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.Author summary: Many biological studies rely on repeated experiments to capture natural variation and reduce uncertainty. However, replicate measurements often exhibit higher variance than standard models predict due to biological heterogeneity, batch effects, or faulty samples. This discrepancy makes it difficult to draw reliable conclusions or report uncertainty in a principled manner. In this study, we introduce a straightforward method for aggregating evidence across multiple replicates to estimate a single, well-calibrated probability distribution over model parameters. By first inferring the implications of each replicate independently and then combining them using an outlier-robust framework, we ensure that a few problematic samples do not skew the final result. Our approach is broadly applicable to various computational inference methods. We demonstrate its utility using simulated evolutionary data, experimental evolution time series in yeast, and cultural transmission datasets of bird song, providing a robust pathway for reliable inference from high-variability biological data.