clement-lee / hybridprocess

R package for fitting and simulation of hybrid process

hybridProcess

The goal of hybridProcess is to provide functions for fitting and simulation of hybrid processes, one kind of non-homogeneous Poisson processes (NHPP). Specifically, the intensity of this kind of NHPP is proportional to the product of a power term, and an exponential term, of time.

Installation

You can install hybridProcess from github with:

# install.packages("devtools")
devtools::install_github("clement-lee/hybridProcess")

Example

Here is an example of simulating from, and fitting, a hybrid process, with power parameter λ = 0.66, exponent θ = 0.1, and scale parameter ϕ = 5.0.

# library(hybridProcess)
## Simulation
set.seed(1234L)
x <- sim_hybrid(
  T = 1000, x = 0.0, beta = 0.0, kappa = 0.0,
  lambda = 0.66, phi = 5.0, theta = 0.1,
  psi = 0.0, tau = Inf
)
## Fitting
obj0 <- optim(c(0.1, 0.1, 0.1), llik_nhpp_hybrid, x = x, control = optimctrl())
obj0$par # compare with true parameter values
#> [1] 0.6945695 0.1081603 4.0358572

Further information

The example above uses a function sim_hybrid() that is more flexible than a simple hybrid process. A wrapper function sim_wrapper() enables simulation of a collection of hybrid processes, each of which can be initiated at a different time point, with the possible inclusion of a covariate. Such data can be fitted by a hierarchical model of hybrid processes, via the function run_mcmc().

For details of the hierarchical model, as well as the definitions of other parameters in sim_hybrid(), please refer to this ArXiv paper.