  We study the impact that uncertainties on assumed relations between galaxy
bias parameters have on constraints of the local PNG $f_{\rm NL}$ parameter. We
focus on the relation between the linear density galaxy bias $b_1$ and local
PNG bias $b_\phi$ in an idealized forecast setup with multitracer galaxy power
spectrum and bispectrum data. We consider two parametrizations of galaxy bias:
1) one inspired by the universality relation where $b_\phi = 2\delta_c\left(b_1
- p\right)$ and $p$ is a free parameter; and 2) another in which the product of
bias parameters and $f_{\rm NL}$, like $f_{\rm NL} b_\phi$, is directly fitted
for. The constraints on the $f_{\rm NL}-p$ plane are markedly bimodal, and both
the central value and width of marginalized constraints on $f_{\rm NL}$ depend
sensitively on the priors on $p$. Assuming fixed $p=1$ in the constraints with
a fiducial value of $p=0.55$ can bias the inferred $f_{\rm NL}$ by $0.5\sigma$
to $1\sigma$; priors $\Delta p \approx 0.5$ around this fiducial value are
however sufficient in our setup to return unbiased constraints. In power
spectrum analyses, parametrization 2, that makes no assumptions on $b_\phi$,
can distinguish $f_{\rm NL} \neq 0$ with the same significance as
parametrization 1 assuming perfect knowledge of $b_\phi$ (the value of $f_{\rm
NL}$ is however left unknown). A drawback of parametrization 2 is that the
addition of the bispectrum information is not as beneficial as in
parametrization 1. Our results motivate strongly the incorporation of
mitigation strategies for bias uncertainties in PNG constraint analyses, as
well as further theoretical studies on the relations between bias parameters to
better inform those strategies.
