BKP: An R Package for Beta Kernel Process Modeling

Estimating input-dependent probability surfaces from binary, binomial, categorical, or multinomial response data is a common task in statistics and machine learning.

Latent Gaussian process classifiers provide flexible nonparametric models for such problems, but posterior inference with discrete responses typically requires approximation or simulation.

We discuss an implementation of probability-scale beta and Dirichlet kernel models in the \pkg{BKP} package for \proglang{R}.

The package implements the Beta Kernel Process (BKP), which uses kernel-weighted pseudo-count aggregation and beta-binomial conjugacy to obtain closed-form conjugate posterior summaries and posterior predictive distributions for binomial probabilities.

It also implements the Dirichlet Kernel Process (DKP) for multi-class responses, together with TwinBKP and TwinDKP, scalable twinning-based global-local approximations for larger datasets.

The resulting workflow supports transparent kernel-weighted evidence borrowing, several kernel families, fixed and data-adaptive priors, effective-sample-size calibration, loss-based hyperparameter tuning, and standard S3 methods for fitting, prediction, simulation, visualization, and extraction of posterior summaries.

Reproducible examples demonstrate probability-surface estimation, binary and multi-class classification, computational comparison, and real-data applications to \emph{Loa loa} infection prevalence mapping and Mourning Warbler distribution modeling.