Bayesian Heteroskedastic Gaussian Processes

Performs Bayesian posterior inference for heteroskedastic Gaussian processes. Models are trained through MCMC including elliptical slice sampling (ESS) of latent noise processes and Metropolis-Hastings sampling of kernel hyperparameters. Replicates are handled efficientyly through a Woodbury formulation of the joint likelihood for the mean and noise process (Binois, M., Gramacy, R., Ludkovski, M. (2018) ) For large data, Vecchia-approximation for faster computation is leveraged (Sauer, A., Cooper, A., and Gramacy, R., (2023), ). Incorporates 'OpenMP' and SNOW parallelization and utilizes 'C'/'C++' under the hood.

This repo consists of an in progress interface for the implementation of a Bayesian HetGP

Run R CMD INSTALL bhGP from outside this folder. If already installed and package is updated: remove package, restart R, and then run this install command.

R files include:

• functions.R : all functions for log likelihood and Sigma contruction

• mcmc.R : Does mcmc and ess sampling for theta, nugget vector, etc.

• gibbs.R : Gibbs sampler for MCMC for seperable, iso-tropic, and combination

• fit.R : Fits bhGP to the data (X,Y)

• predict.R: Predicts at new locations Xp

• mcmc_vecchia.R : Does mcmc and ess sampling for theta, nugget vector, w/ vecchia

• gibbs_vecchia.R : Gibbs sampler for MCMC for seperable, iso-tropic, and combination w/ vecchia

• gibbs_vdims_N.R: Gibbs for full N version w/ variance changing in some dimenstions

• predict_vecchia.R: Predicts at new locations Xp w/ vecchia

• trim.R: trims mcmc object

• plots.R: Trace plots and prediction plots

• vecchia.R: Helper vecchia functions

• general.R: Helper functions

• checks.R : checks initilizations

• inits.R: initialization stratergy

src files include:

• vecchia.cpp: Vecchia related fucntions

• cov.cpp: Builds cov matrices

• invdet.c: inv and det fns

• general.c: used for invdet

• RcppExports.cpp: created for package

Updates

• vdims is working now

• removed sq from matern for SV

• predict lam_ub is now by default FALSE

• stratergy = "flat" now working

• priors on theta_lam adjusted ---> ocean example working out better

• ls_check = TRUE by default??? maybe not.

• checks.R --> check_scale() ---> remove print statement

• check all prints before reupload.

------------------------- Next to Dos --------------------------------------

• for nmcmc = 1, make predictions also possible (to be done)

• will need to make joint U preds faster.

Version 1.0.2

• corrects span error
• fixed stratergy for initialization