feat: univariate Gaussian likelihood in Gaussian prior

src/models/Models.jl

@@ -15,5 +15,6 @@ using LogExpFunctions
 include("shells.jl")
 include("correlated.jl")
 include("eggbox.jl")
+include("univariagaussiangaussian.jl")
 
 end # module

src/models/univariategaussiangaussian.jl

@@ -0,0 +1,37 @@
+using Distributions
+using NestedSamplers
+using StatsBase
+
+@doc raw"""
+Models.UnivariateGaussianGaussian()
+
+Creates a model with Normal prior and Normal likelihood.
+
+```math
+\mathbf\theta \sim \mathcal{N}\left(\mu_p, \sigma_p\right)
+```
+```math
+\mathbf{d} \sim \mathcal{N}\left(\mathbf\theta, \sigma_d\right)
+```
+the analytical evidence of the model is
+
+```math
+Z = \mathcal{N}\left(\mu_p, \sqrt{\sigma_p^2 + \sigma_d^2}\right)
+```
+
+## Examples
+```jldoctest
+julia> model, lnZ = Models.UnivariateNormalNormal(2, 0.5, 1, 0);
+
+julia> lnZ
+-2.6305103088617776
+```
+"""
+
+function UnivariateGaussianGaussian(μp::Float64, σp::Float64, σd::Float64, d::Float64=0.0)
+    priors = [Normal(μp, σp)]                   # θ ~ N(μ, σ)
+    loglike(θ) = logpdf(Normal(d, σd),θ[1])     # d ~ N(θ, σd)
+    model = NestedModel(loglike, priors)
+    true_lnZ = logpdf(Normal(μp, sqrt(σp^2 + σd^2)), d) # lnZ is analytical in the data and the prior hyperparameters
+    return model, true_lnZ
+end