bssm: ssm_sde – R documentation

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ssm_sde

Univariate state space model with continuous SDE dynamics

Description

Constructs an object of class ssm_sde by defining the functions for the drift, diffusion and derivative of diffusion terms of univariate SDE, as well as the log-density of observation equation. We assume that the observations are measured at integer times (missing values are allowed).

Usage

ssm_sde(
  y,
  drift,
  diffusion,
  ddiffusion,
  obs_pdf,
  prior_pdf,
  theta,
  x0,
  positive
)

Arguments

`y`	Observations as univariate time series (or vector) of length n.
`drift, diffusion, ddiffusion`	An external pointers for the C++ functions which define the drift, diffusion and derivative of diffusion functions of SDE.
`obs_pdf`	An external pointer for the C++ function which computes the observational log-density given the the states and parameter vector theta.
`prior_pdf`	An external pointer for the C++ function which computes the prior log-density given the parameter vector theta.
`theta`	Parameter vector passed to all model functions.
`x0`	Fixed initial value for SDE at time 0.
`positive`	If `TRUE`, positivity constraint is forced by `abs` in Milstein scheme.

Details

As in case of ssm_nlg models, these general models need a bit more effort from the user, as you must provide the several small C++ snippets which define the model structure. See vignettes for an example.

Value

Object of class ssm_sde.

Examples

## Not run: 
library("sde")
set.seed(1)
# theta_0 = rho = 0.5
# theta_1 = nu = 2
# theta_2 = sigma = 0.3
x <- sde.sim(t0 = 0, T = 50, X0 = 1, N = 50,
       drift = expression(0.5 * (2 - x)),
       sigma = expression(0.3),
       sigma.x = expression(0))
y <- rpois(50, exp(x[-1]))

# Template can be found in the vignette
Rcpp::sourceCpp("ssm_sde_template.cpp")
pntrs <- create_xptrs()

sde_model <- ssm_sde(y, pntrs$drift, pntrs$diffusion,
 pntrs$ddiffusion, pntrs$obs_density, pntrs$prior,
 c(rho = 0.5, nu = 2, sigma = 0.3), 1, positive = FALSE)

est <- particle_smoother(sde_model, L = 12, particles = 500)

ts.plot(cbind(x, est$alphahat, 
  est$alphahat - 2*sqrt(c(est$Vt)), 
  est$alphahat + 2*sqrt(c(est$Vt))), 
  col = c(2, 1, 1, 1), lty = c(1, 1, 2, 2))

# Takes time with finer mesh, parallelization with IS-MCMC helps a lot
out <- run_mcmc(sde_model, L_c = 4, L_f = 8, 
  particles = 50, iter = 2e4,
  threads = 4L)


## End(Not run)

bssm

Bayesian Inference of Non-Linear and Non-Gaussian State Space Models

v1.1.4

GPL (>= 2)

Authors

Jouni Helske [aut, cre] (<https://orcid.org/0000-0001-7130-793X>), Matti Vihola [aut] (<https://orcid.org/0000-0002-8041-7222>)

Initial release

2021-04-13