Variable Selection Using aModified Gibbs Sampler Algorithm with Application on Rock Strength Dataset

اختيار المتغيرات مهمة ضرورية ومطلوبة في مجال النمذجة الإحصائية. حاولت العديد من الدراسات تطوير وتوحيد طرق اختيار المتغيرات، ولكن من الصعب القيام بذلك. السؤال الأول الذي يحتاج الباحث أن يسأل نفسه عنه هو ما هو أهم المتغيرات التي يجب استخدامها لوصف الاستجابة لمجموعة بيانات معينة. في هذا العمل، تمت مناقشة طريقة جديدة في الاستدلال بايزي لأختيار المتغيرات باستخدام تقنيات عينات Gibbs. بعد تحديد النموذج، تم اشتقاق التوزيعات الخلفية لجميع المعلمات. تم اختبار طريقة الاختيار للمتغير الجديد باستخدام 4 مجاميع من البيانات. تمت مقارنة الطريقة الجديدة مع بعض الطرق المعروفة التي هي قليل مربعات الخطأ (OLS)، عامل انكماش مطلق واختيار (Lasso)، وتسوية تيكونوف (Ridge). أظهرت دراسات المحاكاة أن أداء طريقتنا أفضل من الأخرى حسب الخطأ ووقت الاستهلاك. تم تطبيق الطرق على مجموعة بيانات Rock Strength، وكانت الطريقة الجديدة التي تم تقديمها أكثر كفاءة ودقة.Variable selection is an essential and necessary task in the statistical modeling field. Several studies have triedto develop and standardize the process of variable selection, but it isdifficultto do so. The first question a researcher needs to ask himself/herself what are the most significant variables that should be used to describe a given dataset’s response. In thispaper, a new method for variable selection using Gibbs sampler techniqueshas beendeveloped.First, the model is defined, and the posterior distributions for all the parameters are derived.The new variable selection methodis tested usingfour simulation datasets. The new approachiscompared with some existingtechniques: Ordinary Least Squared (OLS), Least Absolute Shrinkage and Selection Operator (Lasso), and Tikhonov Regularization (Ridge). The simulation studiesshow that the performance of our method is better than the othersaccording to the error and the time complexity. Thesemethodsare applied to a real dataset, which is called Rock StrengthDataset.The new approach implemented using the Gibbs sampler is more powerful and effective than other approaches.All the statistical computations conducted for this paper are done using R version 4.0.3 on a single processor computer

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