Our predictions for particle physics processes are realized in a chain of complex simulators. They allow us to generate high-fidelity simulated data, but they are not well-suited for inference on the theory parameters with observed data. We explain why the likelihood function of high-dimensional LHC data cannot be explicitly evaluated, why this matters for data analysis, and reframe what the field has traditionally done to circumvent this problem. We then review new simulation-based inference methods that let us directly analyze high-dimensional data by combining machine learning techniques and information from the simulator. Initial studies indicate that these techniques have the potential to substantially improve the precision of LHC measurements. Finally, we discuss probabilistic programming, an emerging paradigm that lets us extend inference to the latent process of the simulator.
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