Bayes-optimal Solution for Environmental Prediction Using Human Sensitivity

From the theoretical viewpoint of statistical physics, we investigate the dynamical properties for predicting environment utilizing human sensitivity of a sensor network for a small-scale system with an air conditioner. We analyse how environmental variables evolve in such a small room by a dynamical procedure in accordance with Bayesian inference with expected a posterior estimation and statistical physics with the Master equation and mean-field theory. We clarify that the temperature-humidity index (THI) smoothly approaches to the optimum value due to the use of the Bayes-optimal solution and that both temperature and relative humidity is close to the original variables along a curve on the temperature-humidity plane. Then, we discover that the THI also approximates the optimum value by a method without using a term that improves the optimum THI, although the convergence time is longer than that of the Bayes-optimal solution.