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.
In chapter 4 of Statistical Rethinking, we build a regression model of height with parameters α, β and σ. We can define the model for the prior probability of this model in monty by running
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
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:
We can draw samples from the model if we provide a
monty_rng
object
We can compute the (log) density at a point in parameter space
The computed properties for the model are:
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:
You can also use this to do things like:
Where c
is drawn from a normal distribution with a mean
that is the average of a
and b
.
You can also pass in a list of data with values that should be available in the DSL code. For example, our first example:
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.