I have been using ESS with much success lately and I have a question I can't seem to figure out myself.
Does a whitening transformation of the prior affect ESS performance? In other words, does ESS take advantage of the particular covariance structure to propose better moves?
To clarify, say my prior and likelihood for problem 1 are $$p(x) = N(0, \Sigma) \text{ and } \mathcal{L}(x)$$
Using a whitening transformation $$x = L z \text{ where } L L^T = \Sigma$$ transform to problem 2 with prior and likelihood $$p(z) = N(0,I) \text{ and } \mathcal{L}'(z) = \mathcal{L}(x(z)) |{dz \over dx}|$$
Problems 1 and 2 are equivalent, but the former exposes more information to ESS. Is ESS expected to perform better on problem 1?
I have been using ESS with much success lately and I have a question I can't seem to figure out myself.
Does a whitening transformation of the prior affect ESS performance? In other words, does ESS take advantage of the particular covariance structure to propose better moves?
To clarify, say my prior and likelihood for problem 1 are $$p(x) = N(0, \Sigma) \text{ and } \mathcal{L}(x)$$
Using a whitening transformation $$x = L z \text{ where } L L^T = \Sigma$$ transform to problem 2 with prior and likelihood $$p(z) = N(0,I) \text{ and } \mathcal{L}'(z) = \mathcal{L}(x(z)) |{dz \over dx}|$$
Problems 1 and 2 are equivalent, but the former exposes more information to ESS. Is ESS expected to perform better on problem 1?