estimate-jumpRegression-method: Estimation for regression model dependent on Poisson process
In SimoneHermann/BaPreStoPro: Bayesian Prediction of Stochastic Processes

Description Usage Arguments Proposal densities References Examples

Bayesian estimation of the parameter of the regression model y_i = f(t_i, N_{t_i}, θ) + ε_i with N_t\sim Pois(Λ(t, ξ)), ε_i\sim N(0,γ^2\widetilde{s}(t)).

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## S4 method for signature 'jumpRegression'
estimate(model.class, t, data, nMCMC, propSd,
  adapt = TRUE, proposal = c("normal", "lognormal"), it.xi = 10)

`model.class`	class of the regression model based on the NHPP including all required information, see `jumpRegression-class`
`t`	vector of time points
`data`	vector of observation variables
`nMCMC`	length of Markov chain
`propSd`	vector of proposal variances for (θ, ξ)
`adapt`	if TRUE (default), proposal variance is adapted
`proposal`	proposal density for θ: "normal" (default) or "lognormal" (for positive parameters)
`it.xi`	number of iterations for MH step for ξ inside the Gibbs sampler

For θ, there is the possibility to choose "normal" or "lognormal". 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.

Heeke, G., S. Hermann, R. Maurer, K. Ickstadt, and C. H. Mueller (2015). Stochastic Modeling and Statistical Analysis of Fatigue Tests on Prestressed Concrete Beams under Cyclic Loadings. SFB 823 discussion paper 25/15.

t <- seq(0,1, by = 0.01)
model <- set.to.class("jumpRegression", fun = function(t, N, theta) exp(theta[1]*t) + theta[2]*N,
                   parameter = list(theta = c(2, 2), gamma2 = 0.25, xi = c(3, 0.5)),
                   Lambda = function(t, xi) (t/xi[2])^xi[1])
data <- simulate(model, t = t, plot.series = FALSE)
est <- estimate(model, t, data, 1000)
plot(est)
## Not run: 
# work in progress
est_hid <- estimate(model, t, data$Y, 1000)
plot(est_hid)

## End(Not run)