I’m new to Stan and gaussian processes, but I have a problem at hand where these can potentially be very useful.
I want to build a non-parametric gaussian process using an exponentiated quadratic kernel to model count data with a negative binomial distribution. My y is a vector of count data and my x is a vector of natural numbers.
I followed Michael’s excellent blog post ( https://betanalpha.github.io/assets/case_studies/gp_part1/part1.html ), although I have a few doubts on how to modify the existing example to consider a neg_binomial_2 distribution.
Could you point me to any example that could achieve this, similarly to the example below (I found this thread https://groups.google.com/forum/#!msg/stan-users/XjHD_2FvVlE/PAjfY62zDkwJ but I couldn’t understand/find the final model)?
matrix[N, N] cov = cov_exp_quad(x, alpha, rho) + diag_matrix(rep_vector(square(sigma), N));
matrix[N, N] L_cov = cholesky_decompose(cov);
y ~ multi_normal_cholesky(rep_vector(0, N), L_cov);
I also would like to fit this model to two different y’s and find where these two GPs differ significantly (I’ll also need to contain a specific offset to each y). I presume I can obtain this by assessing calculating | GP1(x) - GP2(x) | and validating if the difference is higher than the expected standard variation of each GP1 and GP2.
I apologise in advance for the basic questions and thank you any opinion/suggestion you might have.