Solvers

solve(prob::AbstractStateSpaceProblem; kwargs...)

Solve a state-space problem using its automatically selected algorithm.

For a LinearStateSpaceProblem, this selects KalmanFilter when the problem provides a Gaussian initial-state prior, Gaussian observation noise, observed data, matrix-valued A, B, and C, and leaves noise = nothing. Otherwise it uses DirectIteration. Pass an algorithm explicitly to override this selection.

Arguments

• prob: State-space problem to solve.

Keyword Arguments

All keyword arguments are forwarded to the selected solver. In particular, save_everystep = false stores only the initial and final states.

Examples

julia> A = [0.95 0.1; 0.0 0.2];

julia> B = [0.0; 0.01;;];

julia> prob = LinearStateSpaceProblem(A, B, zeros(2), (0, 10));

julia> sol = solve(prob);

julia> length(sol.u)
11

DirectIteration()

Forward iteration algorithm for state-space problems. Iterates the state transition equation forward in time, computing the state trajectory u, observations z, noise history W, and (if observables are provided) the joint log-likelihood logpdf.

This is the default algorithm for all problem types.

See also: KalmanFilter.

KalmanFilter()

Kalman filter algorithm for LinearStateSpaceProblem. Computes filtered state estimates, posterior covariances, and the marginal log-likelihood.

Automatically selected when the problem provides:

• u0_prior_mean and u0_prior_var (Gaussian prior),
• observables (observed data),
• observables_noise (observation noise covariance),
• noise = nothing (latent noise is not fixed).

The solution contains filtered means in sol.u, posterior covariances in sol.P, predicted observations in sol.z, and the marginal log-likelihood in sol.logpdf.

See also: DirectIteration.

ConditionalLikelihood()

Conditional likelihood (prediction error decomposition) algorithm for fully-observed state-space models. At each step, predicts the next observation from the observed current state using the transition equation, and accumulates the Gaussian log-likelihood of the innovation.

Works with all problem types (LinearStateSpaceProblem, StateSpaceProblem, QuadraticStateSpaceProblem, PrunedQuadraticStateSpaceProblem). The only requirement is additive Gaussian observation noise.

Requires:

• observables (observed data y₁, …, y_T),
• observables_noise (innovation covariance R).

The solution contains predicted observations in sol.z (when an observation equation is present), the conditional log-likelihood in sol.logpdf, and the state trajectory (clamped to observables) in sol.u.

See also: DirectIteration, KalmanFilter.