Estimate R and k from clusters sizes using MLE

cluster_size_estimation

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
# Code to estimate R and k from clusters sizes using MLE via quickfit
# Adam Kucharski (2023)
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

library(devtools)
library(rstan)
library(MASS)

#devtools::install_github("adamkucharski/quickfit")
#devtools::install_github('sbfnk/bpmodels')
library(quickfit)
library(bpmodels)

# Monkeypox data, 1970s:
cluster_sizes <- c(rep(1,27),rep(2,11))

# Estimate R and k

log_l <- function(x,a,b){
  bpmodels::chain_ll(x,"nbinom",stat="size",
                     mu=a,size=b) 
  }

quickfit::calculate_profile(log_l,
                            data_in=cluster_sizes,
                            n_param=2,
                            a_initial = 0.5,
                            b_initial = 1,
                            precision=0.01)