  We perform a Bayesian statistical analysis of the constraints on the
nonlinear Effective Theory given by the Higgs electroweak chiral Lagrangian. We
obtain bounds on the effective coefficients entering in Higgs observables at
the leading order, using all available Higgs-boson signal strengths from the
LHC runs 1 and 2. Using a prior dependence study of the solutions, we discuss
the results within the context of natural-sized Wilson coefficients. We further
study the expected sensitivities to the different Wilson coefficients at
various possible future colliders. Finally, we interpret our results in terms
of some minimal composite Higgs models.
