BaPreStoPro (version 0.1)

estimate,Diffusion-method: Estimation for diffusion process

Description

Bayesian estimation of the parameters $\phi$ and $\gamma^2$ of the stochastic process $dY_t = b(\phi,t,Y_t)dt + \gamma \widetilde{s}(t,Y_t)dW_t$.

Usage

"estimate"(model.class, t, data, nMCMC, propSd, adapt = TRUE, proposal = c("normal", "lognormal"))

Arguments

model.class

class of the diffusion process model including all required information, see Diffusion-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)

References

Hermann, S., K. Ickstadt and C. H. Mueller (2016). Bayesian Prediction of Crack Growth Based on a Hierarchical Diffusion Model. Applied Stochastic Models in Business and Industry, DOI: 10.1002/asmb.2175.

Examples

model <- set.to.class("Diffusion", parameter = list(phi = 0.5, gamma2 = 0.01))
t <- seq(0, 1, by = 0.01)
data <- simulate(model, t = t, y0 = 0.5, plot.series = TRUE)
est_diff <- estimate(model, t, data, 1000)
plot(est_diff)