def __init__(self, **kwargs):
StateSpaceModel.__init__(self, **kwargs)
if self.sigma0 is None:
self.sigma0 = self.sigmaX / np.sqrt(1. - self.rho**2)
self.kf = kalman.Kalman(F=self.rho, G=1., covX=self.sigmaX**2,
covY=self.sigmaY**2,
cov0=self.sigma0**2)
def loglik(self, theta, t=None):
# Note: for simplicity we ignore argument t here,
# and compute the full log-likelihood
ll = np.zeros(theta.shape[0])
for n, th in enumerate(theta):
mod = ReparamLinGauss(**smc_samplers.rec_to_dict(th))
kf = kalman.Kalman(data=data, ssm=mod)
kf.filter()
ll[n] = np.sum(kf.logpyt)
return ll
from particles import kalman
from particles import state_space_models
# parameter values
sigmaX = 1.
sigmaY = .2
rho = 0.9
T = 1000
N = 200
# define ss model, simulate data
ssm = kalman.LinearGauss(sigmaX=sigmaX, sigmaY=sigmaY, rho=rho)
true_states, data = ssm.simulate(T)
# computes true log-likelihood
kf = kalman.Kalman(ssm=ssm, data=data)
kf.filter()
true_loglik = np.sum(kf.logpyt)
# FK model
fk_model = state_space_models.GuidedPF(ssm=ssm, data=data)
# Run SMC algorithm for different values of ESS_min
alphas = list(np.linspace(0., .1, 11)) + list(np.linspace(0.15, 1., 18))
results = particles.multiSMC(fk=fk_model,
N=N,
ESSrmin=alphas,
nruns=200,
nprocs=1)
# PLOTS
def __init__(self, **kwargs):
StateSpaceModel.__init__(self, **kwargs)
self.kf = kalman.Kalman(F=self.F, G=self.G, covX=self.covX,
covY=self.covY, mu0=self.mu0, cov0=self.cov0)
# Define ssm, simulate data
T = 100
my_ssm = kalman.LinearGauss(sigmaX=1., sigmaY=.2, rho=.9)
true_states, data = my_ssm.simulate(T)
# FK models
models = OrderedDict()
models['bootstrap'] = ssms.Bootstrap(ssm=my_ssm, data=data)
models['guided'] = ssms.GuidedPF(ssm=my_ssm, data=data)
models['APF'] = ssms.AuxiliaryPF(ssm=my_ssm, data=data)
# Uncomment line below if you want to include the "Boostrap APF"
# (APF with proposal set to dist. of X_t|X_{t-1}) in the comparison
#models['bootAPF'] = ssm.AuxiliaryBootstrap(ssm=my_ssm, data=data)
# Compute "truth"
kf = kalman.Kalman(ssm=my_ssm, data=data)
kf.filter()
true_loglik = np.cumsum(kf.logpyt)
true_filt_means = [f.mean for f in kf.filt]
# Get results
N = 10**3
results = particles.multiSMC(fk=models, N=N, nruns=25, moments=True)
# PLOTS
# =====
plt.style.use('ggplot')
savefigs = False # whether you want to save figs as pdfs
# black and white
sb.set_palette(sb.dark_palette("lightgray", n_colors=len(models),
rho, sigX, sigY, sig0 = 0.9, 1., 0.2, 3.
uni_ssm = kalman.LinearGauss(rho=rho, sigmaX=sigX, sigmaY=sigY, sigma0=sig0)
univariate = False # test univariate or multivariate model?
if univariate:
ssm = uni_ssm
F, G, mu0 = rho, 1., 0.
covX, covY, cov0 = sigX**2, sigY**2, sig0**2
else:
ssm = mv_ssm
# data
x, y = ssm.simulate(T)
# Our Kalman filter
mykf = kalman.Kalman(ssm=ssm, data=y)
mykf.smoother() # this does both filtering and smoothing
# Their Kalman filter
theirkf = pykalman.KalmanFilter(transition_matrices = F,
observation_matrices = G,
transition_covariance=covX,
observation_covariance=covY,
initial_state_mean=mu0,
initial_state_covariance=cov0)
their_data = np.array(y).squeeze()
their_filt_means, their_filt_covs = theirkf.filter(their_data)
their_filt_means = their_filt_means.squeeze()
# Comparing filtering means and covs
