Apologies for the delayed response. I experimented with introducing the constraint as you suggested. However, I’m noticing that the Monte Carlo error across chains remains high. It seems that the step size may be too small, leading to insufficient exploration of the space within the ~5,000-10,000 step range I tested. I’ll work on preparing a minimal working example (MWE) and share it soon.
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My bad. I was calculating the pdf in spherical coordinates but forgot to include the factors from the volume element, i.e., \sqrt{G} = r^{2}\sin(\theta). The sampler works quite well, especially when I choose a largish \sigma (i.e., when \exp(g(r)) = r^{a}e^{-(r-\alpha)^{2}/2\sigma^{2}}).
I find a relative ess (for the quantity I am interested in, which is the function energy(θ::Vector{Float64}, ϕ::Vector{Float64}) from an earlier post) with a=2, \sigma=0.10, for a 20 dimensional space (i.e. one embedded in (\mathbb{R}^{3})^{10} equal to 0.60 (with 16 chains of length 2500 each). I will try to experiment around a bit with a range of distributions that I am interested in and some other metrics I typically use.
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