Nonparametric Bayes Factors Based On Empirical Likelihood Ratios

Area of Science:

• Statistical Methodology
• Nonparametric Statistics
• Bayesian Inference

Background:

• Bayes methodology relies on parametric likelihoods and prior distributions.
• Empirical Likelihood (EL) offers a distribution-free alternative for statistical hypothesis testing.
• EL shares desirable properties with conventional parametric likelihoods.

Purpose of the Study:

• To propose and examine Bayes factors (BF) derived using the empirical likelihood (EL) ratio approach.
• To adapt EL techniques for hypothesis testing and confidence interval estimation.
• To evaluate the performance of the proposed EL-based BF method.

Main Methods:

• Development of Bayes factors (BF) using the empirical likelihood (EL) ratio.
• Application of EL-based BF for hypothesis testing, drawing parallels with Kass & Wasserman.
• Utilizing Monte Carlo simulations to assess theoretical results and test power.

Main Results:

• The proposed empirical likelihood Bayes factor (EL-BF) method exhibits asymptotic properties comparable to classical Bayes factors.
• The EL-BF approach provides a distribution-free alternative for statistical inference.
• Simulations demonstrated the effectiveness and power of the proposed testing procedure.

Conclusions:

• The empirical likelihood (EL) ratio provides a robust foundation for developing Bayes factors (BF).
• The proposed EL-based BF method is a viable distribution-free alternative for hypothesis testing.
• This approach extends to the construction of confidence interval estimators for unknown parameters.