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In this colloquium, I will review recent developments in simulation based inference that move the experimental analyses closer to the routine application of novel inference methods that are statistically optimal even in the presence of systematic uncertainties. I will discuss how the underlying modeling challenge can be met by an incrementally refinable approach that allows to improve the description of the data using all the knowledge that's already available in the field and in smalls steps, without invalidating partial results. Recent results by ATLAS and projections for new measurements of the proton structure will be the illustrative examples.