TransportMaps.Distributions.Examples.ScalarLinearGaussMarkovProcess.Distributions

Module Contents

Classes

Prior

Multivariate Standard Normal distribution \(\pi\).

Transition

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

LogLikelihood

Define the log-likelihood for the additive linear Gaussian model

Functions

generate_data(nsteps)

class TransportMaps.Distributions.Examples.ScalarLinearGaussMarkovProcess.Distributions.Prior[source]

Bases: TransportMaps.Distributions.FrozenDistributions.StandardNormalDistribution

Multivariate Standard Normal distribution \(\pi\).

Parameters:

d (int) – dimension

class TransportMaps.Distributions.Examples.ScalarLinearGaussMarkovProcess.Distributions.Transition[source]

Bases: TransportMaps.Distributions.Decomposable.LinearGaussianSequentialInferenceDistributions.LinearGaussianAR1TransitionDistribution

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

class TransportMaps.Distributions.Examples.ScalarLinearGaussMarkovProcess.Distributions.LogLikelihood(y)[source]

Bases: TransportMaps.Likelihoods.LikelihoodBase.AdditiveLinearGaussianLogLikelihood

Define the log-likelihood for the additive linear Gaussian model

The model is

\[{\bf y} = {\bf c} + {\bf T}{\bf x} + \varepsilon \;, \quad \varepsilon \sim \mathcal{N}(\mu, \Sigma)\]

where \(T \in \mathbb{R}^{d_y \times d_x}\), \(\mu \in \mathbb{R}^{d_y}\) and \(\Sigma \in \mathbb{R}^{d_y \times d_y}\) is symmetric positve definite

Parameters:
  • y (ndarray [\(d_y\)]) – data

  • c (ndarray [\(d_y\)] or Map) – system constant or parametric map returning the constant

  • T (ndarray [\(d_y,d_x\)] or Map) – system matrix or parametric map returning the system matrix

  • mu (ndarray [\(d_y\)] or Map) – noise mean or parametric map returning the mean

  • covariance (ndarray [\(d_y,d_y\)] or Map) – noise covariance or parametric map returning the covariance

  • precision (ndarray [\(d_y,d_y\)] or Map) – noise precision matrix or parametric map returning the precision matrix

TransportMaps.Distributions.Examples.ScalarLinearGaussMarkovProcess.Distributions.generate_data(nsteps)[source]