monty
includes a simple probabilistic domain-specific
language (DSL) that is inspired by stan
and Statistical Rethinking. It is designed
to make some tasks a bit easier, particularly when defining priors for
your model. We expect that this DSL is not sufficiently advanced to
represent most interesting models but it may get more clever and
flexible in the future. In particular we do not expect the DSL to be
useful in writing likelihood functions for comparison to data; we expect
that if your model is simple enough for this you would be better off
using stan
or some similarly flexible system.
Some simple examples
In chapter 4 of Statistical Rethinking, we build a regression model of height with parameters , and . 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$new()
theta <- prior$direct_sample(rng)
theta
#> [1] 167.700794 -5.085348 8.899977
We can compute the (log) density at a point in parameter space
prior$density(theta)
#> [1] -11.31011
The computed properties for the model are:
prior$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`
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
.
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.