Description Usage Arguments Proposal densities Examples
Bayesian estimation of a stochastic process dY_t = b(φ,t,Y_t)dt + s(γ^2,t,Y_t)dW_t + h(θ,t,Y_t)dN_t.
1 2 3 |
model.class |
class of the jump diffusion model including all required information, see |
t |
vector of time points |
data |
vector of observation variables |
nMCMC |
length of Markov chain |
propSd |
vector of proposal variances for (φ, θ, γ^2, ξ) |
adapt |
if TRUE (default), proposal variance is adapted |
proposal |
proposal density for phi, theta: "normal" (default) or "lognormal" (for positive parameters), see description below |
it.xi |
number of iterations for MH step for ξ inside the Gibbs sampler |
For γ^2, always the lognormal density is taken, since the parameter is always positive. For θ and φ, there is the possibility to choose "normal" or "lognormal" (for both together). The proposal density for ξ depends on the starting value of ξ. If all components are positive, the proposal density is lognormal, and normal otherwise.
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 | # non-informative
model <- set.to.class("jumpDiffusion", Lambda = function(t, xi) (t/xi[2])^xi[1],
parameter = list(theta = 0.1, phi = 0.05, gamma2 = 0.1, xi = c(3, 1/4)))
t <- seq(0, 1, by = 0.01)
data <- simulate(model, t = t, y0 = 0.5, plot.series = TRUE)
est <- estimate(model, t, data, 1000)
plot(est)
# informative
model <- set.to.class("jumpDiffusion", Lambda = function(t, xi) (t/xi[2])^xi[1],
parameter = list(theta = 0.1, phi = 0.05, gamma2 = 0.1, xi = c(3, 1/4)),
priorDensity = list(phi = function(phi) dnorm(phi, 0.05, 0.01),
theta = function(theta) dgamma(1/theta, 10, 0.1*9),
gamma2 = function(gamma2) dgamma(1/gamma2, 10, 0.1*9),
xi = function(xi) dnorm(xi, c(3, 1/4), c(1,1))))
t <- seq(0, 1, by = 0.01)
data <- simulate(model, t = t, y0 = 0.5, plot.series = TRUE)
est <- estimate(model, t, data, 1000)
plot(est)
## Not run:
est_hidden <- estimate(model, t, data$Y, 1000)
plot(est_hidden)
## End(Not run)
|
1000 iterations are calculated
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