Efficient multi-level Gaussian process regression

This repository contains the efficient implementation of multi-level Gaussian process regression from the paper "Computationally efficient multi-level Gaussian process regression for functional data observed under completely or partially regular sampling designs" and an example of how to run it.

Check out the preprint here: https://arxiv.org/abs/2406.13691

Overview

• functions.stan contains functions for all parts of the implementation: the log-likelihood, the conditional posterior simulation, etc.
• regular_model.stan is a model template for using the functions to sample from the posterior in the completely regular sampling design.
• irregular_model.stan is a model template for the partially regular (irregular) sampling design.
• example.R shows how to sample from the models or expose the functions in R.
• sim.stan is used to simulate data from the model.
• sim_irregular.stan contains a helper function for doing the simulations.
• sim_list_to_tib.R contains a helper function for transforming the list output of the simulation to a tibble for convenience.

A note on modifying the models for your case

All the functions in functions.stan use the exponentiated quadratic kernel, but this is not necessary for our simplifications. If you want to modify the code to use a different kernel, you should search for gp_exp_quad_cov in functions.stan and change it to your kernel of choice. You may have to change the kernel hyperparameters as well. If you do want to use the exponentiated quadratic kernel, then you can use regular_model.stan or irregular_model.stan directly by simply changing the priors to suit your case.