`TransportMaps.Distributions.Decomposable.LinearGaussianSequentialInferenceDistributions`¶

Module Contents¶

Classes¶

`LinearNormalAR1TransitionDistribution`	Transition probability distribution \(g({\bf x}_{k-1},{\bf x}_k) = \pi_{{\bf X}_k \vert {\bf X}_{k-1}={\bf x}_{k-1}}({\bf x}_k) = \pi({\bf x}_k - F_k {\bf x}_{k-1} - {\bf c}_k)\) where \(\pi \sim \mathcal{N}(\mu_k,Q_k)\).
`ConditionallyLinearNormalAR1TransitionDistribution`	Transition probability distribution \(g(\theta,{\bf x}_{k-1},{\bf x}_k) = \pi_{{\bf X}_k \vert {\bf X}_{k-1}={\bf x}_{k-1}}({\bf x}_k, \Theta=\theta) = \pi({\bf x}_k - F_k(\theta) {\bf x}_{k-1} - {\bf c}_k(\theta))\) where \(\pi \sim \mathcal{N}(\mu_k(\theta),Q_k(\theta))\).

Attributes¶

`LinearGaussianAR1TransitionDistribution`
`ConditionallyLinearGaussianAR1TransitionDistribution`

class TransportMaps.Distributions.Decomposable.LinearGaussianSequentialInferenceDistributions.LinearNormalAR1TransitionDistribution(ck, Fk, mu, covariance=None, precision=None, coeffs=None)[source]¶

Bases: TransportMaps.Distributions.Decomposable.SequentialInferenceDistributions.Lag1TransitionDistribution

Transition probability distribution \(g({\bf x}_{k-1},{\bf x}_k) = \pi_{{\bf X}_k \vert {\bf X}_{k-1}={\bf x}_{k-1}}({\bf x}_k) = \pi({\bf x}_k - F_k {\bf x}_{k-1} - {\bf c}_k)\) where \(\pi \sim \mathcal{N}(\mu_k,Q_k)\).

This represents the following Markov transition model:

\[\begin{split}{\bf x}_k = c_k + F_k {\bf x}_{k-1} + {\bf w}_k \\ {\bf w}_k \sim \mathcal{N}(\mu,Q_k)\end{split}\]

where the control \({\bf c}_k := B_k {\bf u}_k\) can be used for control purposes

Parameters:

ck (ndarray [\(d\)] or Map) – constant part or map returning the constant part given some parameters
Fk (ndarray [\(d,d\)] or Map) – state transition matrix (dynamics) or map returning the linear part given some parametrs
mu (ndarray [\(d\)] or Map) – mean \(\mu_k\) or parametric map for \(\mu_k(\theta)\)
covariance (ndarray [\(d,d\)] or Map) – covariance \(Q_k\) or parametric map for \(Q_k(\theta)\)
precision (ndarray [\(d,d\)] or Map) – precision \(Q_k^{-1}\) or parametric map for \(Q_k^{-1}(\theta)\)

TransportMaps.Distributions.Decomposable.LinearGaussianSequentialInferenceDistributions.LinearGaussianAR1TransitionDistribution[source]¶

class TransportMaps.Distributions.Decomposable.LinearGaussianSequentialInferenceDistributions.ConditionallyLinearNormalAR1TransitionDistribution(ck, Fk, mu, covariance=None, precision=None, coeffs=None)[source]¶