use a higher value for the switching window to reflect less certainty there
exp_ecrp_var[momp_start_idx:momp_end_idx + 1] = 0.1179
# set up our MCMC options
opts = bayessb.MCMCOpts()
opts.model = model
opts.tspan = tspan
opts.nsteps = 200
opts.likelihood_fn = likelihood
opts.prior_fn = prior
opts.step_fn = step
opts.estimate_params = estimate_params
# the specific value of seed isn't important, it just makes the run reproducible
opts.seed = 1
# note that solver tolerance values are set in earm_1_3_standalone.py
return opts