# 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¶

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

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]

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 $$\pi \sim \mathcal{N}(\mu_k(\theta),Q_k(\theta))$$.

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 $$Q_k^{-1}(\theta)$$

• coeffs (ndarray) – fixing the coefficients $$\theta$$

property n_coeffs[source]
property coeffs[source]
TransportMaps.Distributions.Decomposable.LinearGaussianSequentialInferenceDistributions.ConditionallyLinearGaussianAR1TransitionDistribution[source]