Thomas Bayes and Pierre-Simon Laplace were two pioneers in the world of probability theory. Bayes developed Bayesian Probability, Bayesian Reasoning, and the Bayes’ Theorem, and Laplace is often credited for putting Bayes’ additions to the field of conditional probability on the map. While more traditional approaches to probability focus on frequency of outcomes and the propensity of a phenomenon, the Bayes’ Theorem takes a slightly different approach that is more in tune with a state of knowledge or a belief system towards how conditional probability should be handled.
The math behind the Bayes’ Theorem is demonstrated and explained within the context of two different examples. A common example used to explain Bayesian Probability pertaining to the probability that a woman with a positive mammogram does indeed have breast cancer is discussed, along with a fun political example related to the current race between Donald Trump and Hillary Clinton. All of this is shown to drive home the point of how powerful the various metrics in the market truly are, such as delta, theta, gamma, and vega. Thankfully, we never have to actually calculate any conditional probabilities on the fly because the market’s constant movement and updating of all pertinent information in real-time shows us everything we need to know. The key is to understand all of these inputs on a granular level.
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