BaPreStoPro (version 0.1)

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

Description

Bayesian estimation of a non-homogeneous Poisson process (NHPP) with cumulative intensity function $\Lambda(t, \xi)$.

Usage

"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 $\xi$

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)))