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Understand Bayes Rule, Likelihood, Prior and Posterior
A case study based introduction to using Bayes rule and how it compares with a frequentist, pessimistic and optimistic approaches to drawing conclusions
This post will help you understand Bayesian inference at an intuitive level with the help of a simple case study. I hope that once you read this article, you will be very clear on how the well-known “Bayes theorem” is used, what do the terms in the theorem mean (prior, posterior, likelihood) and how this compares with other approaches to decision making (pessimist /optimist/frequentist). We will use a simple case study to help explain the concepts. For those who are interested, I have provided simulation results for the given case study and a link to R code for further exploration. Let’s start with the case study:
Case Study
There is a very dangerous but rare disease called dangeritis with 0.1% prevalence (1 in 1000 people get it). One morning you wake with chest pain (one of the symptoms of dangeritis). With no history of heart disease, you take a test of dangeritis as a precautionary measure. You suspect that the pain you had is muscular but you take the test just to be sure. Unfortunately, the test turns out positive suggesting that you have…
