TuringGLM.jl and offsets / exposure

Specific Domains Probabilistic programming
1

The roaches example, Poisson Regression · TuringGLM.jl ignores the exposure. In BRMS this is done using a formula term like this " … + offset(log(exposure))` . GLM.jl handles this with an extra argument to the call. Does TuringGLM support offsets in some way that is not obvious?

2

Based on the code of TuringGLM it might be best to use DynamicPPL directly. I think the model that is created is:

    @model function poisson_model(
        y, X; predictors=size(X, 2), μ_X=μ_X, σ_X=σ_X, prior=prior
    )
        α ~ prior.intercept
        β ~ filldist(prior.predictors, predictors)
        y ~ arraydist(LazyArray(@~ LogPoisson.(α .+ X * β)))
        return nothing
    end

With default priors from the source, and if I understand the offset correctly (a fixed term directly from the data), the model should be something like:

@model function poisson_model(y, X, offset; n_predictors=size(X, 2))
    α ~ TDist(3)
    β ~ filldist(2.5*TDist(3), n_predictors)
    y ~ arraydist(LogPoisson.(α .+ X*β .+ offset))
    return nothing
end

Some details handled by TuringGLM remain like standardizing variables.