有序 Probit 迴歸模型 (ordinal probit model) 常用於當反應變數為有順序性的類別變數時。而我們透過貝氏變數選擇的方式，在有序 Probit 迴歸模型的架構下，選取真正對反應變數有影響力的解釋變數，並篩選掉沒有影響力的解釋變數。針對貝氏變數選擇的方式，具體而言我們會對各解釋變數引入各自的指標變數，用以指示該變數為重要與否。並提出一個馬可夫鍊蒙地卡羅 (MCMC) 演算法來抽樣所有指標變數的後驗分配樣本，用以判斷各解釋變數對於反應變數的影響力。上述的方法我們會套用在模擬資料和實際案例上，觀察變數選擇的成效及分類預測的效果是否符合預期。另外在實際案例中，由於資料有許多兩兩相關係數極高的情形，我們也有嘗試調整指標變數的使用方式，將解釋變數分組，將所提演算法衍生至群選擇 (group selection) 方法。如此一來，對於整組的解釋變數，要不一起保留，要不一起被篩選掉。此方法在特定情況或具有特定先備知識下可以有更好的表現或變數挑選結果。

The Ordinal Probit Regression Model is used when the response variable is an ordinal categorical variable. Under this model assumption, we aim to apply Bayesian Variable Selection to identify the important variables that truly influence the response variable. In the proposed Bayesian Variable Selection method, we introduce an indicator for each variable and develop a corresponding MCMC algorithm to generate posterior samples of these indicators for further inference. The proposed method is applied to both simulated data and real-world data to evaluate whether the variable selection and prediction results meet expectations. In the real-world example, we observe that certain variables show high pairwise correlations, which pose challenges for the analysis. To address this, we extend the proposed selection method to group selection, where variables are grouped based on prior knowledge, and an indicator is assigned to each group. This group selection approach improves performance and provides better results in our real-world case.