Optimizing threshold-schedules for sequential approximate Bayesian computation: applications to molecular systems.

Area of Science:

• Computational Biology
• Statistical Inference
• Machine Learning

Background:

• Likelihood-free Approximate Bayesian Computation (ABC) algorithms are vital for complex biological models.
• These methods construct sequential probability distributions using decreasing thresholds (ε) around observed data.
• The choice of threshold sequence significantly impacts computational efficiency and accuracy.

Purpose of the Study:

• To address the challenge of threshold selection in sequential ABC algorithms.
• To propose a novel method for determining threshold schedules that improve posterior inference.
• To enhance the computational efficiency and success rate of ABC applications.

Main Methods:

• We demonstrate that the common quantile-based threshold selection can lead to inaccurate posterior distributions.
• We propose using the threshold-acceptance rate curve to guide threshold schedule selection.
• An algorithm utilizing the unscented transform is developed for efficient prediction of this curve.

Main Results:

• The proposed threshold-acceptance rate curve method helps avoid local optima in parameter inference.
• This approach balances minimizing the threshold with maintaining computational efficiency.
• The unscented transform-based algorithm efficiently predicts the threshold-acceptance rate curve for state space models.

Conclusions:

• Threshold selection is a critical challenge in Approximate Bayesian Computation.
• The threshold-acceptance rate curve offers a robust strategy for optimizing ABC performance.
• The developed algorithm provides an efficient tool for implementing this improved threshold selection.