Adds predict method to make it easier to work with the predictive posterior

[torfjelde]

With this method you can now do:

julia> using Turing

julia> @model function linear_reg(x, y, σ = 0.1)
           β ~ Normal(0, 1)

           for i ∈ eachindex(y)
               y[i] ~ Normal(β * x[i], σ)
           end
       end
DynamicPPL.ModelGen{var"###generator#384",(:x, :y, :σ),(:σ,),Tuple{Float64}}(##generator#384, (σ = 0.1,))

julia> f(x) = 2 * x + 0.1 * randn()
f (generic function with 1 method)

julia> Δ = 0.1
0.1

julia> xs_train = 0:Δ:10; ys_train = f.(xs_train);

julia> xs_test = [10 + Δ, 10 + 2 * Δ]; ys_test = f.(xs_test);

julia> # Infer
       m_lin_reg = linear_reg(xs_train, ys_train);

julia> chain_lin_reg = sample(m_lin_reg, NUTS(100, 0.65), 200);
┌ Info: Found initial step size
└   ϵ = 0.003125

julia> m_lin_reg_test = linear_reg(xs_test, Vector{Union{Missing, Float64}}(undef, length(ys_test)));

julia> predictions = Turing.Inference.predict(m_lin_reg_test, chain_lin_reg)
Object of type Chains, with data of type 100×2×1 Array{Float64,3}

Iterations        = 1:100
Thinning interval = 1
Chains            = 1
Samples per chain = 100
parameters        = y[1], y[2]

2-element Array{ChainDataFrame,1}

Summary Statistics
  parameters     mean     std  naive_se     mcse       ess   r_hat
  ──────────  ───────  ──────  ────────  ───────  ────────  ──────
        y[1]  20.1978  0.0921    0.0092  missing  224.2130  0.9904
        y[2]  20.3739  0.1056    0.0106  missing  273.7488  0.9919

Quantiles
  parameters     2.5%    25.0%    50.0%    75.0%    97.5%
  ──────────  ───────  ───────  ───────  ───────  ───────
        y[1]  20.0378  20.1254  20.1863  20.2668  20.3704
        y[2]  20.1650  20.3117  20.3800  20.4430  20.5696


julia> ys_pred = collect(vec(mean(predictions[:y].value; dims = 1)))
2-element Array{Float64,1}:
 20.19778013967426
 20.373873670853182

julia> sum(abs2, ys_test - ys_pred)
0.0016295979352728104

One question: should this method be exported? I'm currently overloading StatsBase.predict because Turing will often used together with StatsBase and so I figured overloading rather than defining our own is preferable to avoid warnings. This is also up for discussion; I'm fine either way.

[devmotion]

I'm currently overloading StatsBase.predict because Turing will often used together with StatsBase and so I figured overloading rather than defining our own is preferable to avoid warnings.

IMO we should definitely overload StatsBase.predict and not define our own method, but that's orthogonal to the question if we should (re-)export it. Maybe it's more convenient for users if we reexport it, but I don't have a strong opinion on that question.

[codecov]

Codecov Report

Merging #1286 into master will increase coverage by 0.48%.
The diff coverage is 95.83%.

@@            Coverage Diff             @@
##           master    #1286      +/-   ##
==========================================
+ Coverage   67.81%   68.29%   +0.48%     
==========================================
  Files          25       25              
  Lines        1367     1391      +24     
==========================================
+ Hits          927      950      +23     
- Misses        440      441       +1     

Impacted Files	Coverage Δ
src/inference/Inference.jl	91.26% <95.83%> (+1.07%)	⬆️

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[cpfiffer]

No further comments from me! Looks solid as all get-out.