def fisher_information(kA):
dx_dt = abc.dx_dt # simplest system with hopf bifurcation
ka_range = np.linspace(2, 3.8, 19)
datasets = []
N = len(ka_range)
h = 0.01
#produce all observable datasets into D
for ka in ka_range:
datasets.append(abc.generate_dataset_full(dx_dt, [ka]))
sum_partial = 0.
for dataset in datasets:
partial_deriv = (log_likelihood(dataset, abc.generate_dataset_full(dx_dt, [kA + h])) -
log_likelihood(dataset, abc.generate_dataset_full(dx_dt, [kA])))
sum_partial += partial_deriv**2
fi = sum_partial/(4*N*h**2)
return fi
def main():
theta = [2.4, 0.02, 0.2, 6.9]
M0 = np.array([2.0, 5.0, 3.0])
ds = abc.generate_dataset_full(hes1, theta)
noisy_ds = abc.add_gaussian_noise_full(np.copy(ds))
populations = (abc.smc(hes1, noisy_ds, [300.0]))
sys.exit(0)
plt.plot(t, p1, 'r-')
plt.plot(t, p11, 'b-')
plt.subplot(313)
plt.plot(t, p2, 'r-')
plt.plot(t, p21, 'b-')
plt.show()
def main():
theta = [2.4, 0.02, 0.2, 6.9 ]
M0 = np.array([2.0, 5.0, 3.0])
ds = abc.generate_dataset_full(hes1, theta)
noisy_ds = abc.add_gaussian_noise_full(np.copy(ds))
populations = (abc.smc(hes1, noisy_ds, [300.0]))
sys.exit(0)
plt.plot(t, p1,'r-')
plt.plot(t, p11,'b-')
plt.subplot(313)
plt.plot(t, p2,'r-')
plt.plot(t, p21,'b-')
plt.show()
def gene_regulation():
theta = [1., 10.]
t = np.arange(0, 15, 0.1)
X0 = 1.
ds = abc.generate_dataset_full(gene_reg, theta)
noisy_ds = abc.add_gaussian_noise_full(np.copy(ds))
populations = abc.smc(gene_reg, noisy_ds, [300.0])
theta1 = utils.colMeans(np.vstack(populations[:-1]))
X = integrate.odeint(gene_reg, X0, t, args=(theta, ))
plt.plot(t, X, 'r-')
X1 = integrate.odeint(gene_reg, X0, t, args=(theta1, ))
plt.plot(t, X1, 'b-')
plt.plot(t, noisy_ds, 'go')
plt.show()
def gene_regulation():
theta = [1., 10.]
t = np.arange(0, 15, 0.1)
X0 = 1.
ds = abc.generate_dataset_full(gene_reg, theta)
noisy_ds = abc.add_gaussian_noise_full(np.copy(ds))
populations = abc.smc(gene_reg, noisy_ds, [300.0])
theta1 = utils.colMeans(np.vstack(populations[:-1]))
X = integrate.odeint(gene_reg, X0, t, args=(theta, ))
plt.plot(t, X, 'r-')
X1 = integrate.odeint(gene_reg, X0, t, args=(theta1, ))
plt.plot(t, X1, 'b-')
plt.plot(t, noisy_ds, 'go')
plt.show()
def main_hopf():
dx_dt = abc.dx_dt # simplest system with hopf bifurcation
orig_theta = [2.2, 1.]
orig_ds = abc.generate_dataset_full(dx_dt, orig_theta)
#orig_ds = abc.add_gaussian_noise_full(orig_ds)
param_range = np.arange(.5, 7., 0.2)
param_range_1 = np.arange(4, 7, 0.2)
likelihood_vals = np.zeros((len(param_range), len(param_range_1)))
for ind1, th in enumerate(param_range):
for ind2, th1 in enumerate(param_range_1):
sim_ds = abc.generate_dataset_full(dx_dt, [th, th1])
l = log_likelihood(sim_ds, orig_ds)
likelihood_vals[ind1, ind2] = l
print th, th1, l
print "========================"
i,j = np.unravel_index(likelihood_vals.argmax(), likelihood_vals.shape)
print "max likelihood ", likelihood_vals[i, j], " at: ()", i, " ,", j, ")"
fig = plt.figure()
ax = fig.gca(projection='3d')
m1, m2 = np.meshgrid(param_range, param_range_1)
print np.shape(m1), np.shape(m2), np.shape(likelihood_vals)
surf = ax.plot_surface(m1, m2, likelihood_vals.T, rstride=1, cstride=1, cmap=cm.jet, linewidth=0.1, antialiased=True)
fig.colorbar(surf, shrink=0.5, aspect=5)
ax.set_xlabel('kA')
ax.set_ylabel('k2')
ax.set_zlabel('likelihood')
plt.figure()
plt.imshow(likelihood_vals)
plt.show()
