tatistics is one of the tools used in many sciences to analyze data. One of the most commonly used statistical methods, especially in economics, social sciences, etc., is the regression model. Mean regression, expresses the relationship between the conditional mean of a response variable in terms of one or more independent variables. \\\\However, sometimes this method will perform poorly in data analysis. For example, in cases where error distribution is not normal or if variance heterogeneity exists, least-squares estimators are sensitive to outliers and lead to skewed estimates. On the other hand, least squares regression expresses the relationship between covariates and mean response variable, while in many cases, the goal is to find the relationship between independent variables with other segments and dependent variable distribution quantiles.\\\\ In these cases, the quantile regression method can be used. In order to easily implement Bayesian methods to obtain parameter estimation, first a distribution for the response variable is considered, then the Markov Monte Carlo chain methods are used to generate the sample from the later distribution.\\\\ Although the asymmetric Laplace distribution is widely used in the Bayesian quantile regression model, but when the observations include outliers and the distribution of the heavy observations, this distribution will not work properly. Also for each specific quantity such as ${\au _0}$, the skewness of this distribution as a function of ${\au _0}$ it has a constant value, so that it represents a constant value for different quantiles.\\\\In recent years, researchers have attempted to introduce a more flexible skew distribution that is used to estimate the parameters of a Bayesian quantile regression model based on outliers and heavy-tailed observations. In this regard, in this thesis, we propose a Bayesian quantile regression model with skewed exponential power distribution error to solve this problem.\\\\First, by applying the penalized least squares regression methods, we estimate the regression coefficients and the variable selection process using the Lasso and adaptive Lasso fines based on the asymmetric Laplace distribution, as the error variable distribution, which a way to use for dimension reduction by choosing only relevant attributes parameterization. So, Bayesian inference and sample generation from the posterior distribution are made using Gi sampling algorithm. In the following, we introduce the skew exponential power distribution and describe the Bayesian quantile regression model using it as the error distribution. In this distribution family, posterior distribution sampling is performed using the independent Metropolis-Hastings within Gi sampling algorithm, which will also be associated with the variable selection process. Then we use simulation and applied studies to evaluate the performance of the proposed model.