The name is absent

53

the file). We apply the DPM model to estimate the distribution of the house prices
(disregarding the rest of the information in the file).

A particular case of model (3.9) is given in Escobar and West (1995), and imple-
mented in the R-package “DPpackage” (Alejandro Jara, 2007):

I. y_i I μ_i,λ_i ~ N(μ_i,λ_i) for i = 1,... ,n,
II. (μι,λ₁), ...,(μ_n,λ_n) ∣G~G
III. G I Q,fc₀,μι,≠ι ~ DP(α,G₀(∙ I ⅛o,μι,≠ι)),
G₀(μ_i,λ_i I k₀,μ₁,ψ₁') = N(μ_i ∣ m₁, k₀λ_i) Ga(λ ∣ r∕ι,≠ι)
IV. a ~ Ga(a_a,b_ct'),mι ~ N(m2,s2β
ψι ~ Ga(η₂,ψ₂) and k₀ ~ Gα(α⅛₀∕2, ⅛₀∕2),
where N(m,τ) denotes the normal distribution with mean m and precision τ, and
Ga(a,β') the gamma distribution with mean a∣β∖ ηι,a_a,b_a, s₂,η2,ψ2, dk,bk > 0 and
m₂ ∈ JL

Notice that the variables y_i,(μ_i,λi) and (m₁,⅛,ψι) of the model in (3.25) play
the role of the variables xt,θi and 7, respectively, in the general DPM (3.9). Let
У^{п =} {⅛∙∙∙ >y∏} represent the prices of n — 506 houses. Besides, we denote with
μ* = (μ*₁,...,μ*_κ) and λ* = (ʌɪ,..., AJ_f) the vectors of size K containing the unique
values of the μ_i and the λ_i respectively. We use the notation of the previous section
for the variables related with the configurations. When stating a complete conditional
posterior distribution in this section, we make explicit only the relevant quantities
(for example, since the complete conditional posterior distribution of k₀ depends only
on m₁,μ* and A*, we just write k₀ ∣ m₁,μ*, λ*).

We now describe steps (a)-(e) of the MCMC sampling scheme given in the previous
section for this specific example. There is no common parameter σ so that step (c)
is not necessary. Let t(y ∣ m, s, v) denote a student t distribution with location m,
scale s and degrees of freedom υ.

(a) Given the currently imputed values of (μ*, λ*), K and φ, generate a new config-
uration by simulating φ_i,..., φ_n from the complete conditional posterior distri-

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