estimate-hiddenmixedDiffusion-method: Estimation for hierarchical (mixed) hidden diffusion process
In BaPreStoPro: Bayesian Prediction of Stochastic Processes

Description Usage Arguments References Examples

Bayesian estimation of the parameters in the hierarchical model: Z_{ij} = Y_{t_{ij}} + ε_{ij}, dY_t = b(φ_j,t,Y_t)dt + γ \widetilde{s}(t,Y_t)dW_t, φ_j\sim N(μ, Ω), Y_{t_0}=y_0(φ, t_0), ε_{ij}\sim N(0,σ^2) with the particle Gibbs sampler.

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

`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 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

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.

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)