logLik.lineargaussian {bssm}

Extract Log-likelihood of a State Space Model of class bssm_model

Description

Computes the log-likelihood of a state space model defined by bssm package.

Usage

## S3 method for class 'lineargaussian'
logLik(object, ...)

## S3 method for class 'nongaussian'
logLik(
  object,
  particles,
  method = "psi",
  max_iter = 100,
  conv_tol = 1e-08,
  seed = sample(.Machine$integer.max, size = 1),
  ...
)

## S3 method for class 'ssm_nlg'
logLik(
  object,
  particles,
  method = "bsf",
  max_iter = 100,
  conv_tol = 1e-08,
  iekf_iter = 0,
  seed = sample(.Machine$integer.max, size = 1),
  ...
)

## S3 method for class 'ssm_sde'
logLik(
  object,
  particles,
  L,
  seed = sample(.Machine$integer.max, size = 1),
  ...
)

Arguments

object

Model of class bssm_model.

...

Ignored.

particles

Number of samples for particle filter (non-negative integer). If 0, approximate log-likelihood is returned either based on the Gaussian approximation or EKF, depending on the method argument.

method

Sampling method. For Gaussian and non-Gaussian models with linear dynamics,options are "bsf" (bootstrap particle filter, default for non-linear models) and "psi" (\psi-APF, the default for other models). For-nonlinear models option "ekf" uses EKF/IEKF-based particle filter (or just EKF/IEKF approximation in the case of particles = 0).

max_iter

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

conv_tol

Positive tolerance parameter used in Gaussian approximation. Default is 1e-8.

seed

Seed for the C++ RNG (positive integer).

iekf_iter

Non-negative integer. If zero (default), first approximation for non-linear Gaussian models is obtained from extended Kalman filter. If iekf_iter > 0, iterated extended Kalman filter is used with iekf_iter iterations.

L

Integer defining the discretization level defined as (2^L).

Value

A numeric value.

References

Durbin, J., & Koopman, S. (2002). A Simple and Efficient Simulation Smoother for State Space Time Series Analysis. Biometrika, 89(3), 603-615.

Shephard, N., & Pitt, M. (1997). Likelihood Analysis of Non-Gaussian Measurement Time Series. Biometrika, 84(3), 653-667.

Gordon, NJ, Salmond, DJ, Smith, AFM (1993). Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proceedings-F, 140, 107-113.

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

Van Der Merwe, R, Doucet, A, De Freitas, N, Wan, EA (2001). The unscented particle filter. In Advances in neural information processing systems, p 584-590.

Jazwinski, A 1970. Stochastic Processes and Filtering Theory. Academic Press.

Kitagawa, G (1996). Monte Carlo filter and smoother for non-Gaussian nonlinear state space models. Journal of Computational and Graphical Statistics, 5, 1-25.

See Also

particle_smoother

Examples

 
model <- ssm_ulg(y = c(1,4,3), Z = 1, H = 1, T = 1, R = 1)
logLik(model)
model <- ssm_ung(y = c(1,4,3), Z = 1, T = 1, R = 0.5, P1 = 2,
  distribution = "poisson")
  
model2 <- bsm_ng(y = c(1,4,3), sd_level = 0.5, P1 = 2,
  distribution = "poisson")
  
logLik(model, particles = 0)
logLik(model2, particles = 0)
logLik(model, particles = 10, seed = 1)
logLik(model2, particles = 10, seed = 1)