. 2021 Oct 12;10:e69324. doi: 10.7554/eLife.69324

Table 1. Summary of the non-identifiability results.

in lines 1, 3, and 5 are our contributions, while the remaining representations (lines 2 and 4) are known and can be obtained as special cases of our results. Note that here we use $T e l e (λ, μ, K)$ to denote a Telegraph distribution with parameters $λ, μ, K$ . In lines 3 and 4, the parameter $β > 0$ can be chosen freely and determines the mean burst intensity in the resulting compound system. In line 5, the parameters $b, θ > 0$ are again mean burst intensities, and $b$ can be chosen freely in the determination of the distribution of θ.

Copy no. distribution $\tilde{q} (n; η)$	Underlying distribution $\tilde{p} (n; θ)$	Noise distribution $f (θ; η)$
$T e l e (λ, μ^{'}, K^{'})$	$T e l e (λ, μ, K)$	$K \sim {B e t a}_{K^{'}} (λ + μ, μ^{'} - μ)$
$T e l e (λ, μ^{'}, K^{'})$	$P o i s (K)$	$K \sim {B e t a}_{K^{'}} (λ, μ^{'})$
$N e g B i n (λ, \frac{β}{β + 1})$	$T e l e (λ, μ, K)$	$K \sim G a m m a (λ + μ, β)$
$N e g B i n (λ, \frac{β}{β + 1})$	$P o i s (K)$	$K \sim G a m m a (λ, β)$
$N e g B i n (λ^{'}, \frac{b}{b + 1})$	$N e g B i n (λ, \frac{θ}{θ + 1})$	$θ \sim {B e t a P r i m e}_{b} (λ - λ^{'}, λ^{'})$