The Price Prediction with Bayesian Inference and Visualization

Abstract

Classical regression serves two primary purposes: evaluating the structure and strength of the relationship between variables. However, while classical regression provides only a point estimate and confidence interval, Bayesian regression offers a comprehensive range of inferential solutions. This study demonstrates the suitability of the Bayesian approach for regression tasks and its advantage in incorporating additional a priori information, which can strengthen research. To illustrate, we utilized data from the Indian Housing dataset provided by the Kaggle Repository. We found that prior distributions produce analytical, closed-form conclusions, eliminating the need for numerical techniques like Markov Chain Monte Carlo (MCMC). Furthermore, this study provides software implementations, along with formulas for the posterior outcomes that are explained and presented clearly. In the third step, Bayesian tools were employed to evaluate the assumptions that underlie the proposed approach. Specifically, the essential processes of Bayesian inference - prior elicitation, posterior calculation, and robustness to prior uncertainty and model sufficiency - were assessed.