An automatic adaptive method to combine summary statistics in approximate Bayesian computation.

Area of Science:

• Computational Biology
• Statistical Inference
• Systems Biology

Background:

• Approximate Bayesian computation (ABC) is vital for parameter inference in models with intractable likelihoods.
• High-dimensional data, common in biological imaging, poses challenges for traditional ABC methods relying on summary statistics.
• Selecting informative summary statistics and their weighting is crucial but often unclear in ABC.

Purpose of the Study:

• To develop an automatic, adaptive algorithm for weighting summary statistics in approximate Bayesian computation (ABC).
• To enhance parameter inference accuracy for mechanistic models, especially those with high-dimensional data.
• To optimize the ABC distance function by adapting summary statistic weights.

Main Methods:

• An automatic, adaptive algorithm was developed to dynamically assign weights to summary statistics.
• The algorithm maximizes the distance between prior and approximate posterior distributions.
• A nearest neighbour estimator was employed for computational efficiency in estimating distribution distances.

Main Results:

• The proposed adaptive weighting algorithm demonstrated effectiveness across various test problems.
• Applied to stochastic biochemical reaction networks and spatial diffusion models.
• Outperformed existing algorithms in parameter inference tasks.

Conclusions:

• The adaptive weighting algorithm offers a robust solution for improving ABC in complex, high-dimensional scenarios.
• This method enhances the utility of ABC for analyzing biological imaging and other data-intensive experiments.
• Provides a theoretically justified and computationally efficient approach to summary statistic selection in ABC.