def log_likelihood_contributions(
params,
like_contributions,
parse_params_args,
periods,
nmeas_list,
anchoring,
square_root_filters,
update_args,
predict_args,
calculate_sigma_points_args,
restore_args,
):
"""Return the log likelihood contributions per update and individual in the sample.
Users do not have to call this function directly and do not have to bother
about its arguments but the function nicely shows how the likelihood
interpretation of the Kalman filter allow to break the large likelihood
problem of the model into many smaller problems.
First the params vector is parsed into the many quantities that depend on
it. See :ref:`params_and_quants` for details.
Then, for each period of the model first all Kalman updates for the
measurement equations are done. Each Kalman update updates the following
quantities:
* the state array X
* the covariance matrices P
* the likelihood vector like_vec
* the weights for the mixture distribution of the factors W
Then the predict step of the Unscented Kalman filter is applied. The
predict step propagates the following quantities to the next period:
* the state array X
* the covariance matrices P
In the last period an additional update is done to incorporate the
anchoring equation into the likelihood.
"""
restore_unestimated_quantities(**restore_args)
like_contributions[:] = 0.0
parse_params(params, **parse_params_args)
k = 0
for t in periods:
for _j in range(nmeas_list[t]):
# measurement updates
update(square_root_filters, update_args[k])
k += 1
if t < periods[-1]:
calculate_sigma_points(**calculate_sigma_points_args)
predict(t, square_root_filters, predict_args)
if anchoring is True:
update(square_root_filters, update_args[k])
return like_contributions
def test_merwe_sigma_point_construction(self):
expected_sps = np.array(self.fixtures['merwe_points']).reshape(
self.nemf * self.nind, self.nsigma, self.nfac)
calculate_sigma_points(states=self.states, flat_covs=self.lcovs_t,
scaling_factor=0.234520787991, out=self.out,
square_root_filters=True)
aaae(self.out, expected_sps)
def test_merwe_sigma_point_construction(self):
expected_sps = np.array(self.fixtures['merwe_points']).reshape(
self.nemf * self.nind, self.nsigma, self.nfac)
calculate_sigma_points(states=self.states,
flat_covs=self.lcovs_t,
scaling_factor=0.234520787991,
out=self.out,
square_root_filters=True)
aaae(self.out, expected_sps)
def log_likelihood_per_individual(params, like_vec, parse_params_args,
stagemap, nmeas_list, anchoring,
square_root_filters, update_types,
update_args, predict_args,
calculate_sigma_points_args, restore_args):
"""Return the log likelihood for each individual in the sample.
Users do not have to call this function directly and do not have to bother
about its arguments but the function nicely shows how the likelihood
interpretation of the Kalman filter allow to break the large likelihood
problem of the model into many smaller problems.
First the params vector is parsed into the many quantities that depend on
it. See :ref:`params_and_quants` for details.
Then, for each period of the model first all Kalman updates for the
measurement equations are done. Each Kalman update updates the following
quantities:
* the state array X
* the covariance matrices P
* the likelihood vector like_vec
* the weights for the mixture distribution of the factors W
Then the predict step of the Unscented Kalman filter is applied. The
predict step propagates the following quantities to the next period:
* the state array X
* the covariance matrices P
In the last period an additional update is done to incorporate the
anchoring equation into the likelihood.
"""
like_vec[:] = 1.0
restore_unestimated_quantities(**restore_args)
parse_params(params, **parse_params_args)
k = 0
for t, stage in enumerate(stagemap):
for j in range(nmeas_list[t]):
# measurement updates
update(square_root_filters, update_types[k], update_args[k])
k += 1
if t < len(stagemap) - 1:
calculate_sigma_points(**calculate_sigma_points_args)
predict(stage, square_root_filters, predict_args)
if anchoring is True:
j += 1
# anchoring update
update(square_root_filters, update_types[k], update_args[k])
small = 1e-250
like_vec[like_vec < small] = small
return np.log(like_vec)
def log_likelihood_per_individual(
params, like_vec, parse_params_args, stagemap, nmeas_list, anchoring,
square_root_filters, update_types, update_args, predict_args,
calculate_sigma_points_args, restore_args):
"""Return the log likelihood for each individual in the sample.
Users do not have to call this function directly and do not have to bother
about its arguments but the function nicely shows how the likelihood
interpretation of the Kalman filter allow to break the large likelihood
problem of the model into many smaller problems.
First the params vector is parsed into the many quantities that depend on
it. See :ref:`params_and_quants` for details.
Then, for each period of the model first all Kalman updates for the
measurement equations are done. Each Kalman update updates the following
quantities:
* the state array X
* the covariance matrices P
* the likelihood vector like_vec
* the weights for the mixture distribution of the factors W
Then the predict step of the Unscented Kalman filter is applied. The
predict step propagates the following quantities to the next period:
* the state array X
* the covariance matrices P
In the last period an additional update is done to incorporate the
anchoring equation into the likelihood.
"""
like_vec[:] = 1.0
restore_unestimated_quantities(**restore_args)
parse_params(params, **parse_params_args)
k = 0
for t, stage in enumerate(stagemap):
for j in range(nmeas_list[t]):
# measurement updates
update(square_root_filters, update_types[k], update_args[k])
k += 1
if t < len(stagemap) - 1:
calculate_sigma_points(**calculate_sigma_points_args)
predict(stage, square_root_filters, predict_args)
if anchoring is True:
j += 1
# anchoring update
update(square_root_filters, update_types[k], update_args[k])
small = 1e-250
like_vec[like_vec < small] = small
return np.log(like_vec)