View source on GitHub |
Ensemble Kalman filter log marginal likelihood.
tfp.experimental.sequential.ensemble_kalman_filter_log_marginal_likelihood(
state,
observation,
observation_fn,
perturbed_observations=True,
low_rank_ensemble=False,
seed=None,
name=None
)
The Ensemble Kalman Filter is a Monte Carlo version of the traditional Kalman Filter. See also [2]. It assumes the model
X[t] ~ transition_fn(X[t-1])
Y[t] ~ observation_fn(X[t])
This method estimates (logarithm of) the marginal likelihood of the
observation at step t
, Y[t]
, given state
. Typically, state
is the
predictive ensemble at time t
. In that case, this function approximates
Log[p(Y[t] | Y[t-1], Y[t-2],...)]
The approximation is correct under a Linear Gaussian state space model
assumption, as ensemble size --> infinity.
Args | |
---|---|
state
|
Instance of EnsembleKalmanFilterState at step k ,
conditioned on previous observations Y_{1:k} . Typically this is the
output of ensemble_kalman_filter_predict .
|
observation
|
Tensor representing the observation at step k .
|
observation_fn
|
callable returning an instance of
tfd.MultivariateNormalLinearOperator along with an extra information
to be returned in the EnsembleKalmanFilterState .
|
perturbed_observations
|
Whether the marginal distribution p(Y[t] | ...)
is estimated using samples from the observation_fn 's distribution. If
False , the distribution's covariance matrix is used directly. This
latter choice is less common in the literature, but works even if the
ensemble size is smaller than the number of observations.
|
low_rank_ensemble
|
Whether to use a LinearOperatorLowRankUpdate (rather than a dense Tensor) to represent the observation covariance. The "low rank" is the ensemble size. This is useful only if (i) the ensemble size is much less than the number of observations, and (ii) the LinearOperator associated with the observation_fn has an efficient inverse |
seed
|
PRNG seed; see tfp.random.sanitize_seed for details.
|
name
|
Python str name for ops created by this method.
Default value: None
(i.e., 'ensemble_kalman_filter_log_marginal_likelihood' ).
|
Returns | |
---|---|
log_marginal_likelihood
|
Tensor with same dtype as state .
|
Raises | |
---|---|
InsufficientEnsembleSizeError
|
If perturbed_observations=True and the
ensemble size is not at least one greater than the number of observations.
|
References
[1] Geir Evensen. Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. Journal of Geophysical Research, 1994.
[2] Matthias Katzfuss, Jonathan R. Stroud & Christopher K. Wikle Understanding the Ensemble Kalman Filter. The Americal Statistician, 2016.