DiscreteModel

class probnum.filtsmooth.DiscreteModel

Bases: probnum.filtsmooth.Transition

Transition models for discretely indexed processes.

Transformations of the form

\[x_{t + \Delta t} \sim p(x_{t + \Delta t} | x_t) .\]

As such, compatible with Bayesian filtering and smoothing algorithms.

See also

ContinuousModel
Transition models for continuously indexed processes.
BayesFiltSmooth
Bayesian filtering and smoothing algorithms.

Attributes Summary

dimension Dimension of the transition model.

Methods Summary

__call__(arr_or_rv, RandomVariable], start, …) Transition a random variable or a realization of one.
transition_realization(real, start, stop, …) Transition a realization of a random variable from time \(t\) to time \(t+\Delta t\).
transition_rv(rv, start, stop, **kwargs) Transition a random variable from time \(t\) to time \(t+\Delta t\).

Attributes Documentation

dimension

Dimension of the transition model.

Methods Documentation

__call__(arr_or_rv: Union[numpy.ndarray, RandomVariable], start: float = None, stop: float = None, **kwargs) -> ('RandomVariable', typing.Dict)

Transition a random variable or a realization of one.

The input is either interpreted as a random variable or as a realization. Accordingly, the respective methods are called: transition_realization() or transition_rv().

transition_realization(real, start, stop, **kwargs)[source]

Transition a realization of a random variable from time \(t\) to time \(t+\Delta t\).

For random variable \(x_t\), it returns the random variable defined by

\[x_{t + \Delta t} \sim p(x_{t + \Delta t} | x_t = r) .\]

This is different to transition_rv() which computes the parametrization of \(x_{t + \Delta t}\) based on the parametrization of \(x_t\).

Nb: Think of transition as a verb, i.e. this method “transitions” a realization of a random variable.

Parameters:
  • real – Realization of the random variable.
  • start – Starting point \(t\).
  • stop – End point \(t + \Delta t\).
Returns:

  • RandomVariable – Random variable, describing the state at time \(t + \Delta t\) based on realization at time \(t\).
  • dict – Additional information in form of a dictionary, for instance the cross-covariance in the prediction step, access to which is useful in smoothing.

See also

transition_rv()
Apply transition to a random variable.
transition_rv(rv, start, stop, **kwargs)[source]

Transition a random variable from time \(t\) to time \(t+\Delta t\).

For random variable \(x_t\), it returns the random variable defined by

\[x_{t + \Delta t} \sim p(x_{t + \Delta t} | x_t) .\]

This returns a random variable where the parametrization depends on the paramtrization of \(x_t\). This is different to transition_rv() which computes the parametrization of \(x_{t + \Delta t}\) based on a realization of \(x_t\).

Nb: Think of transition as a verb, i.e. this method “transitions” a random variable.

Parameters:
  • rv – Realization of the random variable.
  • start – Starting point \(t\).
  • stop – End point \(t + \Delta t\).
Returns:

  • RandomVariable – Random variable, describing the state at time \(t + \Delta t\) based on realization at time \(t\).
  • dict – Additional information in form of a dictionary, for instance the cross-covariance in the prediction step, access to which is useful in smoothing.

See also

transition_realization()
Apply transition to a realization of a random variable.