BaPreStoPro (version 0.1)

estimate,hiddenDiffusion-method: Estimation for hidden diffusion process

Description

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

Usage

"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 $\phi$

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)