  We present the first application of a variance-based sensitivity analysis
(SA) to a model that aims to predict the evolution and properties of the whole
galaxy population. SA is a well-established technique in other quantitative
sciences, but is a relatively novel tool for the evaluation of astrophysical
models. We perform a multi-parameter exploration of the GALFORM semi-analytic
galaxy formation model, to compute how sensitive the present-day K-band
luminosity function is to varying different model parameters. The parameter
space is scanned using a low-discrepancy sampling technique proposed by
Saltelli. We first demonstrate the usefulness of the SA approach by varying
just two model parameters, one which controls supernova feedback and the other
the heating of gas by AGN. The SA analysis matches our physical intuition
regarding how these parameters affect the predictions for different parts of
the galaxy luminosity function. We then use SA to compute Sobol' sensitivity
indices varying seven model parameters, connecting the variance in the model
output to the variance in the input parameters. The sensitivity is computed in
luminosity bins, allowing us to probe the origin of the model predictions in
detail. We discover that the SA correctly identifies the least- and most
important parameters. Moreover, the SA also captures the combined responses of
varying multiple parameters at the same time. Our study marks a much needed
step away from the traditional "one-at-a-time" parameter variation often used
in this area and improves the transparency of multi-parameter models of galaxy
formation.
