Source-linked AI summary
UltraNest -- a robust, general purpose Bayesian inference engine
Johannes Buchner
TL;DR
Bayesian inference pipelines need reliable parameter estimation and model comparison, but existing methods can miss posterior modes and be difficult to operate robustly. UltraNest addresses this with reactive nested sampling, self-diagnosing exploration, conservative uncertainty estimation, and region-based constrained sampling. It is intended for complex posterior distributions where users prioritize a gold-standard exploration of the full posterior over speed.
Problem
Reliable Bayesian parameter estimation and model comparison are difficult when existing workflows can miss important posterior modes and require substantial user interaction.
Method
UltraNest combines self-diagnosing nested-sampling algorithms, reactive tree-based exploration, conservative uncertainty estimation, and intersecting region constructions for constrained sampling.
Results
UltraNest is developed for complex posteriors requiring exploration of the entire posterior distribution in one run, prioritizing robustness and correctness before speed.
Takeaways & Limitations
UltraNest is especially suited to multi-modal or non-Gaussian parameter spaces, computationally expensive models, and robust pipelines.
Abstract
from arXiv · showhide
UltraNest is a general-purpose Bayesian inference package for parameter estimation and model comparison. It allows fitting arbitrary models specified as likelihood functions written in Python, C, C++, Fortran, Julia or R. With a focus on correctness and speed (in that order), UltraNest is especially useful for multi-modal or non-Gaussian parameter spaces, computational expensive models, in robust pipelines. Parallelisation to computing clusters and resuming incomplete runs is available.
Summary
UltraNest is designed as a robust Bayesian inference engine for computationally expensive models and robust pipelines, with cluster parallelisation and run resumption available.
- UltraNest targets computationally expensive models and robust pipelines.
- Parallelisation to computing clusters and resuming incomplete runs are available.
Statement of need
Reliable Bayesian inference requires both parameter estimation and model comparison, but existing workflows can miss important posterior modes and are difficult to operate robustly. UltraNest addresses this need with theoretically justified, self-diagnosing methods that prioritize correctness.
- Scientific model comparison involves constraining parameters and comparing models.
- Existing Bayesian fitting packages can be difficult to run reliably with minimal user interaction.
- MCMC convergence checks may appear satisfactory while missing a distant, important posterior peak.
- Nested sampling estimates posterior samples, marginal likelihoods, and Bayes factors while performing global scans suited to multi-modal settings.
- UltraNest develops state-of-the-art techniques for exploration, diagnostics, and uncertainty handling that are free of tuning parameters and theoretically justified.
- UltraNest replaces heuristic implementations with self-diagnosing algorithms and conservative uncertainty propagation, prioritizing robustness and correctness over speed.
Method
UltraNest combines reactive nested sampling, conservative uncertainty estimation, region-based constrained sampling, and Monte Carlo methods to explore complex posterior spaces.
- Nested sampling: Vanilla nested sampling replaces the worst live point through likelihood-constrained prior sampling as prior volume shrinks.
- Reactive NS: UltraNest represents live-point exploration with a tree and breadth-first search ordered by likelihood.
- Reactive NS: Reactive NS generalizes Dynamic NS and supports error propagation with a variable number of live points.
- Integration procedure: Bootstrapped explorers estimate evidence and weights from tree subsamples, producing an uncertainty distribution.
- Integration procedure: Bootstrapped integrators include scatter in likelihoods and volume estimates in evidence uncertainty measures.
- LRPS procedures in UltraNest: UltraNest intersects MLFriends with bootstrapped ellipsoids in u-space and v-space, helping with constraints such as funnels.
Features
UltraNest provides runtime and posterior visualisation, diagnostics, parallelisation, resumption, and support for models written in several programming languages, with extensive documentation.
- Features include runtime visualisation, posterior visualisations, and diagnostic tests of run quality.
- UltraNest supports MPI parallelisation and resuming runs.
- Models can be written in Python, C, C++, Fortran, Julia, R, and Javascript.
- Extensive documentation is available.