content_image/310357.jpg content_image/310359.jpg content_image/310366.jpg content_image/310365.jpg
<img src='content_image/310357.jpg'>

which is recognized as the kernel of a generalized inverse-Gaussian (GIG) distribution where, 

Hence, ν$_{i}$ | z, β, h, σ, γ ∼ GIG (0 . 5 , a$_{i}$, b ) for i = 1 , 2 , . . . , n . 

<img src='content_image/310359.jpg'>

(4) The conditional posterior of h is obtained element-wise from the complete posterior density (15) conditional on γ and remaining parameters as follows: 

<img src='content_image/310366.jpg'>

where the third line introduces the following notations: 

<img src='content_image/310365.jpg'>

and the fourth line adds and subtracts ( σ 2 $_{h$_{i}$}$) − $^{1}$µ2 h$_{i}$ to complete the square. The last expres- sion is recognized as the kernel of a half-normal distribution and hence, h$_{i}$ | z, β, ν, σ, γ ∼ N $^{+}$( µ$_{h}$$_{i}$, σ 2 $_{h$_{i}$}$) for i = 1 , 2 , . . . , n . 

(5) Similar to Jeliazkov et al. (2008) and Rahman (2016), the transformed cut-point δ is sampled from the full likelihood (9), marginally of ( z, ν, h ). The proposed values are generated from a random-walk chain, δ ′ = δ$_{c}$ + u , where u ∼ N (0$_{J}$$_{−}$$_{3}$ , ι 2 ˆ D$_{2}$ ), ι$_{2}$ is a tuning pa- 

