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Table A.1.

Priors adopted on the hyperparameters used in our analyses.

Hyperparameter Prior
log(ℛref·Gpc3 yr) U $ {\cal {{U}}} $(-2, 1)
α N ( 2 , 3 ) $ {\cal {{N}}}(-2, 3) $
log(fp) U $ {\cal {{U}}} $(-6, 0)
βq N $ {\cal {{N}}} $(0, 3)
αz N $ {\cal {{N}}} $(0, 4)
β U $ {\cal {{U}}} $(0, 10)
zp U $ {\cal {{U}}} $(0.2, 4)
Mmin U ( 5 M , 15 M ) $ {\cal {{U}}}(5\,M_\odot , 15\,M_\odot ) $
Mmax U ( 50 M , 100 M ) $ {\cal {{U}}}(50\,M_\odot , 100\,M_\odot ) $
μm U ( 15 M , 60 M ) $ {\cal {{U}}}(15\,M_\odot , 60\,M_\odot ) $
σm U ( 1.5 M , 15 M ) $ {\cal {{U}}}(1.5\,M_\odot , 15\,M_\odot ) $
log(δmmin/ M) U ( 1 , 0.5 ) $ {\cal {{U}}}(-1, 0.5) $
log(δmmax/ M) U ( 0.5 , 1.5 ) $ {\cal {{U}}}(0.5, 1.5) $

Λhigh & Λlow Identical prior to p(Λ) above
log(ΔzΛ) U $ {\cal {{U}}} $(-1, 1)
z ¯ Λ $ \bar z_{\Lambda } $ U ( 0 , 0.8 ) $ {\cal {{U}}}(0, 0.8) $
log(ΔmΛ/M) U $ {\cal {{U}}} $(-1, 3)
m ¯ Λ $ \bar m_{\Lambda } $ U ( 20 M , 75 M ) $ {\cal {{U}}}(20\,M_\odot , 75\,M_\odot ) $

Notes: U ( a , b ) $ {\cal {{U}}}(a,b) $ indicates a uniform prior normalized between a and b, and N ( a , b ) $ {\cal {{N}}}(a,b) $ a Gaussian prior with mean a and standard deviation b. When varying a given hyperparameter as a function of mass or redshift, priors on the asymptotic values are identical to the priors listed in the upper portion of the table. When varying the mean of the Gaussian peak in the black hole mass spectrum, for example, we adopt p ( μ m , low ) = p ( μ m , high ) = p ( μ m ) = U ( 15 M , 60 M ) $ p(\mu _{m,{\textrm {low}}}) = p(\mu _{m,{\textrm {high}}}) = p(\mu _m) = {\cal {{U}}}(15\,M_\odot ,60\,M_\odot ) $.

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