BayesNest

BayesNest is a lightweight, log-space nested sampler for Bayesian inference, supporting complex posterior structures including multimodal, curved, and non-Gaussian distributions. It supports multiple constrained sampling strategies including:

• Naive rejection sampling
• Ellipsoidal sampling (MultiNest-style)
• MCMC-constrained sampling
• Slice sampling
• Diffusive sampling (tempered MCMC)

BayesNest computes both posterior samples and Bayesian model evidence

Features

• Log evidence computation
• Posterior sampling with log-weights
• Support for multimodal and curved posteriors
• Corner plot visualization of parameter distributions
• Multiple constrained samplers (uniform, ellipsoid, mcmc, slice, diffusive)
• Convergence diagnostics via log-evidence trace plots
• Minimal, dependency-light design

Installation

pip install bayesnest

Examples

All examples are located in the examples/ directory of the repo.

1: Linear Gaussian Model

python examples/linear_gaussian_example.py

This example:

• Simulates data from a linear Gaussian model y = ax + b + noise

• Use nested sampling to estimate the posterior distribution over slope a and intercept b

• Print the posterior mean and log evidence

• Generate a 2D corner plot of the posterior distribution plot

• Plots the convergence of the log-evidence estimate

2: Multimodal Posterior

A synthetic example with two separated Gaussian modes is also found in the github repo

python examples/multimodal_example.py

This synthetic example defines a 2D likelihood with two well-separated Gaussian peaks and:

• Sample using ellipsoidal decomposition

• Reveal both modes clearly in the posterior distribution plot

• Demonstrate ellipsoid nested sampling’s strength in handling multimodal distributions

Expected output:

• A bimodal posterior in the corner plot

• A log-evidence trace that reflects both modes properly being integrated

3: Rosenbrock

python examples/rosenbrock_example.py

This classic benchmark stresses the sampler with a narrow, curved valley in 5D.

• Uses slice sampling to effectively explore curved likelihood regions
• Computes posterior samples and log-evidence
• Generates a pairwise corner plot

Expected output:

• The expected 2D plot between theta_0 and theta_1 should show a tight, curved valley, starting from -1 to 1
• Posterior mean near theta_i = 1 for all i