Property Valuation: A Comparison between Classical and Bayesian Inference

Abstract

The fifth industrial revolution, marked by the integration of human potential with the analytical capabilities of modern machines, has transformed the field of property valuation. Technologies such as artificial intelligence, machine learning, and Monte Carlo simulations enable more precise and agile analyses in complex scenarios. In this context, Bayesian statistics stand out by treating variables as random and incorporating prior distributions, offering flexibility and greater robustness in problem modeling. This study evaluates the market value of a property using two inferential approaches: classical and Bayesian. The market value, defined as the most probable transaction amount under normal supply and demand conditions, was estimated through linear regression using the least squares method and simulations based on Markov Chains (MCMC). The comparative analysis revealed that while classical inference is limited to point estimates, the Bayesian approach provides a richer probabilistic representation, allowing credibility intervals that capture price variability. The results indicate that Bayesian inference offers greater reliability, particularly in highly uncertain scenarios. Through robust simulations, such as the Hamiltonian Monte Carlo (HMC) algorithm, the Bayesian approach provides more detailed insights for decision-making. It is concluded that this methodology is an essential tool for advancing property valuation, and its application should be expanded to include qualitative variables and alternative distributions in future studies