estimate-hiddenDiffusion-method: Estimation for hidden diffusion process

In BaPreStoPro: Bayesian Prediction of Stochastic Processes

Description

Bayesian estimation of the model Z_i = Y_{t_i} + ε_i, dY_t = b(φ,t,Y_t)dt + γ \widetilde{s}(t,Y_t)dW_t, ε_i\sim N(0,σ^2), Y_{t_0}=y_0(φ, t_0) with a particle Gibbs sampler.

Usage

## S4 method for signature 'hiddenDiffusion'
estimate(model.class, t, data, nMCMC, propSd,
  adapt = TRUE, proposal = c("normal", "lognormal"), Npart = 100)

Arguments

model.class	class of the hidden diffusion model including all required information, see hiddenDiffusion-class
t	vector of time points
data	vector of observation variables
nMCMC	length of Markov chain
propSd	vector of proposal variances for φ
adapt	if TRUE (default), proposal variance is adapted
proposal	proposal density: "normal" (default) or "lognormal" (for positive parameters)
Npart	number of particles in the particle Gibbs sampler

References

Andrieu, C., A. Doucet and R. Holenstein (2010). Particle Markov Chain Monte Carlo Methods. Journal of the Royal Statistical Society B 72, pp. 269-342.

Examples

model <- set.to.class("hiddenDiffusion", y0.fun = function(phi, t) 0.5,
             parameter = list(phi = 5, gamma2 = 1, sigma2 = 0.1))
t <- seq(0, 1, by = 0.01)
data <- simulate(model, t = t, plot.series = TRUE)
est <- estimate(model, t, data$Z, 100)  # nMCMC should be much larger!
plot(est)

## Not run: 
# OU
b.fun <- function(phi, t, y) phi[1]-phi[2]*y
model <- set.to.class("hiddenDiffusion", y0.fun = function(phi, t) 0.5,
               parameter = list(phi = c(10, 1), gamma2 = 1, sigma2 = 0.1),
               b.fun = b.fun, sT.fun = function(t, x) 1)
t <- seq(0, 1, by = 0.01)
data <- simulate(model, t = t, plot.series = TRUE)
est <- estimate(model, t, data$Z, 1000)
plot(est)

## End(Not run)

BaPreStoPro documentation built on May 2, 2019, 3:34 p.m.