Think Bayes, 2nd Edition

Chapter 20. Approximate Bayesian Computation

This chapter introduces a method of last resort for the most complex problems, Approximate Bayesian Computation (ABC). I say it is a last resort because it usually requires more computation than other methods, so if you can solve a problem any other way, you should. However, for the examples in this chapter, ABC is not just easy to implement; it is also efficient.

The first example is my solution to a problem posed by a patient with a kidney tumor. I use data from a medical journal to model tumor growth, and use simulations to estimate the age of a tumor based on its size.

The second example is a model of cell counting, which has applications in biology, medicine, and zymurgy (beer-making). Given a cell count from a diluted sample, we estimate the concentration of cells.

Finally, as an exercise, you’ll have a chance to work on a fun sock-counting problem.

The Kidney Tumor Problem

I am a frequent reader and occasional contributor to the online statistics forum at http://reddit.com/r/statistics. In November 2011, I read the following message:

“I have Stage IV Kidney Cancer and am trying to determine if the cancer formed before I retired from the military. … Given the dates of retirement and detection is it possible to determine when there was a 50/50 chance that I developed the disease? Is it possible to determine the probability on the retirement date? My tumor was 15.5 cm x 15 cm at detection. Grade II.

I contacted the author of the ...