Created
July 25, 2013 23:18
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PyMC with dynamic model
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import pymc | |
# load the model | |
import pk_model as mod | |
# fit the model with mcmc | |
mc = pymc.MCMC(mod) | |
mc.use_step_method(pymc.AdaptiveMetropolis, [mod.kcp, mod.kpc, mod.ke]) | |
mc.sample(iter=2000, burn=1000, thin=20, verbose=1) |
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import pymc as pc | |
import numpy as np | |
from scipy.integrate import odeint | |
time = np.linspace(0, 5, 10) | |
cc_data = np.array([1.000e+00, 1.613e-01, 5.576e-02, 2.583e-02, 1.264e-02, | |
6.243e-03, 3.086e-03, 1.525e-03, 7.543e-04, 3.729e-04]) | |
cp_data = np.array([0., 0.1218, 0.0690, 0.0347, 0.0172, | |
0.0085, 0.00421, 0.0020, 0.0010, 0.00050]) | |
kcp = pc.Uniform('kcp', 0.0, 10.) | |
kpc = pc.Uniform('kpc', 0.0, 10.) | |
ke = pc.Uniform('ke' , 0.0, 10.) | |
tspan = time | |
y0 = [cc_data[0], cp_data[0]] | |
# deterministic compartmental model | |
@pc.deterministic | |
def PK(k1=kcp, k2=kpc, k3=ke): | |
def pk_model(y, t): | |
y_cc, y_cp = y[0], y[1] | |
dcc_dt = k1 * y_cp - (k2 + k3) * y_cc | |
dcp_dt = k2 * y_cc - k1 * y_cp | |
dydt = [dcc_dt, dcp_dt] | |
return dydt | |
soln = odeint(pk_model, y0, tspan) | |
cc, cp = soln[:,0], soln[:,1] | |
return [cc, cp] | |
cc = pc.Lambda('cc', lambda PK=PK: PK[0]) | |
cp = pc.Lambda('cp', lambda PK=PK: PK[1]) | |
prec = pc.Gamma('precision', alpha=0.1, beta=0.1) | |
# data likelihood | |
A = pc.Normal('A', mu=cc, tau=prec, value=cc_data, observed=True) | |
B = pc.Normal('B', mu=cp, tau=prec, value=cp_data, observed=True) |
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