# Bayesian cross-validation by parallel Markov Chain Monte Carlo

arXiv: https://arxiv.org/abs/2310.07002 · HTML: https://mlsanity.com/paper/2310.07002/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2023.

## Built on by (most cited first, 3 of 3)

- [BlackJAX: Composable Bayesian inference in JAX](https://mlsanity.com/paper/2402.10797/) (2024)
- [Scalable Bayesian Learning with posteriors](https://mlsanity.com/paper/2406.00104/) (2024)
- [Bayesian model selection and misspecification testing in imaging inverse problems only from noisy and partial measurements](https://mlsanity.com/paper/2510.27663/) (2025)

## Abstract (arXiv)

Brute force cross-validation (CV) is a method for predictive assessment and model selection that is general and applicable to a wide range of Bayesian models. Naive or `brute force' CV approaches are often too computationally costly for interactive modeling workflows, especially when inference relies on Markov chain Monte Carlo (MCMC). We propose overcoming this limitation using massively parallel MCMC. Using accelerator hardware such as graphics processor units (GPUs), our approach can be about as fast (in wall clock time) as a single full-data model fit. Parallel CV is flexible because it can easily exploit a wide range data partitioning schemes, such as those designed for non-exchangeable data. It can also accommodate a range of scoring rules. We propose MCMC diagnostics, including a summary of MCMC mixing based on the popular potential scale reduction factor (widehatR) and MCMC effective sample size (widehatESS) measures. We also describe a method for determining whether an widehatR diagnostic indicates approximate stationarity of the chains, that may be of more general interest for applications beyond parallel CV. Finally, we show that parallel CV and its diagnostics can be implemented with online algorithms, allowing parallel CV to scale up to very large blocking designs on memory-constrained computing accelerators.