The name is absent

55

e Hyperparameters of G₀, 7 : simulate from the complete conditional posterior
distributions

, I * X * X , , I I TΠ₂S₂ + A¾ Lt-1 /ʃfeʌfe . V—' X ɪ
p(m₁ I μ , λ , r) = N mɪ ∣ --------- , S₂ + k₀ ∖ λ_fc ,

∖ S₂ + fc₀ Lfe=I ^λ⅛            fc=l /

(κ ∖
≠1 I η₂ + Kη_l,ψ₂ + ∑λ*_k I ,
fe=l /

and,

/, I *      ∖ r< ( 1 I    ÷ ^c¾ βk₀ ÷ Σ2 ^τk(f^j'k ~ ^ml)²λ

p(k₀ I τ , m₁, r) = Ga I k₀ ∣----—-,------------------ ) .

Finally, we estimate the density of the house prices at a point yf based on the (ap-
proximated) sample of size M from the joint posterior distribution of the parameters:
(μ*^m, λ*^m, φ^m, K^m, a^m, k%^l, mψ, η^m), for m = 1,..., M, via (3.17) by,

₁ M _m                            к™                  j

Λ/ I »”) = ʌʃ Σ ɪʌ'to ɪ Æ,ŋ +     ∑^N(,y, I Λ∙"∙) ,

1 Vl              LΛ         IL                                          Lt         I h                                                I

m=l                                      k=l                   J

where (μ∏+ι,λζ+ι) is a new sample from g_io given in (3.2.4) whose parameters are
specified by the corresponding parameters of the m — th simulated observation:
L,m γ_rim _rim
⅝ î ^rn,l > ^rI ∙

We use the same values for the hyperparameters given in the set of hyperparame-
ters “prior4” in the example in the help of the function “DPdensity” in the R package
“DPpackage”. In the R example, the density of the velocities, relative to our own
galaxy, of 82 galaxies from six well-separated conic sections of the space is estimated.
The values are a_a = 2,b_a = l,m₂ = 0,s₂ = 10^-5,α⅛_o = l,∕⅞₀ = 100,771 = η₂ — 3,
and ψ₂ — 0.5. After a 1000 iteration burn-in period we generated M = 10,000 ob-
servations from the posterior distribution of the parameters by taking an observation
every ten Gibbs iterations. All this using the R function “DPdensity”. The estimated
density is shown in Figure 3.2.

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