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conditional_laws.py
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conditional_laws.py
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import numpy as np
from scipy.linalg import solve_toeplitz, toeplitz
def simul_alpha(model, noise_H, noise_K):
'''
Simulate alpha in Gibbs sampler knowing all other parameters
'''
params, data, constants = model.params, model.data, model.constants
past, present = constants['past'](), constants['present']()
T = np.concatenate((params['T13']()[:past], data['T2']()))
T = np.array([np.ones((present)), T])
cov_top = noise_H.get_toeplitz(present, params['H']())
b = solve_toeplitz(cov_top, T.T)
P1 = np.dot(T, b)
P2 = np.dot(data['RP'](), b)
omega = np.linalg.inv(1/params['sigma_p']()**2 * P1 + np.identity(2))
delta = 1/params['sigma_p']()**2 * P2 + np.array([0,1])
return np.random.multivariate_normal(mean = np.dot(delta, omega), cov = omega)
def simul_beta(model, noise_H, noise_K):
'''
Simulate beta in Gibbs sampler knowing all other parameters
'''
params, data, constants = model.params, model.data, model.constants
past, future = constants['past'](), constants['future']()
T = np.concatenate((params['T13']()[:past], data['T2'](), params['T13']()[past:]))
F = np.array([np.ones((future)), data['S'](), data['V'](), data['C']()])
cov_top = noise_K.get_toeplitz(future, params['K']())
b = solve_toeplitz(cov_top, F.T)
P1 = np.dot(F, b)
P2 = np.dot(T, b)
omega = np.linalg.inv(1/params['sigma_T']()**2 * P1 + np.identity(4))
delta = 1/params['sigma_T']()**2 * P2 + np.array([0,1,1,1])
return np.random.multivariate_normal(mean = np.dot(delta, omega), cov = omega)
def simul_s_p(model, noise_H, noise_K):
'''
Simulate sigma_p in Gibbs sampler knowing all other parameters
'''
params, data, constants = model.params, model.data, model.constants
past, present = constants['past'](), constants['present']()
T = np.concatenate((params['T13']()[:past], data['T2']()))
T = np.array([np.ones((present)), T])
cov_top = noise_H.get_toeplitz(present, params['H']())
P1 = np.dot(params['alpha'](), T)
b = solve_toeplitz(cov_top, data['RP']() - P1)
P2 = np.dot((data['RP']() - P1).T,b)
q = 2 + present/2
r = 0.1 + 1/2 * P2
return np.sqrt(1/np.random.gamma(shape = q, scale = 1/r))
def simul_s_T(model, noise_H, noise_K):
'''
Simulate sigma_T in Gibbs sampler knowing all other parameters
'''
params, data, constants = model.params, model.data, model.constants
past, future = constants['past'](), constants['future']()
T = np.concatenate((params['T13']()[:past], data['T2'](), params['T13']()[past:]))
F = np.array([np.ones((future)), data['S'](), data['V'](), data['C']()])
cov_top = noise_K.get_toeplitz(future, params['K']())
P1 = np.dot(params['beta'](), F)
b = solve_toeplitz(cov_top, T - P1)
P2 = np.dot((T - P1).T,b)
q = 2 + future/2
r = 0.1 + 1/2 * P2
return np.sqrt(1/np.random.gamma(shape = q, scale = 1/r))
def simul_T(model, noise_H, noise_K):
'''
Simulate T13 in Gibbs sampler knowing all other parameters
'''
params, data, constants = model.params, model.data, model.constants
past, present, future = constants['past'](), constants['present'](), constants['future']()
F = np.array([np.ones((future)), data['S'](), data['V'](), data['C']()]).T
inv_covH = np.pad(np.linalg.inv(noise_H.get_cov(present, params['H']())), pad_width=(0,future-present), mode = 'constant')
inv_covK = np.linalg.inv(noise_K.get_cov(future, params['K']()))
P1 = np.dot(inv_covH, np.pad(data['RP'](), pad_width=(0,future-present), mode = 'constant') - params['alpha']()[0])
P2 = np.dot(inv_covK, np.dot(F, params['beta']()))
omega = np.linalg.inv((params['alpha']()[1]/params['sigma_p']())**2*inv_covH + 1/params['sigma_T']()**2 * inv_covK)
delta = params['alpha']()[1]/params['sigma_p']()**2 * P1 + 1/params['sigma_T']()**2 * P2
mu = np.dot(delta, omega)
# T = mu + np.dot(np.linalg.cholesky(omega), np.random.randn(len(mu)))
M1 = omega[past:present, past:present]
M1_inv = np.linalg.inv(M1)
M2 = np.concatenate((omega[:past, past:present], omega[present:future, past:present]), axis = 0)
M3 = np.concatenate((np.concatenate((omega[:past,:past],omega[:past, present:future]), axis = 1), np.concatenate((omega[present:future,:past], omega[present:future,present:future]), axis = 1)), axis = 0)
M3_inv = np.linalg.inv(M3)
# Bloc 1-3
new_mean13 = np.concatenate((mu[:past], mu[present:future])) + np.dot(M2,np.dot(M1_inv, data['T2']() - mu[past:present]))
new_cov13 = M3 - np.dot(M2, np.dot(M1_inv, M2.T))
T13 = new_mean13 + np.dot(np.linalg.cholesky(new_cov13), np.random.randn(len(new_mean13)))
# Bloc 2
new_mean2 = mu[past:present] + np.dot(M2.T,np.dot(M3_inv, T13 - np.concatenate((mu[:past], mu[present:future]))))
new_cov2 = M1 - np.dot(M2.T, np.dot(M3_inv, M2))
T2 = new_mean2 + np.dot(np.linalg.cholesky(new_cov2), np.random.randn(len(new_mean2)))
return T13, T2
def simul_H(model, noise_H, noise_K):
'''
Simulate H in Gibbs sampler knowing all other parameters
'''
params, data, constants = model.params, model.data, model.constants
H = model.params['H']()
if noise_H.n_params == 0:
return H
step_H = constants['step_H']()
n_iteration = constants['n_iteration']()
# Simulation of H
acc = 0
for k in range(n_iteration):
new_H = noise_H.draw_MH(H, step_H)
log_p1 = noise_H.log_p(params, data, constants, 'H', new_H)
log_p2 = noise_H.log_p(params, data, constants, 'H', H)
log_q1 = noise_H.log_q(H, new_H, step_H)
log_q2 = noise_H.log_q(new_H, H, step_H)
alpha = log_p1 + log_q1 - log_p2 - log_q2
a = np.random.uniform()
if np.log(a) <= alpha: # Accept
H = new_H
acc += 1
return H
def simul_K(model, noise_H, noise_K):
'''
Simulate K in Gibbs sampler knowing all other parameters
'''
params, data, constants = model.params, model.data, model.constants
K = model.params['K']()
if noise_K.n_params == 0:
return K
step_K = constants['step_K']()
n_iteration = constants['n_iteration']()
# Simulation of K
acc = 0
for k in range(n_iteration):
new_K = noise_K.draw_MH(K, step_K)
log_p1 = noise_K.log_p(params, data, constants, 'K', new_K)
log_p2 = noise_K.log_p(params, data, constants, 'K', K)
log_q1 = noise_K.log_q(K, new_K, step_K)
log_q2 = noise_K.log_q(new_K, K, step_K)
alpha = log_p1 + log_q1 - log_p2 - log_q2
a = np.random.uniform()
if np.log(a) <= alpha: # Accept
K = K = new_K
acc += 1
return K