## 2 Methods
### Thermal Dissatisfaction Rate Prediction
#### 2.1.2 Prediction Model  
In analyzing the real-time dissatisfaction rate of thermal environment groups, the prior distribution indicated the distribution of dissatisfaction rate corresponding to a particular _PMV_ value. Although the _PMV-PPD_ model could hardly reflect the influence of individual variability on human thermal comfort, the model could characterize the average indoor multi-user thermal comfort and thermal dissatisfaction rate. Therefore, the _PMV-PPD_ model was used to describe the prior information on thermal comfort and calculated the average group thermal comfort and thermal. The objective quantity of dissatisfaction rate was calculated. Based on the central limit theorem of probability theory, a Gaussian distribution was used to characterize the prior information on the thermal dissatisfaction rate, as shown in Equation (2).  
\[\pi(\theta)=\frac{1}{\sqrt{2\pi\sigma}}e^{-\frac{(\theta-PPD)^{2}}{2\sigma^{2} }}, \tag{2}\]  
Figure 1: Flow chart of this study.  
where \(\theta\) denotes the thermal dissatisfaction rate, \(\theta\in[0,1]\); \(\sigma\) denotes the variance of the prior distribution of the thermal dissatisfaction rate. According to the \(PMV\) thermal comfort index, the \(PPD\) is the group average thermal dissatisfaction rate calculated, as shown in Equation (3).  
\[PPD=1-0.95\times\exp(-0.03353\times PMV^{4}-0.2179\times PMV^{2}) \tag{3}\]  
Multi-user thermal discomfort body language expressions were independent of each other. The binomial distribution could characterize the probability of thermal discomfort body language occurrence in \(n\) independent Bernoulli experiments. Therefore, the binomial distribution was selected to describe the distribution of thermal discomfort body language in the group in this paper. At a particular moment, assuming that the number of people in the room is \(n\) and the number of people expressing thermal discomfort body language is \(x\), the distribution of the number of people with thermal discomfort body language in the field research is shown in Equation (4).  
\[f(x|\theta)=C_{n}^{x}\theta^{x}(1-\theta)^{n-x} \tag{4}\]  
Based on information on thermal discomfort body language, the posterior distribution of the thermal dissatisfaction rate was obtained by synthesizing prior knowledge to express the prediction results with individualized differences. Based on the Bayesian prediction theory, the posterior distribution of the thermal dissatisfaction rate is shown in Equation (5).  
\[h(\theta|x)=\frac{\pi(\theta)f(x|\theta)}{\int_{0}^{1}\pi(\theta)f(x|\theta)d \theta}, \tag{5}\]  
where \(h(\theta|x)\) denotes the posterior distribution of the thermal dissatisfaction rate, combining group thermal comfort characteristics and individualized thermal comfort differences.  
The above formula combines the collected environmental parameters and human physiological parameters to determine the objective amount of thermal dissatisfaction rate. It monitors people's subjective thermal comfort feelings towards the environment using on-site research on thermal discomfort body language, etc. According to the posterior distribution of the thermal dissatisfaction rate, the predicted value of the thermal dissatisfaction rate was calculated by the Bayesian theoretical point estimation method. The expected value of the posterior distribution was used as the predicted result considering the actual thermal environment so that the group universal thermal dissatisfaction rate can be corrected in real-time to achieve the timely update of personnel thermal dissatisfaction status, as shown in Equation (6).  
\[BPD=\int_{0}^{1}\theta h(\theta|x)\,d\theta. \tag{6}\]