Probability Modeling

Abstract

Probability is a field of mathematics that quantifies and models the likelihood of some event occurring, making it identical to statistics in various ways. In fact, the two fields quantitatively describe the same things, but in different ways, as many analytical models incorporate elements of both. In defining the exact nature of probability, there are two separate views that can be understood in terms already addressed in this book. Frequentists refer to the rate of observation of various potential values of a variable, while Bayesians work on the underlying assumption of a statistical distribution like a normal distribution, and infer likelihoods based on that distribution. Contrary to common belief, these are not contradictory views of probability—they are complementary. While frequentists utilize sampling methods and the analysis of descriptive data, with the implications based on that, Bayesians heavily rely on inferential analysis with known behaviors of observation and data distribution acting as the source of evidential analysis. A common example used to describe probability is the roulette wheel, which is a type of gambling in which a large wheel is spun and a ball falls onto one number/color combination among 38 possible outcomes while people bet on which will be observed.