Estimates and Standard Errors for Ratios of Normalizing Constants from Multiple Markov Chains via Regeneration

Area of Science:

• Statistics
• Computational Statistics

Background:

• The biased sampling problem involves estimating ratios of unknown normalizing constants for probability densities.
• Existing methods for estimating these ratios lack rigorous standard error estimation, particularly for non-i.i.d. data.

Purpose of the Study:

• To develop and validate methods for estimating ratios of normalizing constants.
• To provide rigorous standard error estimation for these ratios, extending beyond independent and identically distributed (i.i.d.) data.

Main Methods:

• Developed a class of estimates for ratios of normalizing constants applicable to Markov chain samples.
• Employed regenerative simulation to derive standard errors for the ratio estimates.

Main Results:

• The proposed estimates are suitable for both i.i.d. and Markov chain sampling scenarios.
• Regenerative simulation provides valid standard error estimates for the ratios of normalizing constants.

Conclusions:

• The study addresses a critical gap in statistical inference by enabling robust standard error estimation for ratios of normalizing constants.
• The developed methods offer a unified approach for both i.i.d. and Markov chain data, enhancing the reliability of statistical estimates.