Automated Factor Slice Sampling.

Area of Science:

• Statistics
• Computational Statistics
• Machine Learning

Background:

• Markov chain Monte Carlo (MCMC) methods are versatile for sampling complex probability distributions.
• Designing efficient MCMC samplers, especially for high-dimensional problems with variable dependencies, is challenging and time-consuming.
• Current MCMC approaches often require manual tuning, limiting their general applicability and efficiency.

Purpose of the Study:

• To develop an automated and efficient Markov chain Monte Carlo (MCMC) algorithm.
• To introduce the factor slice sampler, a novel generalization of the univariate slice sampler.
• To create a robust tuning approach for MCMC algorithms, applicable to both standard and factor slice samplers.

Main Methods:

• Proposed the "factor slice sampler," which generalizes the univariate slice sampler by incorporating the selection of a coordinate basis (factors) as a tunable parameter.
• Developed an automated approach for selecting tuning parameters to construct efficient factor slice samplers.
• Applied the automated tuning strategy to standard univariate slice samplers as well.

Main Results:

• Demonstrated the efficiency and broad applicability of the automated MCMC algorithm through various examples.
• The factor slice sampler and automated tuning approach significantly reduce the effort required for MCMC algorithm design.
• The proposed methods are effective even for multivariate distributions with strong variable dependencies.

Conclusions:

• The automated factor slice sampler provides a general and efficient solution for sampling complex distributions.
• This approach streamlines MCMC algorithm development, making it more accessible and less labor-intensive.
• The automated tuning strategy enhances the performance of both novel and existing MCMC samplers.