The name is absent

64

• φ = (y>₁,..., φ_n) is the vector of indicator variables indexing the value of
(β↑,δ↑),..., (βκ,δ*_κ) related with (βi,δ_i) for г = l,...,n. Thatis, φ_i = к,
if (∕¾Λ) = G¾*Λ)∙

This configuration determines the following set of variables:

• S_k := {i : ψi — k} is the set of sample indices of (βi,δβ related to (∕0⅛,5⅛) for
k = 1,...,M.

• n_k := #S_k.

We will denote as K~^l, nβ'^t and Sβ^τ for к — 1,..., К~^г, (β*,δ*)~^t = (^ɪ, <5j^,)^-∖ ...,
to the configuration corresponding to (β,δ')~^l (βι,δι),..., (β_i-_l,δ_i+β),
(∕¾₊₁,⅝₊ι),... ,(∕3_n, δ_n). We now describe the corresponding steps (a)-(e) of Section
3.2 and extra step (f) for the proposed model.

(a) Given the current imputed values (K, (β*, δ*), φ), generate a new configuration
by simulating φ_l,..., φ_n from the complete conditional posterior distribution,

P{φ_i = k∖N_i, (β, δ)-ⁱ, φ~ⁱ, K~ⁱ) = ¾_fc, for к = 0,..., K~^l
where,

{sβββⁱ Γ(,s⅛ + M₃ )
{μ_i + s₆t₀)^ss+N_i3 r(ʤ) ]’

q_ik = cn~_kⁱβ*_k ^m2δ*_k ^Ni3e_Xp{-^_k + δ*_k)}, for j = 1,..., K~ⁱ,
and c is a normalization constant such that ¾o ÷ ■ ∙ ∙ ÷      — 1. Whenever we

sample φ_i = 0, we generate a new observation (β_i, δ_i) from

G^fα(∕¾∣s_j3 + Ni2,Sβtβ ÷ μβ × Ga(¾∣s⅛ + Ni2, sβs + μ_i),

and update, accordingly, the new configuration by K — K + 1 and φ_i = n + 1.

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