telescopes with varying sensitivities and fields of view carry important information about that the nature of FRB source counts. Motivated by this, we will now derive the posterior probability distribution for the source-count parameter $\alpha$.

[llllllllll]{}\
Name & $d$ \[m\] & $T_{\rm sys}$ \[K\] & $\eta_{\rm eff}$ & $\Delta\nu$ \[MHz\] & $\tau_{\rm ds} [ms]$ & $N_{\rm ant}$ & $N_{\rm day}$ & $\zeta$ & Reference\
\
ATA & 6.0 & 92 & 0.6 & 210 & 3.9 & 1.0 & 16.475 & 5.5 & @siemion2012\
ARC & 220.0 & 50 & 0.6 & 322.6 & 0.8 & 1.0 & 82.6 & 7.0 & @spitler2014\
VLA & 25.0 & 50 & 0.6 & 256 & 2.4 & 27 & 6.917 & 7.5 & @law2015\
AS1 & 0.1 & 850 & 1.0 & 590 & 2.7 & 1 & 285 & 6.0 & @saint2014\
AS2 & 1.2 & 850 & 1.0 & 590 & 2.7 & 1 & 591.7 & 6.0 & @saint2014\

\[tab:survey\_params\]

Although the Parkes constraint on $\alpha$ was independent of the normalization of the source counts, this is not the case here. We assume the following integral source-counts in this section [@law2015]: $$\label{eqn:eventrate}
\mathcal{N}(>{\mathcal{F}_{\rm obs}}) = \frac{1.2\times 10^4}{4\pi}\left(\frac{{\mathcal{F}_{\rm obs}}}{1.8\textrm{~Jy~ms}}\right)^{-\alpha}\textrm{sr$^{-1}$day$^{-1}$},$$ and 