Bayesian State-Space Models

Posterior estimation, filtering, and simulation using custom prior models for standard and nonlinear state-space models

A Bayesian state-space model treats the state-space model parameters Θ as random variables, rather than fixed but unknown quantities, with joint prior distribution Π(Θ). This treatment leads to a more flexible model and intuitive inferences. Bayesian models also support linear and nonlinear state and observation equations, and enable you to specify specific non-Gaussian state disturbances, observation innovations, or custom observation distributions.

To start a Bayesian state-space model analysis, choose the right object for your model:

  • For a Bayesian view of the standard state-space model, optionally with linear non-Gaussian state disturbances or observation innovations, use bssm.

  • For a Bayesian model with nonlinear state transitions or measurement sensitivity function with linear errors, or for a model with a custom observation probability density, use bnlssm.

For an overview of supported state-space model forms and to learn how to create a model in MATLAB®, see Create Continuous State-Space Models for Economic Data Analysis.

Objects

bssmCreate Bayesian state-space model (Since R2022a)
ssmCreate standard linear Gaussian state-space model
bnlssmCreate Bayesian nonlinear non-Gaussian state-space model (Since R2023b)

Functions

expand all

bssmCreate Bayesian state-space model (Since R2022a)
ssm2bssmConvert standard state-space model to Bayesian state-space model (Since R2022a)
bnlssmCreate Bayesian nonlinear non-Gaussian state-space model (Since R2023b)
filterForward recursion of Bayesian nonlinear non-Gaussian state-space model (Since R2023b)
smoothBackward recursion of Bayesian nonlinear non-Gaussian state-space model (Since R2024a)
simsmoothBayesian nonlinear non-Gaussian state-space model simulation smoother (Since R2024a)
estimateEstimate posterior distribution of Bayesian state-space model parameters (Since R2022a)
estimateEstimate posterior distribution of Bayesian nonlinear non-Gaussian state-space model parameters (Since R2024b)
simulateSimulate posterior draws of Bayesian state-space model parameters (Since R2022a)
simulateSimulate posterior draws of Bayesian nonlinear non-Gaussian state-space model parameters (Since R2024b)
tuneTune Bayesian state-space model posterior sampler (Since R2022a)
tuneTune Bayesian nonlinear non-Gaussian state-space model posterior sampler (Since R2024b)

Topics