Statistical modeling is the process of applying statistical analysis to a dataset. A statistical model is a mathematical representation (or mathematical model) of observed data. When data analysts apply various statistical models to the data they are investigating, they are able to understand and interpret the information more strategically. Rather than sifting through the raw data, this practice allows them to identify relationships between variables, make predictions about future sets of data, and visualize that data so that non-analysts and stakeholders can consume and leverage it. Statistical models, typically consisting of a collection of probability distributions, are used to describe patterns of variability that random variables or data may display. Describing the invariance of such models is often done via group theory. Although the mathematical notion of a group is relatively simple, the ideas of group theory provide a very convenient way to describe how statistical models change when random variables are transformed. In particular, statistical models that are closed under a class of transformations are called invariant. Often this invariance has important implications for inferential problems associated with the model. The principle of invariance asserts that whenever a problem is invariant under a group of transformations, then the solution to the problem should also be invariant. Applications of this principle occur in both estimation and hypothesis-testing problems.