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We show that density models describing multiple observables with (i) hardboundaries and (ii) dependence on external parameters may be created using anauto-regressive Gaussian mixture model. The model is designed to capture howobservable spectra are deformed by hypothesis variations, and is made moreexpressive by projecting data onto a configurable latent space. It may be usedas a statistical model for scientific discovery in interpreting experimentalobservations, for example when constraining the parameters of a physical modelor tuning simulation parameters according to calibration data. The model mayalso be sampled for use within a Monte Carlo simulation chain, or used toestimate likelihood ratios for event classification. The method is demonstratedon simulated high-energy particle physics data considering the anomalouselectroweak production of a $Z$ boson in association with a dijet system at theLarge Hadron Collider, and the accuracy of inference is tested using arealistic toy example. The developed methods are domain agnostic; they may beused within any field to perform simulation or inference where a datasetconsisting of many real-valued observables has conditional dependence onexternal parameters.

Learning to discover: expressive Gaussian mixture models for multi-dimensional simulation and parameter inference in the physical sciences