  Recognizing the potential of effective field theories to posit multiple BSM
scenarios in similar footing, with a possibility to compare them, we inspect
the effects of 11 single scalar-multiplet extensions of the SM on the combined
set of electroweak precision observables and Higgs signal strength data, by
systematically integrating out the heavy multiplets and computing the resulting
SMEFT operators and Wilson coefficients (WCs) up to one-loop level. Noting that
multiple BSM models give rise to a degenerate set of WCs, we then perform
Bayesian statistical inference both directly on the BSM parameters and on the
associated set of independent WCs. Using the posteriors of the BSM parameters,
we infer the respective (correlated) WC-distributions and compare both the
model-independent and dependent analyses by overlaying the 2-D marginal
WC-posteriors from both processes, thus laying the ground for a data-driven
attempt to compare diverse BSM theories of different origins, and hopefully, a
possible way to approach the intractable inverse problem. We also demonstrate,
with an example model, the crucial role of theoretical constraints to rule out
large chunks of BSM parameter spaces. The entirety of numerical results is
available in GitHub.
