#' Calculate the log-likelihood for an epidemic, up to a constant of proportionality (Simple code).
#'
#' This function is used tp calculate the likelihood of a General Stochastic Epidemic, and brings together all the previously
#' specified functions; prod_part, interval_intersect, and integral_part.
#'
#' @param inf.times A vector of the infection times of all individuals (Inf if not infected).
#' @param rem.times A vector of the removal times of all infected individuals.
#' @param beta.mat The infection rate matrix.
#'
#' @keywords likelihood log loglikelihood infection GSE
#' @export
#'
#' @return Returns the value of the log likelihood, up to a constant of proportionality.
#'
#' @examples
#' This function is utilised in the inference functions.
simple_log_likelihood = function(inf.times, rem.times, beta.mat){
# Calculate the product part
prod = simple_prod_part(inf.times, rem.times, beta.mat)
# Calculate the integral part
integral = simple_integral_part(inf.times, rem.times, beta.mat)
# Calculate the log likelikehood
prod - integral
}
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