From: Modeling gene expression measurement error: a quasi-likelihood approach
observed scale y
normal scale x
μ = (/2sinh(u) - a)/b
σ2 = - 1
s2 = log(1 + σ2)
E(y)= μ
E(x) = u
var(y) = (μ - β)2σ2 + ρ2
var(x) = s2
y = asinh(a + by)
x ~ N(u, s2)