Combine two models — monty_model

Combine two models by multiplication. We'll need a better name here. In Bayesian inference we will want to create a model that represents the multiplication of a likelihood and a prior (in log space) and it will be convenient to think about these models separately. Multiplying probabilities (or adding on a log scale) is common enough that there may be other situations where we want to do this.

Usage

monty_model_combine(a, b, properties = NULL, name_a = "a", name_b = "b")

Arguments

a: The first model
b: The second model
properties: A monty_model_properties object, used to control (or enforce) properties of the combined model.
name_a: Name of the first model (defaulting to 'a'); you can use this to make error messages nicer to read, but it has no other practical effect.
name_b: Name of the first model (defaulting to 'b'); you can use this to make error messages nicer to read, but it has no other practical effect.

Value

A monty_model object

Details

Here we describe the impact of combining a pair of models

density: this is the sum of the log densities from each model
parameters: the union of parameters from each model is taken
domain: The most restrictive domain is taken for each parameter. Parameters that do not appear in one model are assumed to have infinite domain there.
gradient: if both models define a gradient, this is the sum of the gradients. If either does not define a gradient, the resulting model will not have gradient support. Set has_gradient = TRUE within `properties if you want to enforce that the combination is differentiable. If the models disagree in their parameters, parameters that are missing from a model are assumed (reasonably) to have a zero gradient.
direct_sample: this one is hard to do the right thing for. If neither model can be directly sampled from that's fine, we don't directly sample. If only one model can be sampled from and if it can sample from the union of all parameters then we take that function (this is the case for a prior model when combined with a likelihood). Other cases will be errors, which can be avoided by setting has_direct_gradient = FALSE in properties.
is_stochastic: a model is stochastic if either component is stochastic.

The properties of the model will be combined as above, reflecting the properties of the joint model.

The model field will be an ordered, unnamed, list containing the two elements corresponding to the first and second model (not the monty_model, but the underlying model, perhaps?). This is the only part that makes a distinction between the two models here; for all components above they are equivalent.

Examples

# A simple example; a model that contains something of interest,
# and a simple prior from monty_dsl
likelihood <- monty_example("banana")
prior <- monty_dsl({
  alpha ~ Normal(0, 1)
  beta ~ Normal(0, 10)
})
posterior <- likelihood + prior
posterior
#> 
#> ── <monty_model> ───────────────────────────────────────────────────────────────
#> ℹ Model has 2 parameters: 'alpha' and 'beta'
#> ℹ This model:
#> • can compute gradients
#> • accepts multiple parameters
#> ℹ See `?monty_model()` for more information

# The same thing, more explicitly:
monty_model_combine(likelihood, prior)
#> 
#> ── <monty_model> ───────────────────────────────────────────────────────────────
#> ℹ Model has 2 parameters: 'alpha' and 'beta'
#> ℹ This model:
#> • can compute gradients
#> • accepts multiple parameters
#> ℹ See `?monty_model()` for more information

# Control properties of the combined model:
monty_model_combine(likelihood, prior,
                    monty_model_properties(has_gradient = FALSE))
#> 
#> ── <monty_model> ───────────────────────────────────────────────────────────────
#> ℹ Model has 2 parameters: 'alpha' and 'beta'
#> ℹ This model:
#> • accepts multiple parameters
#> ℹ See `?monty_model()` for more information