12  The monty DSL

The monty DSL provides a more intuitive way to define statistical models with monty. It is currently relatively basic and focuses on providing support for defining priors in Bayesian models. It fully support differentiability allowing to use gradient based samplers on these models.

library(monty)

12.1 A simple example

In chapter 4 of Statistical Rethinking, we build a regression model of height with parameters \(\alpha\), \(\beta\) and \(\sigma\). We can define the model for the prior probability of this model in monty by running

prior <- monty_dsl({
  alpha ~ Normal(178, 20)
  beta ~ Normal(0, 10)
  sigma ~ Uniform(0, 50)
})

This will define a new monty_model() object that represents the prior, but with all the bits that we might need depending on how we want to use it:

We have model parameters

prior$parameters
#> [1] "alpha" "beta"  "sigma"

These are defined in the order that they appear in your definition (so alpha is first and sigma is last)

We can compute the domain for your model:

prior$domain
#>       [,1] [,2]
#> alpha -Inf  Inf
#> beta  -Inf  Inf
#> sigma    0   50

We can draw samples from the model if we provide a monty_rng object

rng <- monty_rng_create()
theta <- monty_model_direct_sample(prior, rng)
theta
#> [1] 155.30396 -12.79361  27.66180

We can compute the (log) density at a point in parameter space

prior$density(theta)
#> [1] -12.51049

The computed properties for the model are:

prior$properties
#> 
#> ── <monty_model_properties> ────────────────────────────────────────────────────
#> • has_gradient: `TRUE`
#> • has_direct_sample: `TRUE`
#> • is_stochastic: `FALSE`
#> • has_parameter_groups: `FALSE`
#> • has_observer: `FALSE`
#> • allow_multiple_parameters: `TRUE`

12.2 Distribution functions

In the above example we use distribution functions for the normal and uniform distributions. The distribution functions available for the monty DSL are the same as those for the odin DSL, the full list of which can be found here.

12.3 Dependent distributions

It is possible within the DSL to have the distribution of parameters to depend upon the value of other parameters:

m <- monty_dsl({
    a ~ Normal(0, 1)
    b ~ Normal(a, 1)
})

This is particularly useful for the implementation of hyperpriors when using the DSL to define priors.

Order of equations is important when using dependent distributions in the monty DSL! You cannot have the distribution of a parameter depend upon a parameter that is defined later. Thus rewriting the above example as

m <- monty_dsl({
    b ~ Normal(a, 1)
    a ~ Normal(0, 1)
})

would produce an error.

12.4 Calculations in the DSL

Sometimes it will be useful to perform calculations in the code; you can do this with assignments. Most trivially, giving names to numbers may help make code more understandable:

m <- monty_dsl({
  mu <- 10
  sd <- 2
  a ~ Normal(mu, sd)
})

You can also use this to do things like:

m <- monty_dsl({
  a ~ Normal(0, 1)
  b ~ Normal(0, 1)
  mu <- (a + b) / 2
  c ~ Normal(mu, 1)
})

Where c is drawn from a normal distribution with a mean that is the average of a and b.

12.5 Pass in fixed data

You can also pass in a list of data with values that should be available in the DSL code. For example, our first example:

prior <- monty_dsl({
  alpha ~ Normal(178, 20)
  beta ~ Normal(0, 10)
  sigma ~ Uniform(0, 50)
})

Might be written as

fixed <- list(alpha_mean = 170, alpha_sd = 20,
              beta_mean = 0, beta_sd = 10,
              sigma_max = 50)
prior <- monty_dsl({
  alpha ~ Normal(alpha_mean, alpha_sd)
  beta ~ Normal(beta_mean, beta_sd)
  sigma ~ Uniform(0, sigma_max)
}, fixed = fixed)

Values you pass in this way are fixed (hence the name!) and cannot be modified after the model object is created.