  The Full Bayesian Significance Test (FBST) possesses many desirable aspects,
such as not requiring a non-zero prior probability for hypotheses while also
producing a measure of evidence for $H_0$. Still, few attempts have been made
to bring the FBST to nonparametric settings, with the main drawback being the
need to obtain the highest posterior density (HPD) in a function space. In this
work, we use Gaussian processes to provide an analytically tractable FBST for
hypotheses of the type $$ H_0: g(\boldsymbol{x}) =
\boldsymbol{b}(\boldsymbol{x})\boldsymbol{\beta}, \quad \forall \boldsymbol{x}
\in \mathcal{X}, \quad \boldsymbol{\beta} \in \mathbb{R}^k, $$ where $g(\cdot)$
is the regression function, $\boldsymbol{b}(\cdot)$ is a vector of linearly
independent linear functions -- such as $\boldsymbol{b}(\boldsymbol{x}) =
\boldsymbol{x}'$ -- and $\mathcal{X}$ is the covariates' domain. We also make
use of pragmatic hypotheses to verify if the adherence of linear models may be
approximately instead of exactly true, allowing for the inclusion of valuable
information such as measurement errors and utility judgments. This contribution
extends the theory of the FBST, allowing its application in nonparametric
settings and providing a procedure that easily tests if linear models are
adequate for the data and that can automatically perform variable selection.
