"To Bin or not to Bin?" A formal analysis of partition based regression for Outdoor Thermal Comfort. (December 2021) - Nevat, Ido
Abstract: 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. Highlights: Formal mathematical definition of the partition-based linear regression model for Outdoor Thermal Comfort (OTC). Development of a statistical test to determine if and under which partitioning conditions the Normality assumptions hold, thus allowing to use inferential procedures. Derivation of the theoretical properties of the model, its statistical properties and its prediction distribution. Development of a new probabilistic metric, the Probabilistic Acceptability Criterion (PAC), which generalizes the deterministic acceptability criterion metric. Novel algorithm for choosing the optimal binning method via a combination of goodness-of-fit test and Cross-Validation method.