Simulate King Metropolis' Travels

metropolis_sim.R

markov_step <- function(island){
  islands <- LETTERS[1:5]
  islands_pop <- list(A = 100,
                      B = 200,
                      C = 300,
                      D = 400,
                      E = 500)
  
  proposed_i <- sample(islands[islands != island],
                       size = 1)
  
  accept_prob <- min(1,
                     islands_pop[[proposed_i]]/islands_pop[[island]])
  
  u <- runif(1)
  accepted <-  u <= accept_prob
  value <- ifelse(accepted,
                  proposed_i,
                  island)
  
  value
  
}


n_sim <- 10000
isl = "A"
track <- c(isl)

for (i in 1:n_sim){
  isl <- markov_step(isl)
  track <- c(track, isl)
}

ggplot(data = data.frame(track),
       aes(x = track, fill = track)) + 
  geom_bar(color = "black") + 
  theme_minimal() + 
  theme(panel.grid = element_blank(),
        legend.position = "none") +
  labs(x = "Island",
       y = "Nights Spent")