BaPreStoPro (version 0.1)

predict,est.NHPP-method: Prediction for a non-homogeneous Poisson process

Description

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

Usage

"predict"(object, variable = c("eventTimes", "PoissonProcess"), t, burnIn, thinning, Lambda.mat, which.series = c("new", "current"), Tstart, M2pred = 10, rangeN = c(0, 5), cand.length = 1000, pred.alg = c("Trajectory", "Distribution", "simpleTrajectory", "simpleBayesTrajectory"), sample.length, grid = 1e-05, plot.prediction = TRUE)

Arguments

object

class object of MCMC samples: "est.NHPP", created with method estimate,NHPP-method

variable

if prediction of event times ("eventTimes") or of Poisson process variables ("PoissonProcess")

t

vector of time points to make predictions for (only for variable = "PoissonProcess")

burnIn

burn-in period

thinning

thinning rate

Lambda.mat

matrix-wise definition of drift function (makes it faster)

which.series

which series to be predicted, new one ("new") or further development of current one ("current")

Tstart

optional, if missing, first (which.series = "new") or last observation variable ("current") is taken

M2pred

optional, if current series to be predicted and t missing, M2pred variables will be predicted with the observation time distances

rangeN

vector of candidate area for differences of N, only if pred.alg = "Distribution" and variable = "PoissonProcess"

cand.length

length of candidate samples (if method = "vector")

pred.alg

prediction algorithm, "Distribution", "Trajectory", "simpleTrajectory" or "simpleBayesTrajectory"

sample.length

number of samples to be drawn, default is the number of posterior samples

grid

fineness degree of sampling approximation

plot.prediction

if TRUE, prediction intervals are plotted

References

Hermann, S. (2016a). BaPreStoPro: an R Package for Bayesian Prediction of Stochastic Processes. SFB 823 discussion paper 28/16.

Hermann, S. (2016b). Bayesian Prediction for Stochastic Processes based on the Euler Approximation Scheme. SFB 823 discussion paper 27/16.

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)
est <- estimate(model, t, data$Times, 1000)  # nMCMC should be much larger!
plot(est)
pred <- predict(est, Lambda.mat = function(t, xi) (t/xi[,2])^xi[,1],
   variable = "PoissonProcess", pred.alg = "Distribution")

## Not run: 
# pred_NHPP <- predict(est, Lambda.mat = function(t, xi) (t/xi[,2])^xi[,1])
# pred_NHPP <- predict(est, variable = "PoissonProcess",
#    Lambda.mat = function(t, xi) (t/xi[,2])^xi[,1])
# pred_NHPP2 <- predict(est, which.series = "current",
#    Lambda.mat = function(t, xi) (t/xi[,2])^xi[,1])
# pred_NHPP3 <- predict(est, variable = "PoissonProcess", which.series = "current",
#                       Lambda.mat = function(t, xi) (t/xi[,2])^xi[,1])
# pred_NHPP4 <- predict(est, pred.alg = "simpleTrajectory", M2pred = length(data$Times))
# ## End(Not run)
pred_NHPP <- predict(est, variable = "PoissonProcess", pred.alg = "simpleTrajectory",
                     M2pred = length(data$Times))
pred_NHPP <- predict(est, variable = "PoissonProcess", pred.alg = "simpleBayesTrajectory",
                     M2pred = length(data$Times), sample.length = 100)