We discuss how to efficiently and reliably estimate the level of agreement and disagreement on parameter determinations from different experiments, fully taking into account non-Gaussianities in the parameter posteriors. We develop two families of scalable algorithms that allow us to perform this type of calculations in increasing number of dimensions and for different levels of tensions. One family of algorithms rely on kernel density estimates of posterior distributions while the other relies on machine learning modeling of the posterior distribution with normalizing flows. We showcase their effectiveness and accuracy with a set of benchmark examples and find both methods agree with each other and the true tension within $0.5��$ in difficult cases and generally to $0.2��$ or better. This allows us to study the level of internal agreement between different measurements of the clustering of cosmological structures from the Dark Energy Survey and their agreement with measurements of the Cosmic Microwave Background from the Planck satellite.

Code available at https://github.com/mraveri/tensiometer with a documented notebook at https://tensiometer.readthedocs.io/en/latest/non_gaussian_tension.html . Minor modifications wrt v1, including a new pedagogical example. Matches version accepted in PRD