def laplace_z(calc):
m = minimize(pot_value,
xd,
args=calc,
method='L-BFGS-B',
jac=True,
options={
'disp': False
}).x
# A = pot_hess(m)
A = calc.hessian(m)
L = np.linalg.cholesky(A)
half_log_det_A = np.sum(np.log(np.diag(L)))
return -pot_value(m, calc)[0] + lap_c1 - half_log_det_A
f = minimize(pot_value,
g,
args=calc,
method='L-BFGS-B',
jac=True,
options={'disp': False})
if (f.fun < f_val):
f_val = f.fun
m = f.x
# Estimate likelihood with Laplace approximation
# A = pot_hess(m)
A = calc.hessian(m)
L = np.linalg.cholesky(A)
half_log_det_A = np.sum(np.log(np.diag(L)))
lap = -pot_value(m, calc)[0] + lap_c1 - half_log_det_A
like_values[i, j] = -lap - pot_value(xd, calc)[0]
except:
print("exception encountered in the try block")
None
# If minimize fails set value to previous, otherwise update previous
if like_values[i, j] == 0:
like_values[i, j] = last_like
else:
last_like = like_values[i, j]
# Output results
idx = np.unravel_index(like_values.argmax(), like_values.shape)
print("Fitted alpha and beta values:")
print(XX[idx], YY[idx] * 2. / 1.4e6, like_values[idx])
# MCMC tuning parameters
L = 10 #Number of leapfrog steps
eps = 0.1 #Leapfrog step size
# Set-up MCMC
mcmc_n = 1000
temp_n = 5
inverse_temps = np.array([1., 1. / 2., 1. / 4., 1. / 8., 1. / 16.])
samples = np.empty((mcmc_n, mm)) # X-values
#Initialize MCMC
xx = -np.log(mm) * np.ones((temp_n, mm))
V = np.empty(temp_n)
gradV = np.empty((temp_n, mm))
for j in range(temp_n):
V[j], gradV[j] = pot_value(xx[j], calc)
# Counts to keep track of accept rates
ac = np.zeros(temp_n)
pc = np.zeros(temp_n)
acs = 0
pcs = 1
tic = timeit.default_timer()
# MCMC algorithm
for i in range(mcmc_n):
for j in range(temp_n):
#Initialize leapfrog integrator for HMC proposal
p = np.random.normal(0., 1.,
mm) # fixed Multivariate Standard Gaussian