Blackjax-NS: GPU Bayesian Inference

• Blackjax-NS is a GPU-native Bayesian inference toolkit that employs batched, vectorized nested sampling for accelerated parameter estimation in gravitational-wave analysis.
• It builds on the composable, functional design of BlackJAX and utilizes JAX for hardware-agnostic acceleration across CPUs, GPUs, and TPUs.
• The framework implements an acceptance-walk nested sampling kernel to achieve high parallelism and maintain statistical equivalence with established CPU pipelines.

The Blackjax-NS Framework is a GPU-native Bayesian inference toolkit, architected for efficient, batched, and highly parallel parameter estimation and model selection, especially in gravitational-wave (GW) data analysis and related large-scale applications. Built atop the modular, functional BlackJAX inference library and leveraging JAX for hardware-agnostic acceleration, Blackjax-NS implements community-standard nested sampling algorithms and offers substantial performance improvements while retaining statistical equivalence with established CPU pipelines.

1. Foundations: Architecture and Design Principles

The Blackjax-NS Framework is fundamentally grounded in composability and vectorization, inheriting the functional, modular structure of BlackJAX (Cabezas et al., 16 Feb 2024). Each sampler and kernel in BlackJAX is implemented as a pure function, mapping an input state (often including positions, momenta, step sizes, and diagnostics) to an output state, free of side effects. This design enables seamless composition of sampling "atoms" (e.g., leapfrog integrators, Metropolis-Hastings accept/reject steps) into more complex algorithms.

In Blackjax-NS, this approach is extended to enable batched and massively parallel nested sampling workflows, suitable for GPU execution. The framework is built to accept un-normalized log density functions as is standard in probabilistic programming, allowing direct interfacing with a wide class of models.

Key architectural features include:

• Batched Operations: Simultaneous evolution of multiple "live" points or MCMC chains per iteration.
• Functional API: Stateless operators that ease vectorized implementation and parallelism.
• Hardware Agnosticism: JAX enables transparent targeting of CPUs, GPUs, and TPUs through XLA compilation and auto-vectorization.

2. Acceptance–Walk Nested Sampling Kernel

A central contribution of the Blackjax-NS Framework is the GPU-native, batched translation of the "acceptance-walk" nested sampling kernel—a Differential Evolution (DE) based proposal scheme widely used in community-standard pipelines such as bilby and dynesty (Prathaban et al., 4 Sep 2025).

Core Algorithm:

• Live Point Replacement: At each iteration, a batch (typically half of the live points) is removed and replaced, rather than the single-point replacement of conventional CPU samplers.
• Proposal Mechanism: For each new point,

$$\theta_{\text{candidate}} = \theta_{\text{current}} + \gamma \cdot (\theta_i - \theta_j)$$

where $\theta_i$ and $\theta_j$ are randomly selected live points, and $\gamma$ is a scaling factor (unity or stochastically sampled). Acceptance criterion:

$$\mathcal{L}(\theta_{\text{candidate}}) > \mathcal{L}_{\text{min}}$$

• MCMC Walk Length Control: For efficient GPU usage, all chains in a batch adopt a uniform, batch-level walk length, adapted after each batch to target a specific acceptance count (e.g., 60).
• Live Point Adjustment: To reach comparable convergence with CPU-based runs, the number of GPU live points is set by

$$n_{\text{GPU}} \approx 2 \ln(2) n_{\text{CPU}} \approx 1.4 n_{\text{CPU}}$$

This batched, vectorized approach aligns compute patterns for GPU parallelism and mitigates thread divergence, a core obstacle in naive porting of classical MCMC algorithms to accelerators.

3. Performance Metrics and Hardware Acceleration

Empirical benchmarks (Prathaban et al., 4 Sep 2025) demonstrate speedups of 20–40× in GW binary black hole parameter estimation compared with the original bilby CPU pipeline, while yielding statistically indistinguishable posterior and evidence estimates. For example, a 4-second simulated binary black hole run required 47.8 CPU-hours (16-core instance) in bilby, and only 1.25 hours on a single GPU using Blackjax-NS. Cost analysis further shows an approximate 2.4× reduction in wall-clock costs given equivalent hourly pricing between CPU and GPU resources.

Two layers of performance improvement contribute:

• Inter-sample Parallelization ("batched sampling"): The dominant factor; thousands of candidate points evolved concurrently.
• Intra-likelihood Parallelization: GPU-native waveform evaluation across frequency bins (using "ripple"), with additional, though more modest, acceleration.

The architectural separation of these two improvements enables explicit quantification of hardware-induced speedup, providing a rigorous baseline for future algorithmic innovation.

4. Statistical Foundations: Bayesian Inference and Evidence

The workflow adheres to standard Bayesian formulations,

$$\mathcal{P}(\theta|d,H) = \frac{\mathcal{L}(d|\theta,H)\,\pi(\theta|H)}{Z(d|H)}$$

with the Bayesian evidence,

$$Z(d|H) = \int \mathcal{L}(d|\theta,H)\, \pi(\theta|H)\, d\theta$$

Nested sampling traverses likelihood shells by iteratively sampling within the constrained region $\mathcal{L}(\theta) > \mathcal{L}_{\text{min}}$. The acceptance-walk proposal, using DE moves, ensures effective exploration of complex, high-dimensional posteriors, a necessity in GW data analysis.

5. Probabilistic Programming and Composability

Blackjax-NS naturally interfaces with probabilistic programming languages due to its unnormalized log-density API (Cabezas et al., 16 Feb 2024), sidestepping the need for fully normalized densities. This facilitates:

• Model specification via PPLs.
• Plug-and-play use of advanced samplers for arbitrary models.
• Rapid research prototyping by mixing and matching kernel components.

Composability enables rapid prototyping, benchmarking, and deployment of both standard and novel Bayesian methods, significantly reducing algorithm development cycles.

6. Applications in Gravitational-Wave and Astrophysical Data Analysis

The paramount use-case for Blackjax-NS is Bayesian GW parameter estimation and model selection. The ability to accelerate inference pipelines for binary black hole and neutron star merger signals directly addresses the computational bottlenecks as event rates and waveform model complexity escalate (Prathaban et al., 4 Sep 2025).

Nested sampling performed with Blackjax-NS underpins multimessenger astrophysics, allowing rapid production of robust parameter posteriors and evidence calculations with hardware-efficient, validated community-standard methods.

Beyond GW science, the framework’s kernel abstraction and hardware-agnostic API make it suitable for:

• High-dimensional model selection and parameter inference in cosmology.
• Large-scale simulation-based inference tasks.
• Benchmarking and validation of new Bayesian algorithmic developments.

A plausible implication is that the structure of Blackjax-NS, designed for efficient parallel sampling, is naturally extensible to hybrid pipelines that blend deep learning surrogates for the likelihood with traditional MCMC or nested sampling approaches.

7. Impact and Future Prospects

The Blackjax-NS Framework establishes a rigorous, hardware-efficient reference for Bayesian evidence calculations and posterior inference. By isolating speedup due to hardware alone, it enables fair evaluation of true algorithmic advances versus mere architectural acceleration (Prathaban et al., 4 Sep 2025). Its compatibility with machine learning methods further positions it as a foundation for future inference pipelines that combine classical samplers and deep learning methodologies for scale.

As detector capabilities increase and waveform models grow in complexity, frameworks such as Blackjax-NS will be critical to sustaining fast, reliable inference and scientific analysis at scale.