Abstract
This paper experiments an artificial neural networks model with Bayesian approach on a small real estate sample. The output distribution has been calculated operating a numerical integration on the weights space with the Markov Chain Hybrid Monte Carlo Method (MCHMCM). On the same real estate sample, MCHMCM has been compared with a neural networks model (NNs), traditional multiple regression analysis (MRA) and the Penalized Spline Semiparametric Method (PSSM). All four methods have been developed for testing the forecasting capacity and reliability of MCHMCM in the real estate field. The Markov Chain Hybrid Monte Carlo Method has proved to be the best model with an absolute average percentage error of 6.61%.
Highlights
The appraisal theory is based upon the hypothesis that a real estate sample is randomly drawn by a normal population with real estate sales characterized by known prices [1]
The possibility to characterize the interpolating function in probabilistic terms and, to obtain as output a distribution of sales prices instead of deterministic values, jointly with the capability to work with small samples, are aspects that mainly make us lean in favour of the use of the Bayesian approach to artificial neural networks (ANNs or neural networks model (NNs)) for real estate appraisals
The basic model of the real estate market equilibrium [25] assumes that real estate involves complex goods, with sales prices (Pi) which depend on location-specific environmental characteristics, structural characteristics (Si), social and neighbourhood characteristics (Ni), and locational characteristics (Li): Pi = P(qi, Si, Ni, Li)
Summary
The appraisal theory is based upon the hypothesis that a real estate sample is randomly drawn by a normal population with real estate sales characterized by known prices [1]. Hedonic price models assume that the values of real estate properties are influenced by their characteristics, with predicted values strongly influenced by dimension and quality of available real estate data Is it understood that the minimum dimension of real estate sample necessary to implement a statistical inference model is correlated to the number of independent variables explaining real estate characteristics [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]. The possibility to characterize the interpolating function in probabilistic terms and, to obtain as output a distribution of sales prices instead of deterministic values, jointly with the capability to work with small samples, are aspects that mainly make us lean in favour of the use of the Bayesian approach to artificial neural networks (ANNs or NNs) for real estate appraisals. Taking into account these aspects, a neural networks model with Bayesian learning has been experimented for an urban central area of Naples (Vomero neighbourhood)
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