stan-dev / stan-dev/math

gp_dot_prod_cov allow vector sigma (ard)

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Description

gp_dot_prod_cov currently allows only scalar sigma. it would be useful to allow vector sigma in addition of scalar sigma. This would be useful for making faster inference for sparse models with p>n and scale mixture of normal priors such as horseshoe. Then integration over the linear model weights could be made analytically using gp_dot_prod_cov. Cost of analytic integration scales as O(n^3), but this is fine in many p>>n cases (e.g. I have many examples with n<100). In the horseshoe case, there would still be p local sigmas, but the posterior dimension is almost halved and the shape of the posterior should be also easier, and thus we should be able to see higher effective sample sizes.

As, e.g. gp_exp_quad_cov allows vector lengthscale, it can be used as an example how to add vector sigma and function signature for sigma part would look similar,

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