Probabilistic State Space Models.

This package implements components of continuous-discrete and discrete-discrete state space models, which are the basis for Bayesian filtering and smoothing, but also for probabilistic ODE solvers.


matrix_fraction_decomposition(driftmat, …)

Matrix fraction decomposition (assuming no force).

generate_samples(dynmod, measmod, initrv, times)

Samples true states and observations at pre-determined timesteps “times” for a state space model.

condition_state_on_measurement(measurement, …)

condition_state_on_rv(attained_rv, …)


Transition(input_dim, output_dim)

Interface for Markov transitions in discrete and continuous time.

SDE(dimension, driftfun, dispmatfun, jacobfun)

Stochastic differential equation.

LinearSDE(dimension, driftmatfun, …[, …])

Linear stochastic differential equation (SDE),

LTISDE(driftmat, forcevec, dispmat[, …])

Linear time-invariant continuous Markov models of the form.

Integrator(ordint, spatialdim)

An integrator is a special kind of SDE, where the \(i\) th coordinate models the \(i\) th derivative.

IBM(ordint, spatialdim[, …])

Integrated Brownian motion in \(d\) dimensions.

IOUP(ordint, spatialdim, driftspeed[, …])

Integrated Ornstein-Uhlenbeck process in \(d\) dimensions.

Matern(ordint, spatialdim, lengthscale[, …])

Matern process in \(d\) dimensions.

DiscreteGaussian(input_dim, output_dim, …)

Discrete transitions with additive Gaussian noise.

DiscreteLinearGaussian(input_dim, …[, …])

Discrete, linear Gaussian transition models of the form.

DiscreteLTIGaussian(state_trans_mat, …[, …])

Discrete, linear, time-invariant Gaussian transition models of the form.


Coordinate change transformations as preconditioners in state space models.

NordsieckLikeCoordinates(powers, scales, …)

Nordsieck-like coordinates.

Class Inheritance Diagram

Inheritance diagram of probnum.statespace.Transition, probnum.statespace.SDE, probnum.statespace.LinearSDE, probnum.statespace.LTISDE, probnum.statespace.Integrator, probnum.statespace.IBM, probnum.statespace.IOUP, probnum.statespace.Matern, probnum.statespace.DiscreteGaussian, probnum.statespace.DiscreteLinearGaussian, probnum.statespace.DiscreteLTIGaussian, probnum.statespace.Preconditioner, probnum.statespace.NordsieckLikeCoordinates