Collective posterior inference from highly variable empirical replicates

High-throughput experimental platforms now routinely generate data from dozens or hundreds of independent observations. Simulation-based inference (SBI) offers a powerful framework for estimating model parameters from such complex datasets, but standard methods struggle to scale to the noisy multiple-replicates regime without incurring prohibitive computational costs or careful hyperparameter tuning. Here, we introduce a new method for fast and robust collective posterior inference from multiple independent replicates using a robust product-of-experts aggregation scheme that automatically mitigates the influence of outliers. Evaluating it on synthetic and empirical evolutionary datasets, we find it achieves state-of-the-art estimation accuracy and computational efficiency, including inference from noisy observations. Our method is compatible with any SBI framework, providing a scalable, plug-and-play solution for inference from noisy multiple-replicate datasets.