Think Bayes, 2nd Edition

Chapter 9. Decision Analysis

This chapter presents a problem inspired by the game show The Price is Right. It is a silly example, but it demonstrates a useful process called Bayesian decision analysis.

As in previous examples, we’ll use data and prior distribution to compute a posterior distribution; then we’ll use the posterior distribution to choose an optimal strategy in a game that involves bidding.

As part of the solution, we will use kernel density estimation (KDE) to estimate the prior distribution, and a normal distribution to compute the likelihood of the data.

And at the end of the chapter, I pose a related problem you can solve as an exercise.

The Price Is Right Problem

On November 1, 2007, contestants named Letia and Nathaniel appeared on The Price is Right, an American television game show. They competed in a game called “The Showcase”, where the objective is to guess the price of a collection of prizes. The contestant who comes closest to the actual price, without going over, wins the prizes.

Nathaniel went first. His showcase included a dishwasher, a wine cabinet, a laptop computer, and a car. He bid $26,000.

Letia’s showcase included a pinball machine, a video arcade game, a pool table, and a cruise of the Bahamas. She bid $21,500. The actual price of Nathaniel’s showcase was $25,347. His bid was too high, so he lost. The actual price of Letia’s showcase was $21,578.

She was only off by $78, so she won her showcase and, because her bid was off by less than 250, ...