Constrained parameters in Turing

Specific Domains Probabilistic Programming
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Is it possible to ensure that the posterior distribution of L obey these constraints?

Yep; this can be done for arbitrary constraints by just adding -Inf to the logjoint, i.e. putting

if ... # you're check as to whether the constraints are valid
    Turing.@addlogprob! -Inf
    # Do an early return since this entire sample will
    # be rejected anyways.
    return nothing
end

in your model. But this is a bad idea in a lot of cases, e.g. if you’re working with continuous variables and have equality constraints (like you’re wanting to do) since these will be satisfied with probability 0 :confused:

I am also not sure what effect the prior has on the posterior, i.e. should the prior of L also satisfy the constraints?

Exactly. Whenever you can encode the constraints/symmetrics into your prior, do it:) In the particular example you mention you can for example drop the equality-constraint, and instead construct your L by using L12 in both the (1, 2) and the (2, 1) entry.

If indeed the example you posted is exactly what you want to do, i.e. you want a prior on a positive-definite matrix, then you always have the LKJ distribution + sampling the diagonal-terms separately, or even Wishart with parameters ensuring full-rank.

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