  The determination of the fundamental parameters of the Standard Model (and
its extensions) is often limited by the presence of statistical and theoretical
uncertainties. We present several models for the latter uncertainties (random,
nuisance, external) in the frequentist framework, and we derive the
corresponding $p$-values. In the case of the nuisance approach where
theoretical uncertainties are modeled as biases, we highlight the important,
but arbitrary, issue of the range of variation chosen for the bias parameters.
We introduce the concept of adaptive $p$-value, which is obtained by adjusting
the range of variation for the bias according to the significance considered,
and which allows us to tackle metrology and exclusion tests with a single and
well-defined unified tool, which exhibits interesting frequentist properties.
We discuss how the determination of fundamental parameters is impacted by the
model chosen for theoretical uncertainties, illustrating several issues with
examples from quark flavour physics.
