Add manifolds for Normal-Gamma distribution

src/ExponentialFamilyManifolds.jl

@@ -17,5 +17,6 @@ include("natural_manifolds/geometric.jl")
 include("natural_manifolds/laplace.jl")
 include("natural_manifolds/lognormal.jl")
 include("natural_manifolds/normal.jl")
+include("natural_manifolds/normal_gamma.jl")
 
 end

src/natural_manifolds/normal_gamma.jl

@@ -0,0 +1,19 @@
+"""
+    get_natural_manifold_base(::Type{NormalGamma}, ::Tuple{}, conditioner=nothing)
+
+Get the natural manifold base for the `NormalGamma` distribution.
+"""
+function get_natural_manifold_base(::Type{NormalGamma}, ::Tuple{Int}, conditioner=nothing)
+    return ProductManifold(
+        Euclidean(1), ShiftedNegativeNumbers(static(0)), ShiftedPositiveNumbers(static(-1/2)),ShiftedNegativeNumbers(static(0))
+    )
+end
+
+"""
+    partition_point(::Type{NormalGamma}, ::Tuple{}, p, conditioner=nothing)
+
+Converts the `point` to a compatible representation for the natural manifold of type `NormalGamma`.
+"""
+function partition_point(::Type{NormalGamma}, ::Tuple{Int}, p, conditioner=nothing)
+    return ArrayPartition(view(p, 1:1), view(p, 2:2), view(p, 3:3), view(p, 4:4))
+end

test/natural_manifolds/normal_gamma_tests.jl

@@ -0,0 +1,7 @@
+@testitem "Check `NormalGamma` natural manifold" begin
+    include("natural_manifolds_setuptests.jl")
+
+    test_natural_manifold() do rng
+        return NormalGamma(10rand(rng), 10rand(rng), 10rand(rng), 10rand(rng))
+    end
+end