Wishart priors resulting in PosDefException: matrix is not positive definite; Cholesky factorization failed

[ipozdeev]

julia v1.10.2
Turing v0.30.7
Distributions v0.25.107

Using Wishart priors results in several functions throwing the above error, which does not make sense to me, e.g. in this MWE maximizing:

using Turing, MCMCChains
using Statistics, LinearAlgebra, PDMats
using Optim

# parameter of the Wishart prior
A = Matrix{Float64}(I, 3, 3);
isposdef(A)  # true
ishermitian(A)  # true

@model function demo(x)
    _A ~ Wishart(5, A);
    _x_mu = sum(_A);
    return x ~ Normal(_x_mu, 1);
end

# condition model on single obs
demo_model = demo(1.0);

map_estimate = optimize(demo_model, MAP());  # error
chain = sample(model, HMC(0.05, 10), 1000);  # error

chain = sample(model, MH(), 1000);  # no error

MAP() throws an error, as does sampling with HMC and NUTS, but not with MH.