Interpretation of posterior predictive checks for a Gaussian Process

I haven’t looked too closely at your PPC code, but it looks like the the root of your issue is that gp.Marginal assumes a Gaussian likelihood, but you’d like to try LogNormal or TruncatedNormal because your observed data is positive valued. What you can do is use gp.Latent instead, which doesn’t assume a likelihood. This example might be helpful here. How many covariates is your GP over? If small, say 2 or less, you might try HSGP as a replacement for gp.Latent to speed things up.

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