Mean-field Analysis of Bayesian Inference Using Expected A Posterior Estimation of Predicting Comfortable Environments Due to Air Conditioner

On the basis of the mean-field theory established in statistical physics we investigate the Bayesian inference using the the expected a posterior (EAP) estimation for predicting a set of environmental variables which realize comfortable environments due to air conditioner. In this method, the posterior probability is estimated using the model prior which realizes the thermal comfort via the temperature-humidity index around the optimal value and the likelihood which expresses expressing transition probability from each comfortable state to realistic one. Then, using the mean-field theory, we find that the present method predicts the variables which approximates the optimal values of the THI at sampling points using the air conditioner power consumption of air conditioner, if we use the parameters appropriately. Further, from the results of the parameter dependence both of the THI and power consumption due to air conditioner. These results were quantitatively confirmed by numerical calculations for several realistic cases.