The name is absent

P(φ_i = k∖y_i, μ*-ⁱ,λ*-ⁱ, φ-ⁱ, K~ⁱ) = q_ik, for к = 0,.. ., K~ⁱ

where,

q_i0 = со. Student ( y_i ∣ m₁, ~ ^k° , 2η₁ ) ,
∖ ψ₁ k₀ +1    /

q_ik = cn_kⁱN(y_i I μ*_k, λ*_k} for к = 1,..., K~ⁱ,

and c is a normalization constant such that qo ÷ ∙ ■ ∙ + qχ-< — 1. Whenever we
sample φ_i = 0, we generate a new observation (μ*, λ*) from

<_7i0(∕Aλ*)= τv(_μ*∣⅞⅛i,(fc_o + l)λ*)

× Ga (λ* ∣ τ∕₁+ n√2,≠₁ +        - mɪ)²)

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

(b) Given K and φ, generate a new set of parameters (μ_k, λ⅛) for к = 1,..., K from
the distribution

P(A^t⅛>^λfcl yⁿ,φ,K,k₀,ψ_l) =

∕v(> I ¾^,C⅛ + ¾μ*)

× ^Ga (^λfc I ⁷?! + «fe/2, ≠ι + i [∑_ιe,¾(y_i - г/t)² +

where y_k is the mean of the observations in S_k, that is y_k = ∑_ies_k yι∣ⁿk-
(d) Updating the total mass parameter a:

1. Let a denote the currently imputed parameter value. Generate a latent
random variable η ~Beta(α + 1, n).

2. Sample the new value of a from

ρ(a I K, η) =π_ηGa(a ∖ a_a + K, b_a — log η')

+(1 - π^)Gα(α ∣ a_a + K - 1, b_a - log 77),

where,
7Γ7y aɑ I ʃf 1

1 - ⅞ n(b_a - log η) '

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