Parkes detections is: $$\begin{aligned}
\mathcal{P}(\textrm{parkes 16} | \alpha) &=& {16 \choose 8}\mathcal{P}^8_{\rm i}(1) \times {8 \choose 4}\mathcal{P}^4_{\rm o}(1)\nonumber \\
&& \times {4 \choose 2}\mathcal{P}^2_{\rm c}(1) \times \mathcal{P}_{\rm i}(4)\nonumber \\
&& \times \mathcal{P}_{\rm i}(2)\end{aligned}$$ where a dependence on $\alpha$ of all the probabilities on the right hand side is implicitly assumed for brevity, and the subscripts denote the position of the principal beam. We now assume that FRBs are all far-field events, i.e., they originate from $n_{\rm f}\lesssim 0.25$ or equivalently from distances $d\gtrsim 20$ km. The posterior probability distribution of the 16 Parkes detections for various values of $\alpha$ as $$\mathcal{P}(\alpha | \textrm{Parkes 16}) = \frac{\mathcal{P}(\textrm{Parkes 16} | \alpha) \mathcal{P}(\alpha)}{\mathcal{P}(\textrm{Parkes 16})}$$ Being agnostic about the FRB progenitors, we choose a flat prior on $\alpha$ in the (unconstraining) range $0.2<\alpha\leq1.8$, and by restricting ourselves to only models with variations on $\alpha$, we can evaluate the evidence in the denominator as $$\mathcal{P}(\textrm{Parkes 16}) = \sum_i \mathcal{P}(\textrm{Parkes 16} | \alpha_i)\mathcal{P}(\alpha_i).$$ Fig. \[fig:alpha\_modsel\] shows the posterior probability of $\alpha$ given the 16 Parkes detections. Very low and very high values of $\alpha$ are disfavored by the relative paucity and abundance respectively of multiple-beam detections. The 90% confidence bound on $\alpha$ is given by $0.52<\alpha 