library("knitr") opts_chunk$set(message = FALSE, warning=FALSE, fig.width = 5.5)

Let's load the necessary packages:

```
library(zoid)
```

We will use the "broken stick" approach to simulate data from the Dirichlet - trinomial model. This model assumes that the group proportions for each observation are Dirichlet, but the observed values are either 0, the total sample size (N) or a number between 0 and N.

Our `broken_stick`

function can be called as follows,

y = broken_stick(n_obs = 10, n_groups = 10, tot_n = 100)

The object `y`

is a list with 2 elements, (1) the true underlying compositions (p) and the realized data (X_obs). They can be accessed as

y$p y$X_obs

By default, the simulation function assumes a uniform prior for the Dirichlet, with hyperparameters = 1. We can change this by specifying our own values of hyperparameters. Using the argument `p`

, we can simulate new values with a slightly larger effective sample size, and pass that into `broken_stick`

p = gtools::rdirichlet(1, alpha = rep(2,10)) y = broken_stick(n_obs = 10, n_groups = 10, tot_n = 100, p = p)

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