Bayes’ Theorem Part 2: How to use Bayes’ Rule when you have multiple prior data points

Last week I started my series of posts about Bayes’ Rule and why it was the foundation of good business decision making . In the next few weeks I will hit on some fun applications but today wanted to build further the foundation for using effectively Bayes’ Rule by discussing continuous parameter values (or multiple existing data points). Again, I borrow heavily from easily the best work on Bayes’ Rule, James Stone’s book Bayes Rule: A Tutorial Introduction to Bayesian Analsysis. This application will be particularly relevant when using Bayes’ Theorem to make the best decisions in your green light process, corporate development, investing or anywhere there are multiple historical results to examine.

Multiple data points are referred to as “continuous variables.” The values of a continuous variable are like densely packed points on a line, where each point corresponds to the value of a real number. The main advantage of working with continuous values is that we can usually describe a probability distribution with an equation, and because an equation is defined in terms of a few key parameters, it is said to provide a parametric description of a probability distribution.

To make the above relevant to you, think of yourself as a VC. You are looking at a potential investment. You start by looking at how similar investments over the last two years performed; this return on investment represents the points on the line. The parameters could be the space the business occupied, management team and level of investment. Rather than potential investments, to keep the analysis simple I will use a coin flip as an example. Continue reading