Bayesian optimization for computationally extensive probability distributions.

Area of Science:

• Computational Statistics
• Machine Learning
• Applied Mathematics

Background:

• Finding maximizers of computationally intensive probability distributions is challenging.
• Existing methods like random search, steepest descent, and Monte Carlo can be inefficient.
• Accurate estimation of probability distribution maximizers is crucial in various scientific and engineering fields.

Purpose of the Study:

• To propose an efficient Bayesian optimization method for identifying superior maximizers of computationally extensive probability distributions.
• To leverage extreme values of acquisition functions from Gaussian processes for targeted exploration.
• To demonstrate the method's effectiveness in the context of posterior distribution analysis for effective physical model estimation.

Main Methods:

• Development of a Bayesian optimization technique utilizing extreme values of Gaussian process acquisition functions.
• Application of the proposed method to analyze posterior distributions in effective physical model estimation.
• Comparison of the Bayesian optimization approach against random search, steepest descent, and Monte Carlo methods.

Main Results:

• The Bayesian optimization method identifies better maximizers of posterior distributions, even with a limited number of sampling points.
• It demonstrates superior performance compared to random search, steepest descent, and Monte Carlo methods.
• The technique efficiently refines results by integrating the steepest descent method.

Conclusions:

• The proposed Bayesian optimization technique is a powerful tool for finding better maximizers of computationally extensive probability distributions.
• It offers an efficient and effective alternative to conventional optimization and search strategies.
• The method shows significant promise for applications requiring precise estimation of probability distribution peaks.