file663a4c3ed972.R

---
title: "R Notebook"
output: html_notebook
---

```{r}
library(purrr)

transition_mc <- function(steps, start, mat) {
  i <- seq_len(nrow(mat))
  
  transition <- ~ sample(i, 1, prob = (i == .) %*% mat)
  
  accumulate(seq_len(steps), transition, .init = start)
}

# Example: 1 wants to go to 2, 2 could go back to 1, 3 is absorbing
transition_matrix <- rbind(
  c(.1, .9, 0),
  c(.45, .45, .1),
  c(0, 0, 1)
)

# 30 steps starting in state 2
transition_mc(30, 2, transition_matrix)
```

```{r}
library(dplyr)
library(tidyr)
library(ggplot2)
theme_set(theme_light())

walks <- data_frame(trial = 1:50) %>%
  mutate(state = map(trial, ~ transition_mc(25, 2, transition_matrix)),
         step = map(trial, ~ seq_len(26))) %>%
  unnest()

walks %>%
  ggplot(aes(step, trial, fill = factor(state))) +
  geom_tile()
```