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In the last few decades, enormous computational speed has become accessible to many. Modern day desktop has good enough memory and processing speed that enables a data analyst to compute probabilities and perform statistical inference by writing computer programs. In such a context, this book can serve as a starting point to anyone who wishes to explore the subject of computational probability. This book has 21 puzzles that can be solved via simulation.

Solving a puzzle has its own advantages. Give a dataset with one dependent variable and a set of predictors to a dozen people asking them to fit a regression model; I bet that you will see at least a dozen models, each of which could be argued as a plausible model. Puzzles are different. There are constraints put around the problem that you are forced to get that ONE RIGHT solution to the problem. In doing so, you develop much more sophisticated thinking skills.

In the introductory chapter of the book, the author provides a basic framework for computational probability by showing ways to simulate and compute probabilities. This chapter gives the reader all the ammunition required to solve the various puzzles of the book. The author provides detailed solutions that includes relevant MATLAB code, to all the 21 puzzles.

Some of my favorite puzzles from the book that are enlightening as well as paradoxical are :

  • ˆ The Gamow-Stern Elevator
  • ˆ The Pipe Smoker’s Discovery
  • ˆ A Toilet Paper Dilemma
  • ˆ Parrondo’s Paradox
  • ˆ How Long Is the Wait to Get the Potato Salad ?
  • ˆ The Appeals court Paradox

Here is the link to my document that flushes out the details of all the 21 puzzles in the book:

What’s in the above document?

I have written R code that aims to computationally solve each of the puzzles in the book. For each puzzle, there are two subsections. First subsection spells out my attempt at solving the puzzle. The second subsection contains my learning from reading through the solution given by the author. The author provides extremely detailed MATLAB code that anyone who has absolutely no exposure to MATLAB can also understand the logic. In many cases I found that the code snippets in the book looked like elaborate pseudo code. There are many good references mentioned for each of the puzzles so that interested readers can explore further aspects. In most of the cases, the reader will realize that closed form solutions are extremely tedious to derive and simulation based procedures make it easy to obtain solutions to many intractable problems.

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