  We present a framework for carrying out global analyses of the Standard Model
Effective Field Theory: SMEFiT. This approach is based on the Monte Carlo
replica method, widely used in the case of NNPDF fits of the proton structure,
for deriving a faithful estimate of the experimental and theoretical
uncertainties. As a proof of concept of the SMEFiT methodology, we present a
study of the constraints on the SMEFT provided by top quark production
measurements from the LHC. We derive bounds for the 34 degrees of freedom
relevant for the interpretation of the LHC top quark data and compare these
bounds with previously reported constraints.
