  We introduce a novel rule-based approach for handling regression problems.
The new methodology carries elements from two frameworks: (i) it provides
information about the uncertainty of the parameters of interest using Bayesian
inference, and (ii) it allows the incorporation of expert knowledge through
rule-based systems. The blending of those two different frameworks can be
particularly beneficial for various domains (e.g. engineering), where, even
though the significance of uncertainty quantification motivates a Bayesian
approach, there is no simple way to incorporate researcher intuition into the
model. We validate our models by applying them to synthetic applications: a
simple linear regression problem and two more complex structures based on
partial differential equations. Finally, we review the advantages of our
methodology, which include the simplicity of the implementation, the
uncertainty reduction due to the added information and, in some occasions, the
derivation of better point predictions, and we address limitations, mainly from
the computational complexity perspective, such as the difficulty in choosing an
appropriate algorithm and the added computational burden.
