Incorporating local step-size adaptivity into the no-U-turn sampler using Gibbs self-tuning

Area of Science:

• Computational Statistics
• Bayesian Inference
• Markov Chain Monte Carlo Methods

Background:

• Adapting step size in No-U-Turn Sampler (NUTS) is complex due to interdependent tuning parameters.
• Optimal path length determination requires a fixed step size, while ideal step size depends on path errors.
• Ensuring sampler reversibility adds further complexity to the tuning process.

Purpose of the Study:

• To develop a novel method for local step-size adaptation within the NUTS algorithm.
• To ensure the reversibility of the NUTS sampler during adaptation.
• To improve the efficiency and reliability of Bayesian inference using NUTS.

Main Methods:

• Proposed a step-size adaptation method as an instance of the Gibbs self-tuning (GIST) framework.
• Developed an approach that guarantees sampler reversibility.
• Acceptance probability is solely dependent on the conditional distribution of the step size.

Main Results:

• The proposed method effectively adapts the step size locally in NUTS.
• Reversibility is guaranteed throughout the adaptation process.
• The method demonstrated effectiveness on challenging distributions like Neal's funnel and high-dimensional normal distributions.

Conclusions:

• The novel GIST-based NUTS adaptation method successfully addresses the challenges of interdependent tuning parameters.
• This approach ensures reversibility and improves sampling performance in complex scenarios.
• The method offers a more robust and efficient tool for Bayesian computation.