Some prior changes to make nicer plots

src/priors/common.jl

@@ -72,7 +72,7 @@ This implementation is likely to change in the future to allow for more flexibil
 initial_distribution(p::AbstractGaussMarkovProcess{T}) where {T} = begin
     d, q = dim(p), num_derivatives(p)
     D = d * (q + 1)
-    initial_variance = ones(T, q + 1)
+    initial_variance = 1e-16*ones(T, q + 1)
     μ0 = T <: LinearAlgebra.BlasFloat ? Array{T}(calloc, D) : zeros(T, D)
     Σ0 = PSDMatrix(IsometricKroneckerProduct(d, diagm(sqrt.(initial_variance))))
     return Gaussian(μ0, Σ0)

src/priors/ioup.jl

@@ -52,6 +52,30 @@ IOUP(num_derivatives; update_rate_parameter) = begin
     IOUP(num_derivatives, missing; update_rate_parameter)
 end
 
+initial_distribution(p::IOUP{T}) where {T} = begin
+    d, q = dim(p), num_derivatives(p)
+    D = d * (q + 1)
+    if q > 0
+        initial_variance = 1e-8 * ones(T, q + 1)
+        μ0 = zeros(T, D)
+        Σ0 = PSDMatrix(
+            IsometricKroneckerProduct(d, diagm(sqrt.(initial_variance))),
+        )
+        return Gaussian(μ0, Σ0)
+    else
+        sde = to_sde(p)
+        μ0 = zeros(T, D)
+        Σ0 = PSDMatrix(
+            IsometricKroneckerProduct(
+                d,
+                Matrix(plyapc(sde.F.B, sde.L.B)'),
+            ),
+        )
+        return Gaussian(μ0, Σ0)
+    end
+end
+
+
 remake(
     p::IOUP{T};
     elType=T,

src/priors/matern.jl

@@ -47,6 +47,12 @@ Matern(; dim, num_derivatives, lengthscale) =
     Matern{typeof(1.0)}(; dim, num_derivatives, lengthscale)
 Matern(num_derivatives, lengthscale) =
     Matern(; dim=1, num_derivatives, lengthscale)
+Matern(nu::Rational, lengthscale) =
+    Matern(; dim=1, nu, lengthscale)
+Matern(; dim, nu::Rational, lengthscale) = begin
+    @assert nu.den == 2 "The Matern process is only defined for half integers nu = p/2"
+    Matern{typeof(1.0)}(;dim, num_derivatives=Int(floor(nu)), lengthscale)
+end
 
 remake(
     p::Matern{T};
@@ -70,7 +76,7 @@ function to_sde(p::Matern)
     l = p.lengthscale
     @assert l isa Number
 
-    ν = q - 1 / 2
+    ν = q + 1 / 2
     λ = sqrt(2ν) / l
 
     F_breve = diagm(1 => ones(q))