To Bin or not to Bin?A formal analysis of partition based regression for Outdoor Thermal Comfort

We consider the problem of statistically modeling the thermal perception as a function of Outdoor Thermal Comfort (OTC) via partitioning based regression models. Such models have been widely used, but may not be fully understood and theoretically justified by practitioners. To close the gaps between statistical theory and applications of OTC analysis, we first provide a formal mathematical representation of the widely used partitioning based regression models. We provide the interpretation of those models from a statistical point of view, and make the modeling assumptions explicit and clear. We then show that these partitioning based regression models can be understood as a semi-parametric regression model, known as Regressogram. We analyze the theoretical properties of the Regressogram and develop a simple algorithm for choosing the optimal number of bins, which is based on a combination of goodness-of-fit test and cross-validation methods. We then derive various quantities which are of importance for climate-informed urban design, including the predictive distribution and a new statistical measure for thermal acceptability, called the Probabilistic Acceptability Criterion (PAC). Overall, the proposed framework is designed to help climate practitioners gain better understanding of OTC regression methods and place the practices currently used on a statistically rigorous footing.

Automated summary

The study explores the modeling issue between thermal perception and Outdoor Thermal Comfort (OTC) using partitioning based regression models, aiming to provide a statistically rigorous approach for understanding and predicting this relationship. The research demonstrates how partitioning based regression models can be understood as semi-parametric regression models, develops an algorithm for selecting the optimal number of bins, and derives important statistical quantities for climate-informed urban design.