gaussian_approx {bssm}

Gaussian Approximation of Non-Gaussian/Non-linear State Space Model

Description

Returns the approximating Gaussian model which has the same conditional mode of p(alpha|y, theta) as the original model. This function is rarely needed itself, and is mainly available for testing and debugging purposes.

Usage

gaussian_approx(model, max_iter, conv_tol, ...)

## S3 method for class 'nongaussian'
gaussian_approx(model, max_iter = 100, conv_tol = 1e-08, ...)

## S3 method for class 'ssm_nlg'
gaussian_approx(model, max_iter = 100, conv_tol = 1e-08, iekf_iter = 0, ...)

Arguments

model

Model to be approximated. Should be of class bsm_ng, ar1_ng svm, ssm_ung, or ssm_mng, or ssm_nlg, i.e. non-gaussian or non-linear bssm_model.

max_iter

Maximum number of iterations as a positive integer. Default is 100 (although typically only few iterations are needed).

conv_tol

Positive tolerance parameter. Default is 1e-8. Approximation is claimed to be converged when the mean squared difference of the modes of is less than conv_tol.

...

Ignored.

iekf_iter

For non-linear models, non-negative number of iterations in iterated EKF (defaults to 0, i.e. normal EKF). Used only for models of class ssm_nlg.

Value

Returns linear-Gaussian SSM of class ssm_ulg or ssm_mlg which has the same conditional mode of p(alpha|y, theta) as the original model.

References

Koopman, SJ and Durbin J (2012). Time Series Analysis by State Space Methods. Second edition. Oxford: Oxford University Press.

Vihola, M, Helske, J, Franks, J. (2020). Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo. Scand J Statist. 1-38. https://doi.org/10.1111/sjos.12492

Examples

data("poisson_series")
model <- bsm_ng(y = poisson_series, sd_slope = 0.01, sd_level = 0.1,
  distribution = "poisson")
out <- gaussian_approx(model)
for(i in 1:7)
 cat("Number of iterations used: ", i, ", y[1] = ",
   gaussian_approx(model, max_iter = i, conv_tol = 0)$y[1], "\n", sep ="")