estimate-NHPP-method: Estimation for a non-homogeneous Poisson process

In SimoneHermann/BaPreStoPro: Bayesian Prediction of Stochastic Processes

Description

Bayesian estimation of a non-homogeneous Poisson process (NHPP) with cumulative intensity function Λ(t, ξ).

Usage

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

Arguments

model.class	class of the NHPP model including all required information, see NHPP-class
t	vector of time points
data	vector of observation variables
nMCMC	length of Markov chain
propSd	vector of proposal variances for ξ
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 (2015). Bayesian Prediction for a Jump Diffusion Process with Application to Crack Growth in Fatigue Experiments. SFB 823 discussion paper 30/15.

Examples

model <- set.to.class("NHPP", parameter = list(xi = c(5, 1/2)),
                   Lambda = function(t, xi) (t/xi[2])^xi[1])
t <- seq(0, 1, by = 0.01)
data <- simulate(model, t = t, plot.series = TRUE)
est <- estimate(model, t, data$Times, 10000, proposal = "lognormal")
plot(est)

##
model <- set.to.class("NHPP", parameter = list(xi = 5),
                   Lambda = function(t, xi) t*xi)
t <- seq(0, 1, by = 0.01)
data <- simulate(model, t = t, plot.series = TRUE)
est <- estimate(model, t, data$N, 10000)
plot(est, par.options = list(mfrow = c(1,1)))

SimoneHermann/BaPreStoPro documentation built on May 9, 2019, 1:46 p.m.