ssm_nlg: General multivariate nonlinear Gaussian state space models
In bssm: Bayesian Inference of Non-Linear and Non-Gaussian State Space Models

ssm_nlg

R Documentation

General multivariate nonlinear Gaussian state space models

Description

Constructs an object of class ssm_nlg by defining the corresponding terms of the observation and state equation.

Usage

ssm_nlg(
  y,
  Z,
  H,
  T,
  R,
  Z_gn,
  T_gn,
  a1,
  P1,
  theta,
  known_params = NA,
  known_tv_params = matrix(NA),
  n_states,
  n_etas,
  log_prior_pdf,
  time_varying = rep(TRUE, 4),
  state_names = paste0("state", 1:n_states)
)

Arguments

`y`	Observations as multivariate time series (or matrix) of length `n`.
`Z, H, T, R`	An external pointers (object of class `externalptr`) for the C++ functions which define the corresponding model functions.
`Z_gn, T_gn`	An external pointers (object of class `externalptr`) for the C++ functions which define the gradients of the corresponding model functions.
`a1`	Prior mean for the initial state as object of class `externalptr`
`P1`	Prior covariance matrix for the initial state as object of class `externalptr`
`theta`	Parameter vector passed to all model functions.
`known_params`	A vector of known parameters passed to all model functions.
`known_tv_params`	A matrix of known parameters passed to all model functions.
`n_states`	Number of states in the model (positive integer).
`n_etas`	Dimension of the noise term of the transition equation (positive integer).
`log_prior_pdf`	An external pointer (object of class `externalptr`) for the C++ function which computes the log-prior density given theta.
`time_varying`	Optional logical vector of length 4, denoting whether the values of Z, H, T, and R vary with respect to time variable (given identical states). If used, this can speed up some computations.
`state_names`	A character vector containing names for the states.

Details

The nonlinear Gaussian model is defined as

y_t = Z(t, \alpha_t, \theta) + H(t, \theta) \epsilon_t, (\textrm{observation equation})

\alpha_{t+1} = T(t, \alpha_t, \theta) + R(t, \theta)\eta_t, (\textrm{transition equation})

where \epsilon_t \sim N(0, I_p), \eta_t \sim N(0, I_m) and \alpha_1 \sim N(a_1, P_1) independently of each other, and functions Z, H, T, R can depend on \alpha_t and parameter vector \theta.

Compared to other 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 examples in the vignette and cpp_example_model.

Value

An object of class ssm_nlg.

Examples

 # Takes a while on CRAN
set.seed(1)
n <- 50
x <- y <- numeric(n)
y[1] <- rnorm(1, exp(x[1]), 0.1)
for(i in 1:(n-1)) {
 x[i+1] <- rnorm(1, sin(x[i]), 0.1)
 y[i+1] <- rnorm(1, exp(x[i+1]), 0.1)
}

pntrs <- cpp_example_model("nlg_sin_exp")

model_nlg <- ssm_nlg(y = y, a1 = pntrs$a1, P1 = pntrs$P1, 
  Z = pntrs$Z_fn, H = pntrs$H_fn, T = pntrs$T_fn, R = pntrs$R_fn, 
  Z_gn = pntrs$Z_gn, T_gn = pntrs$T_gn,
  theta = c(log_H = log(0.1), log_R = log(0.1)), 
  log_prior_pdf = pntrs$log_prior_pdf,
  n_states = 1, n_etas = 1, state_names = "state")

out <- ekf(model_nlg, iekf_iter = 100)
ts.plot(cbind(x, out$at[1:n], out$att[1:n]), col = 1:3)

bssm documentation built on Nov. 2, 2023, 6:25 p.m.