Bayesian Model Initial Parameters

Estimation bayesian
1

How does Pumas calculate initial parameter of the omegas in a Bayesian model for Inverse Gamma distribution ?

For e.g. if I define an omega like this: ω²SCR0 ~ InverseGamma(10/2, 0.145*(10 + 1 + 1)/2) and run init_params(model) I see ω²SCR0 = 0.18625925314116212. I want to know where the 0.186… number is coming from?
Also, is there some underlying meaning in writing 10/2 as opposed to 5, or (10+1+1)/2 instead of 6 in the specification of the distribution ?

2

My view is that if you do an init_params in a Bayesian model it will sample prom the prior.

julia> using Distributions

julia> ω²SCR0 = InverseGamma(10/2, 0.145*(10 + 1 + 1)/2)
InverseGamma{Float64}(
invd: Gamma{Float64}(α=5.0, θ=1.149425287356322)
θ: 0.8699999999999999
)


julia> rand(ω²SCR0)
0.2632303021306265

julia> rand(ω²SCR0)
0.5991101635236422

julia> rand(ω²SCR0)
0.270555800869863

julia> rand(ω²SCR0)
0.11468427269228272

julia> rand(ω²SCR0)
0.09238162211517542

julia> rand(ω²SCR0)
0.29396951024526896
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3

It’s actually the median.

julia> median(InverseGamma(10/2, 0.145*(10 + 1 + 1)/2))
0.18625925314116207
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