fix: update ClosedWilliamsProduct with Logpdf

Author: Nimrais

src/Exponential/Exponential.jl

@@ -28,24 +28,24 @@ function mean(::ClosedFormExpectation, p::ComposedFunction{typeof(log), ExpLogSq
     return 1/(2*σ^2)*(-(μ+eulergamma)^2 - π^2/6 - log(λ)*(-2*(eulergamma+μ) + log(λ)))
 end
 
-function mean(::ClosedWilliamsProduct, p::typeof(identity), q::Exponential)
+function mean(::ClosedWilliamsProduct, p::typeof(log), q::Exponential)
     return 1/mean(q)
 end
 
-function mean(::ClosedWilliamsProduct, p::ExpLogSquare, q::Exponential)
-    μ = p.μ
-    σ = p.σ
+function mean(::ClosedWilliamsProduct, p::ComposedFunction{typeof(log), ExpLogSquare{T}}, q::Exponential) where {T}
+    μ = p.inner.μ
+    σ = p.inner.σ
     λ = mean(q)
     return 1/(2*σ^2)*(-1/λ*(-2*(eulergamma+μ) + log(λ)) - log(λ)/λ)
 end
 
-function mean(::ClosedWilliamsProduct, p::LogNormal, q::Exponential)
-    μ, σ = p.μ, p.σ
+function mean(::ClosedWilliamsProduct, p::Logpdf{LogNormal{T}}, q::Exponential) where {T}
+    μ, σ = p.dist.μ, p.dist.σ
     λ = mean(q)
     return 1/(2*σ^2)*(-1/λ*(-2*(eulergamma+μ) + log(λ)) - log(λ)/λ) - 1/λ
 end 
 
-function mean(::ClosedWilliamsProduct, p::Exponential, ::Exponential)
-    λ2 = mean(p)
+function mean(::ClosedWilliamsProduct, f::Logpdf{Exponential{T}}, ::Exponential) where {T}
+    λ2 = mean(f.dist)
     return -1/λ2
 end

src/logpdf.jl

@@ -5,7 +5,7 @@ import Distributions: Distribution, logpdf
 """
     Logpdf
 
-A structure to represent the logpdf function of a distribution.
+The structure to represent the logpdf function of a distribution.
 """
 struct Logpdf{D}
     dist::D

test/Exponential/williams_tests.jl

@@ -1,4 +1,4 @@
-@testitem "mean(::ClosedWilliamsProduct, q::Exponential, p::typeof(identity))" begin
+@testitem "mean(::ClosedWilliamsProduct, p::log, q::Exponential)" begin
     using Distributions
     using ClosedFormExpectations
     using StableRNGs
@@ -16,12 +16,12 @@
         N = 10^6
         samples = rand(rng, Exponential(λ), 10^6)
         williams_product = map(x -> score(Exponential(λ), x)*log(x), samples)
-        expectation = mean(ClosedWilliamsProduct(), identity, Exponential(λ))
+        expectation = mean(ClosedWilliamsProduct(), log, Exponential(λ))
         @test sigma_rule(expectation, mean(williams_product), std(williams_product), N)
     end
 end
 
-@testitem "mean(::ClosedWilliamsProduct, q::Exponential, p::ExpLogSquare)" begin
+@testitem "mean(::ClosedWilliamsProduct, p::ExpLogSquare, q::Exponential)" begin
     using Distributions
     using ClosedFormExpectations
     using StableRNGs
@@ -42,12 +42,12 @@ end
         samples = rand(rng, Exponential(λ), 10^6)
         fn(x)  = (log ∘ ExpLogSquare(μ, σ))(x)
         williams_product = map(x -> score(Exponential(λ), x)*fn(x), samples)
-        expectation = mean(ClosedWilliamsProduct(), ExpLogSquare(μ, σ), Exponential(λ))
+        expectation = mean(ClosedWilliamsProduct(), log ∘ ExpLogSquare(μ, σ), Exponential(λ))
         @test sigma_rule(expectation, mean(williams_product), std(williams_product), N)
     end
 end
 
-@testitem "mean(::ClosedWilliamsProduct, q::Exponential, p::LogNormal)" begin
+@testitem "mean(::ClosedWilliamsProduct, f::Logpdf{LogNormal}, q::Exponential)" begin
     using Distributions
     using ClosedFormExpectations
     using StableRNGs
@@ -68,7 +68,7 @@ end
         samples = rand(rng, Exponential(λ), 10^6)
         fn(x)  = logpdf(LogNormal(μ, σ), x)
         williams_product = map(x -> score(Exponential(λ), x)*fn(x), samples)
-        expectation = mean(ClosedWilliamsProduct(), LogNormal(μ, σ), Exponential(λ))
+        expectation = mean(ClosedWilliamsProduct(), Logpdf(LogNormal(μ, σ)), Exponential(λ))
         @test sigma_rule(expectation, mean(williams_product), std(williams_product), N)
     end
 end
@@ -90,6 +90,7 @@ end
         samples = rand(rng, Exponential(λ1), N)
         fn(x) = logpdf(Exponential(λ2), x)
         williams_product = map(x -> score(Exponential(λ1), x)*fn(x), samples)
-        @test sigma_rule(mean(ClosedWilliamsProduct(), Exponential(λ2), Exponential(λ1)), mean(williams_product), std(williams_product), N)
+        expectation = mean(ClosedWilliamsProduct(), Logpdf(Exponential(λ2)), Exponential(λ1))
+        @test sigma_rule(expectation, mean(williams_product), std(williams_product), N)
     end
 end