BaPreStoPro (version 0.1)

estimate,hiddenmixedDiffusion-method: Estimation for hierarchical (mixed) hidden diffusion process

Description

Bayesian estimation of the parameters in the hierarchical model: $Z_{ij} = Y_{t_{ij}} + \epsilon_{ij}, dY_t = b(\phi_j,t,Y_t)dt + \gamma \widetilde{s}(t,Y_t)dW_t, \phi_j\sim N(\mu, \Omega), Y_{t_0}=y_0(\phi, t_0), \epsilon_{ij}\sim N(0,\sigma^2)$ with the 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 hierarchical hidden diffusion model including all required information, see hiddenmixedDiffusion-class

t

list or vector of time points

data

list or matrix 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

mu <- c(5, 1); Omega <- c(0.9, 0.04)
phi <- cbind(rnorm(21, mu[1], sqrt(Omega[1])), rnorm(21, mu[2], sqrt(Omega[2])))
y0.fun <- function(phi, t) phi[2]
model <- set.to.class("hiddenmixedDiffusion", y0.fun = y0.fun,
                 b.fun = function(phi, t, y) phi[1],
                 parameter = list(phi = phi, mu = mu, Omega = Omega, gamma2 = 1, sigma2 = 0.01))
t <- seq(0, 1, by = 0.01)
data <- simulate(model, t = t, plot.series = TRUE)

## Not run: 
# est <- estimate(model, t, data$Z[1:20,], 2000)
# plot(est)
# ## End(Not run)