Bayesian Reasoning: Discrete Inference with Sequential Data

Or, One Way I Learned to Quit Believing My Prejudices

In my last article on this topic, I showed that considering background information can play a significant role in helping us make less biased judgments. What I hope to show now is that while we learn by updating the information we have through experience, limited experiences can often lead to prejudices about the way we interpret the world; but even broad and deep experience should rarely lead us to certain conclusions.

To get started, imagine playing a game in which someone asks you to infer the number of sides of a die based on the face numbers that show up in repeated throws of the die. The only information you are given beforehand is that the actual die will be selected from a set of seven die having these number of faces: (4, 6, 8, 10, 12, 15, 18). Assuming you can trust the person who reports the outcome on each throw, after how many rolls of the die will you be willing to specify which die was chosen?

Let's use the R programming language to help us think through the problem. Start by specifying the set of the die possibilities such that each number represents the number of sides of a given die. (You might also want to refer to my previous article on Bayesian analysis to familiarize yourself with some of the terminology that follows.)

To read the entire discussion go here.