Manually Defining a Model

Traditionally, models in Turing are defined using the @model macro:

using Turing

@model function gdemo(x)
    # Set priors.
    s² ~ InverseGamma(2, 3)
    m ~ Normal(0, sqrt(s²))

    # Observe each value of x.
    x .~ Normal(m, sqrt(s²))

    return nothing
end

model = gdemo([1.5, 2.0])
Precompiling Turing...
    842.6 ms  ? OptimizationBase
   1425.4 ms  ? Optimization
   2171.8 ms  ? OptimizationOptimJL
Info Given Turing was explicitly requested, output will be shown live 
WARNING: redefinition of constant OptimizationBase.OPTIMIZER_MISSING_ERROR_MESSAGE. This may fail, cause incorrect answers, or produce other errors.
WARNING: Method definition (::Type{OptimizationBase.OptimizerMissingError})(Any) in module OptimizationBase at /home/runner/.julia/packages/OptimizationBase/sfIfa/src/solve.jl:23 overwritten at /home/runner/.julia/packages/OptimizationBase/sfIfa/src/solve.jl:177.
ERROR: Method overwriting is not permitted during Module precompilation. Use `__precompile__(false)` to opt-out of precompilation.
   5550.7 ms  ? Turing
   5831.6 ms  ? Turing → TuringOptimExt
WARNING: redefinition of constant OptimizationBase.OPTIMIZER_MISSING_ERROR_MESSAGE. This may fail, cause incorrect answers, or produce other errors.
WARNING: Method definition (::Type{OptimizationBase.OptimizerMissingError})(Any) in module OptimizationBase at /home/runner/.julia/packages/OptimizationBase/sfIfa/src/solve.jl:23 overwritten at /home/runner/.julia/packages/OptimizationBase/sfIfa/src/solve.jl:177.
ERROR: Method overwriting is not permitted during Module precompilation. Use `__precompile__(false)` to opt-out of precompilation.
Precompiling Optimization...
    819.5 ms  ? OptimizationBase
Info Given Optimization was explicitly requested, output will be shown live 
WARNING: redefinition of constant OptimizationBase.OPTIMIZER_MISSING_ERROR_MESSAGE. This may fail, cause incorrect answers, or produce other errors.
WARNING: Method definition (::Type{OptimizationBase.OptimizerMissingError})(Any) in module OptimizationBase at /home/runner/.julia/packages/OptimizationBase/sfIfa/src/solve.jl:23 overwritten at /home/runner/.julia/packages/OptimizationBase/sfIfa/src/solve.jl:177.
ERROR: Method overwriting is not permitted during Module precompilation. Use `__precompile__(false)` to opt-out of precompilation.
   1389.7 ms  ? Optimization
WARNING: redefinition of constant OptimizationBase.OPTIMIZER_MISSING_ERROR_MESSAGE. This may fail, cause incorrect answers, or produce other errors.
WARNING: Method definition (::Type{OptimizationBase.OptimizerMissingError})(Any) in module OptimizationBase at /home/runner/.julia/packages/OptimizationBase/sfIfa/src/solve.jl:23 overwritten at /home/runner/.julia/packages/OptimizationBase/sfIfa/src/solve.jl:177.
ERROR: Method overwriting is not permitted during Module precompilation. Use `__precompile__(false)` to opt-out of precompilation.
Precompiling OptimizationBase...
Info Given OptimizationBase was explicitly requested, output will be shown live 
WARNING: redefinition of constant OptimizationBase.OPTIMIZER_MISSING_ERROR_MESSAGE. This may fail, cause incorrect answers, or produce other errors.
WARNING: Method definition (::Type{OptimizationBase.OptimizerMissingError})(Any) in module OptimizationBase at /home/runner/.julia/packages/OptimizationBase/sfIfa/src/solve.jl:23 overwritten at /home/runner/.julia/packages/OptimizationBase/sfIfa/src/solve.jl:177.
ERROR: Method overwriting is not permitted during Module precompilation. Use `__precompile__(false)` to opt-out of precompilation.
    778.9 ms  ? OptimizationBase
WARNING: redefinition of constant OptimizationBase.OPTIMIZER_MISSING_ERROR_MESSAGE. This may fail, cause incorrect answers, or produce other errors.
WARNING: Method definition (::Type{OptimizationBase.OptimizerMissingError})(Any) in module OptimizationBase at /home/runner/.julia/packages/OptimizationBase/sfIfa/src/solve.jl:23 overwritten at /home/runner/.julia/packages/OptimizationBase/sfIfa/src/solve.jl:177.
ERROR: Method overwriting is not permitted during Module precompilation. Use `__precompile__(false)` to opt-out of precompilation.
WARNING: redefinition of constant OptimizationBase.OPTIMIZER_MISSING_ERROR_MESSAGE. This may fail, cause incorrect answers, or produce other errors.
WARNING: redefinition of constant OptimizationBase.OPTIMIZER_MISSING_ERROR_MESSAGE. This may fail, cause incorrect answers, or produce other errors.
┌ Warning: Replacing docs for `CommonSolve.solve :: Tuple{SciMLBase.OptimizationProblem, Any, Vararg{Any}}` in module `OptimizationBase`
└ @ Base.Docs docs/Docs.jl:243
WARNING: redefinition of constant OptimizationBase.OPTIMIZER_MISSING_ERROR_MESSAGE. This may fail, cause incorrect answers, or produce other errors.
┌ Warning: Replacing docs for `CommonSolve.init :: Tuple{SciMLBase.OptimizationProblem, Any, Vararg{Any}}` in module `OptimizationBase`
└ @ Base.Docs docs/Docs.jl:243
┌ Warning: Replacing docs for `CommonSolve.solve! :: Tuple{SciMLBase.AbstractOptimizationCache}` in module `OptimizationBase`
└ @ Base.Docs docs/Docs.jl:243
Precompiling OptimizationOptimJL...
    771.6 ms  ? OptimizationBase
    991.5 ms  ? Optimization
Info Given OptimizationOptimJL was explicitly requested, output will be shown live 
┌ Warning: Module Optimization with build ID ffffffff-ffff-ffff-5231-6f00c9b070d3 is missing from the cache.
│ This may mean Optimization [7f7a1694-90dd-40f0-9382-eb1efda571ba] does not support precompilation but is imported by a module that does.
└ @ Base loading.jl:2541
   1107.6 ms  ? OptimizationOptimJL
┌ Warning: Module Optimization with build ID ffffffff-ffff-ffff-5231-6f00c9b070d3 is missing from the cache.
│ This may mean Optimization [7f7a1694-90dd-40f0-9382-eb1efda571ba] does not support precompilation but is imported by a module that does.
└ @ Base loading.jl:2541
Precompiling TuringOptimExt...
    787.9 ms  ? OptimizationBase
    999.1 ms  ? Optimization
   1111.9 ms  ? OptimizationOptimJL
   3806.9 ms  ? Turing
Info Given TuringOptimExt was explicitly requested, output will be shown live 
┌ Warning: Module Turing with build ID ffffffff-ffff-ffff-58fd-65b9e8ca3415 is missing from the cache.
│ This may mean Turing [fce5fe82-541a-59a6-adf8-730c64b5f9a0] does not support precompilation but is imported by a module that does.
└ @ Base loading.jl:2541
    615.1 ms  ? Turing → TuringOptimExt
┌ Warning: Module Turing with build ID ffffffff-ffff-ffff-58fd-65b9e8ca3415 is missing from the cache.
│ This may mean Turing [fce5fe82-541a-59a6-adf8-730c64b5f9a0] does not support precompilation but is imported by a module that does.
└ @ Base loading.jl:2541

DynamicPPL.Model{typeof(gdemo), (:x,), (), (), Tuple{Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}(gdemo, (x = [1.5, 2.0],), NamedTuple(), DynamicPPL.DefaultContext())

The @model macro accepts a function definition and rewrites it such that call of the function generates a Model struct for use by the sampler.

However, models can be constructed by hand without the use of a macro. Taking the gdemo model above as an example, the macro-based definition can be implemented also (a bit less generally) with the macro-free version

using DynamicPPL

# Create the model function.
function gdemo2(model, varinfo, x)
    # Assume s² has an InverseGamma distribution.
    s², varinfo = DynamicPPL.tilde_assume!!(
        model.context, InverseGamma(2, 3), @varname(s²), varinfo
    )

    # Assume m has a Normal distribution.
    m, varinfo = DynamicPPL.tilde_assume!!(
        model.context, Normal(0, sqrt(s²)), @varname(m), varinfo
    )

    # Observe each value of x[i] according to a Normal distribution.
    for i in eachindex(x)
        _retval, varinfo = DynamicPPL.tilde_observe!!(
            model.context, Normal(m, sqrt(s²)), x[i], @varname(x[i]), varinfo
        )
    end

    # The final return statement should comprise both the original return
    # value and the updated varinfo.
    return nothing, varinfo
end
gdemo2(x) = DynamicPPL.Model(gdemo2, (; x))

# Instantiate a Model object with our data variables.
model2 = gdemo2([1.5, 2.0])
Model{typeof(gdemo2), (:x,), (), (), Tuple{Vector{Float64}}, Tuple{}, DefaultContext}(gdemo2, (x = [1.5, 2.0],), NamedTuple(), DefaultContext())

We can sample from this model in the same way:

chain = sample(model2, NUTS(), 1000; progress=false)
┌ Info: Found initial step size
└   ϵ = 0.8

Chains MCMC chain (1000×16×1 Array{Float64, 3}):

Iterations        = 501:1:1500
Number of chains  = 1
Samples per chain = 1000
Wall duration     = 7.57 seconds
Compute duration  = 7.57 seconds
parameters        = s², m
internals         = n_steps, is_accept, acceptance_rate, log_density, hamiltonian_energy, hamiltonian_energy_error, max_hamiltonian_energy_error, tree_depth, numerical_error, step_size, nom_step_size, lp, logprior, loglikelihood

Use `describe(chains)` for summary statistics and quantiles.

The subsequent pages in this section will show how the @model macro does this behind-the-scenes.

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