R/model_get_pz_CPF.R

In lolmid/unbiased_intractable_targets: Debiased particle MCMC with couplings

#'@rdname get_pz
#'@title Phytoplankton-zooplankton model as in Jones, Parslow, Murray 2010
#'@description This function returns a list with objects such as
#'* rinit, rinit_rand to sample from the initial distribution
#'* rtransition, rtransition_rand to sample from the transition
#'* dtransition to evaluate the transition density
#'* dmeasurement to evaluate the measurement density
#'* dimension, which represents the dimension of the latent process
#'@return A list
#'@export
# PZ model
# theta = (mu_alpha, sd_alpha, c, e, ml, mq)
# transformed so that all parameters are in R
# theta = (mu_alpha, log sd_alpha, logit c, logit e, logit ml, logit mq)
get_pz <- function(){
  # logit <- function(z) log(z / (1 - z))
  expit <- function(z) 1 / (1 + exp(-z))
  
  rinit <- function(nparticles, theta, rand, ...){
    return(exp(matrix(log(2) + rand, nrow = 2)))
  }
  rinit_rand <- function(nparticles, theta){
    return(rnorm(2*nparticles))
  }
  #  
  rtransition <- function(xparticles, theta, time, rand, ...){
    alphas <- theta[1] + exp(theta[2]) * rand
    xparticles <- pz_transition(xparticles, alphas, time-1, expit(theta[3:6]))
    return(xparticles)
  }
  #
  rtransition_rand <- function(nparticles, theta){
    return(rnorm(nparticles))
  }
  #
  dmeasurement <- function(xparticles, theta, observation, ...) {
    return(dnorm(x = observation, mean = log(xparticles[1,]), sd = 0.2, log = TRUE))
  }
  #
  precompute <- function(...){
    return(list())
  }
  #
  pz_model <- list(rinit = rinit, rinit_rand = rinit_rand, rtransition = rtransition,
                   rtransition_rand = rtransition_rand,
                   dmeasurement = dmeasurement, precompute = precompute, dimension = 2)
  return(pz_model)
}