Bayesian and non-Bayesian regression analysis applied on wind speed data

Statistical methods are widely used to analyze the relationship between several independent variables (predictors) and a dependent variable. As wind energy rapidly becomes an important source of renewable energy, it is prudent to deeply evaluate any potential existing relationships among the data. This paper aims to apply the frequentist statistical approach, namely, non-Bayesian and the Bayesian approach, to multiple linear regression to wind speed data to investigate the differences between the two methodologies. This study uses the NREL wind speed data from fifteen different wind farms. In the proposed study, a correlation matrix was implemented to select the significantly correlated variables among all and use it as the dependent variable. This method is followed by a Random Forest machine learning technique for feature selection and considering the most important features that will be used for the Bayesian and non-Bayesian regression models. We first run a multiple linear regression (non-Bayesian regression model) in which we apply the variance inflation factor to detect any multicollinearity problem to get the fitted model. We then apply the Bayesian approach to the fitted model to analyze the relationship between the dependent and independent variables. The results from both non-Bayesian and the Bayesian approaches show close coefficients and parameters estimations. Moreover, using different wind speed data sample sizes of hourly, daily, and weekly data, we found that the daily data provide a strong coefficient estimator and the highest R-squared compared to the hourly and weekly data.

Automated summary

This study utilizes frequentist statistical methods and machine learning techniques to conduct multivariate linear regression analysis on wind speed data, examining the differences between the Bayesian and non-Bayesian approaches and identifying key features. The results demonstrate close coefficient estimations and parameters between the Bayesian and non-Bayesian methods, with daily data showing strong coefficient estimations and the highest R-squared values compared to hourly and weekly data.