# 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

 ```1 2 3``` ```## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```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 10, 2017, 1:42 p.m.