Hi everyone, I’ve been fitting some Gaussian Process models using the Hilbert space approximation, adapting code from the tutorials by @avehtari here and here. I would like to fit a model which uses a Matérn 1/2 kernel, but I am not sure how to adapt the diagSPD_Matern32 function to the other Matér…

So, there are a couple of things going on here. The first component in the approximation is the spectral density, which I derived as: s(\omega) =\frac{2 \rho \alpha}{1+\rho^2 \omega^2} = \frac{2\alpha}{ \frac{1}{\rho}+\rho\omega^2} =\frac{2\alpha}{ \rho((\frac{1}{\rho})^2+\omega^2)}. The second co…

FYI this was recently implemented in brms (you may need to install from github if it hasn’t made it into a release yet). You could use a formula like y ~ gp(x, cov="exponential", k=10) where k is the number of basis functions. Depending on your needs you could either use the brms model directly or…

Here’s what we think it is (any review / error spotting welcome, see related PR ): epiforecasts/EpiNow2/blob/f8228d05d650e4b507dc3519205530de37f2dafc/inst/stan/functions/gaussian_process.stan#L33 /** * Spectral density for 1/2 Matern (Ornstein-…

Do you have a link to the maths vingette? My implementation looks like: vector diagSPD_exp(real alpha, real rho, real L, int m) { vector[m] lambda = (linspaced_vector(m, 1, m)*pi()/(2*L))^2; vector[m] diag = 2*alpha*rho/(1+rho^2*sqrt(lambda)^2); diag = diag.^(0.5); return diag…

Yes, I think you’re right (and your maths matches our derivation in Gaussian Process implementation details • EpiNow2 ) - thanks!

I tested the Matern 5/2 kernel some program and it got more fitting difficulties than the Matern 3/2 kernel (longer runtime). The results however are plausible. Further I suggest to write the code slightly more homogeneous: vector diagSPD_Matern12(real alpha, real rho, real L, int M) { ... retur…

Hi, for the life of me I cannot get the same result as you did for the 𝜈=5/2 case. I get the same overall shape but a factor 16/3 instead of the 3/2 you have: S = \alpha^2 \frac{2 \sqrt{\pi} \Gamma(\nu + 1/2)(2\nu)^{\nu}}{\Gamma(\nu)\rho^{2\nu}}(...)^{-3} \\ = \alpha^2 \frac{2 \sqrt{\pi} \Gamma(3)…

diagSPD for Matérn GP kernels other than 3/2

Modeling

js592 October 22, 2024, 5:36pm 2

See discussion here: Practical Hilbert space approximate Bayesian Gaussian processes for probabilistic programming - #5 by js592

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diagSPD for Matérn GP kernels other than 3/2

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