Description Details Author(s) Examples
Implements an MCMC sampler for the posterior distribution of arbitrary time-homogeneous multivariate stochastic differential equation (SDE) models with possibly latent components. The package provides a simple entry point to integrate user-defined models directly with the sampler's C++ code, and parallelizes large portions of the calculations when compiled with 'OpenMP'.
See package vignettes; vignette("msde-quicktut")
for a tutorial and vignette("msde-exmodels")
for several example models.
Maintainer: Martin Lysy mlysy@uwaterloo.ca
Authors:
Feiyu Zhu
JunYong Tong
Other contributors:
Trevor Kitt [contributor]
Nigel Delaney [contributor]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | # Posterior inference for Heston's model
# compile model
hfile <- sde.examples("hest", file.only = TRUE)
param.names <- c("alpha", "gamma", "beta", "sigma", "rho")
data.names <- c("X", "Z")
hmod <- sde.make.model(ModelFile = hfile,
param.names = param.names,
data.names = data.names)
# or simply load pre-compiled version
hmod <- sde.examples("hest")
# Simulate data
X0 <- c(X = log(1000), Z = 0.1)
theta <- c(alpha = 0.1, gamma = 1, beta = 0.8, sigma = 0.6, rho = -0.8)
dT <- 1/252
nobs <- 1000
hest.sim <- sde.sim(model = hmod, x0 = X0, theta = theta,
dt = dT, dt.sim = dT/10, nobs = nobs)
# initialize MCMC sampler
# both components observed, no missing data between observations
init <- sde.init(model = hmod, x = hest.sim$data,
dt = hest.sim$dt, theta = theta)
# Initialize posterior sampling argument
nsamples <- 1e4
burn <- 1e3
hyper <- NULL # flat prior
hest.post <- sde.post(model = hmod, init = init, hyper = hyper,
nsamples = nsamples, burn = burn)
# plot the histogram for the sampled parameters
par(mfrow = c(2,3))
for(ii in 1:length(hmod$param.names)) {
hist(hest.post$params[,ii],breaks=100, freq = FALSE,
main = parse(text = hmod$param.names[ii]), xlab = "")
}
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