Add MvNormal sampling consistency test (#128)

test/mvnormal.jl

@@ -47,24 +47,64 @@ include("test_utils.jl")
         end
 
         @testset "MvNormal{T,Pathfinder.WoodburyPDMat{T}}" begin
-            n = 10
-            ndraws = 20
-            nhist = 4
-            A = rand_pd_diag_mat(Float64, 10)
-            D = rand_pd_mat(Float64, 2nhist)
-            B = randn(n, 2nhist)
-            Σ = Pathfinder.WoodburyPDMat(A, B, D)
-            μ = randn(n)
-            dist = MvNormal(μ, Σ)
+            @testset "basic" begin
+                n = 10
+                ndraws = 20
+                nhist = 4
+                A = rand_pd_diag_mat(Float64, 10)
+                D = rand_pd_mat(Float64, 2nhist)
+                B = randn(n, 2nhist)
+                Σ = Pathfinder.WoodburyPDMat(A, B, D)
+                μ = randn(n)
+                dist = MvNormal(μ, Σ)
 
-            seed = 42
-            rng = Random.seed!(Random.default_rng(), seed)
-            x, logpx = @inferred Pathfinder.rand_and_logpdf(rng, dist, ndraws)
-            Random.seed!(rng, seed)
-            x2 = rand(rng, dist, ndraws)
-            logpx2 = logpdf(dist, x2)
-            @test x ≈ x2
-            @test logpx ≈ logpx2
+                seed = 42
+                rng = Random.seed!(Random.default_rng(), seed)
+                x, logpx = @inferred Pathfinder.rand_and_logpdf(rng, dist, ndraws)
+                Random.seed!(rng, seed)
+                x2 = rand(rng, dist, ndraws)
+                logpx2 = logpdf(dist, x2)
+                @test x ≈ x2
+                @test logpx ≈ logpx2
+            end
+
+            @testset "consistency of rand" begin
+                n = 10
+                ndraws = 300_000
+                nhist = 4
+                A = rand_pd_diag_mat(Float64, 10)
+                D = rand_pd_mat(Float64, 2nhist)
+                B = randn(n, 2nhist)
+
+                Σ = Pathfinder.WoodburyPDMat(A, B, D)
+                μ = randn(n)
+                dist = MvNormal(μ, Σ)
+                v = diag(Σ)
+                R = Matrix(Σ) ./ sqrt.(v) ./ sqrt.(v')
+
+                x = rand(dist, ndraws)
+                μ_est = mean(x; dims=2)
+                v_est = var(x; mean=μ_est, dims=2)
+                R_est = cor(x; dims=2)
+
+                nchecks = 2n + div(n * (n - 1), 2)
+                α = (0.01 / nchecks) / 2  # multiple correction
+                tol = quantile(Normal(), 1 - α) / sqrt(ndraws)
+
+                # asymptotic standard errors for the marginal estimators
+                μ_std = sqrt.(v)
+                v_std = sqrt(2) * v
+
+                for i in 1:n
+                    @test μ_est[i] ≈ μ[i] atol = (tol * μ_std[i])
+                    @test v_est[i] ≈ v[i] atol = (tol * v_std[i])
+                    for j in (i + 1):n
+                        # use variance-stabilizing transformation, recommended in §3.6 of
+                        # Van der Vaart, A. W. (2000). Asymptotic statistics (Vol. 3).
+                        @test atanh(R_est[i, j]) ≈ atanh(R[i, j]) atol = tol
+                    end
+                end
+            end
         end
 
         @testset "Normal" begin