Unbiased and efficient log-likelihood estimation with inverse binomial sampling.

Area of Science:

• Computational biology
• Neuroscience
• Statistical modeling

Background:

• Log-likelihood is crucial for parameter estimation and model evaluation in scientific research.
• Estimating log-likelihood for complex computational models is often intractable, necessitating simulation-based approximations.
• Existing simulation methods can introduce bias or rely on summary statistics, limiting their accuracy.

Purpose of the Study:

• To introduce and evaluate Inverse Binomial Sampling (IBS) as a novel method for estimating log-likelihood.
• To demonstrate IBS's efficiency, unbiasedness, and robustness in complex simulation-based models.
• To assess IBS's performance against standard simulation techniques in computational and cognitive neuroscience.

Main Methods:

• Inverse Binomial Sampling (IBS) estimates log-likelihood by simulating model outputs until an observation is matched.
• The log-likelihood estimate is derived from the number of samples required for a match.
• Theoretical analysis of estimator variance and empirical assessment using maximum-likelihood estimation.

Main Results:

• IBS provides an unbiased log-likelihood estimate with uniformly bounded variance.
• Calibrated variance estimates can be computed for IBS.
• In computational and cognitive neuroscience case studies, IBS yielded lower parameter errors and higher maximum log-likelihood values compared to alternative methods.

Conclusions:

• Inverse Binomial Sampling (IBS) is a practical, robust, and easily implementable method for log-likelihood evaluation.
• IBS offers a significant improvement over existing simulation-based techniques when exact computation is not feasible.
• The method shows strong potential for advancing model fitting in complex scientific domains.