Browsing by Subject "Bayesian modeling"

Objectives: The objective of this thesis is to illustrate the advantages of Bayesian hierarchical models in housing price modeling. Methods: Five Bayesian regression models are estimated for the housing prices. The models use a robust Student’s t-distribution likelihood and are estimated with Hamiltonian Monte Carlo. Four of the models are hierarchical such that the apartments’ neighborhoods are used as a grouping. Model stacking is also used to produce an ensemble model. Model checks are conducted using the posterior predictive distributions. The predictive distributions are also evaluated in terms of calibration and sharpness and using the logarithmic score with leave-one-out cross validation. The logarithmic scores are calculated using Pareto smoothed importance sampling. The R^2-statistics from the point predictions averaged from the predictive distributions are also presented. Results: The results from the models are broadly reasonable as, for the most part, the coefficients of the explanatory variables and the predictive distributions behave as expected. The results are also consistent with the existence of a submarket in central Helsinki where the price mechanism differs markedly from the rest of the Helsinki-Espoo-Vantaa region. However, model checks indicate that none of the models is well-calibrated. Additionally, the models tend to underpredict the prices of expensive apartments.