PyMC examples by Mat Kelcey

http://matpalm.com/blog/2012/12/27/dead_simple_pymc/

The St. Petersburg paradox

http://en.wikipedia.org/wiki/St._Petersburg_paradox

In economics, the St. Petersburg paradox is a paradox related to probability theory and decision theory. It is based on a particular (theoretical) lottery game (sometimes called St. Petersburg Lottery) that leads to a random variable with infinite expected value, i.e., infinite expected payoff, but would nevertheless be considered to be worth only a very small amount of money. The St. Petersburg paradox is a classical situation where a naïve decision criterion (which takes only the expected value into account) would recommend a course of action that no (real) rational person would be willing to take. Several resolutions are possible.

Investing: Kelly Criterion

Over the last few years - while researching trading strategies - I happened to learn about the Kelly Criterion:
http://en.wikipedia.org/wiki/Kelly_criterion

In probability theory, the Kelly criterion, or Kelly strategy or Kelly formula, or Kelly bet, is a formula used to determine the optimal size of a series of bets. In most gambling scenarios, and some investing scenarios under some simplifying assumptions, the Kelly strategy will do better than any essentially different strategy in the long run. It was described by J. L. Kelly, Jr in 1956

http://www.bjmath.com/bjmath/kelly/kellyfaq.htm

Library Additions: Gambling and Mathematics

I'm interested in learning more about the fine art of becoming a better player of various games of chance (in particular, those that are popular in Las Vegas), and developing a better edge in the management of my own personal portfolio trading strategies.

I believe that developing skills in the former will aide me in my goals for the latter.

And so, I've been slowly amassing a small library of books on various topics related to gambling skills, and some directly (or indirectly) related to the mathematics of such games.

The Mathematics of Blackjack
http://www.bjmath.com

Thus far, I've been able to assemble a small respectable library of books, sourced solely through local thrift stores, and Friends of the Library sales.  My gambling-related collection currently includes the following:

• The Rules of Neighborhood Poker According to Hoyle, by Stewart Wolpin
• According To Hoyle, by Richard L. Frey
• Hold'em Wisdom for All Players, by Daniel Negreanu
• Winning Low Limit HOLD'EM, by Lee Jones
• Gambling Secrets of Nick The Greek, by Ted Thackrey, Jr.
• Playing Blackjack As A Business, by Lawrence Revere
• Total Poker, by David Spanier
• The Complete Guide to Winning Poker, by Albert H. Morehead
• The Official Poker Rules, 1st Edition, World Poker Tour
• The TAO of Poker, by Larry W. Phillips
• Secrets the PROS WOn't Tell You About Winning HOLD'EM Poker, by Lou Krieger
• More Hold'Em Excellence, by Lou Krieger
• Winner's Guide to Texas HOLD'EM Poker, by Ken Warren
• Scarne's Guilde to Modern Poker, by John Scarne
• Tournament Poker for Advanced Players, by David Sklansky
•  The Psychology of Poker, by Alan N. Schoonmaker, Ph.D.
• Read'Em and Reap, by Joe Navarro
• Beyond Bluff's, by James A. McKenna
• Online Poker in easy steps, by Stuart Yarnold
• The Book of Solo Games, by Gyles Brandreth

Some recent additions to my mathematics shelf, include the following:

• Digital Dice, Computational Solutions to Practical Probability Problems, byu Paul J. Nahin
• The Mathematics of Games of Strategy, by Melvin Dresher
• Elementary Concepts of Topology, by Paul Alexandroff
• Mathematical Theory of Computation, by Zohar Manna
• The Golden Ratio, by Mario Livio
• How To Lie With Statistics, by Darrell Huff
• Mathematical Circus, by Martin Gardner
• The Man Who Knew Infinity, A Life of the Genius Ramanujan, by Robert Kanigel
• e: The Story of a Number, by Eli Maor
• Mathematical Snippets, by Theoni Pappas
• The Magic of Mathematics, by Theoni Pappas
• Essays on The Theory of Number, by Richard Dedekind
• How to Solve Word Problems in Geometry, by Dawn Sova, Ph.D.
• Mathematics for the Biological Sciences, by Jagdish C. Arya and Robin W. Lardner
• Rapid Math Tricks and Tips, by Edward H. Julius
• Mathematics for the Trades, by Robert A. Carman and Hal M. Saunders
• Finite Mathematics with Business Applications, by Kemeny et. al.

Learner.org Math Resources

Learner.org has an interesting series called: Math Illuminated

There are also a wide variety of other materials available, tailored to specific age groups:
http://www.learner.org/resources/browse.html?discipline=5&grade=0&imageField2.x=3&imageField2.y=11

About Learner.org

Annenberg Learner uses media and telecommunications to advance excellent teaching in American schools. This mandate is carried out chiefly by the funding and broad distribution of educational video programs with coordinated Web and print materials for the professional development of K-12 teachers. It is part of The Annenberg Foundation and advances the Foundation's goal of encouraging the development of more effective ways to share ideas and knowledge.

RStudio - Shiny

http://www.rstudio.com/shiny/

Shiny makes it super simple for R users like you to turn analyses into interactive web applications that anyone can use. Let your users choose input parameters using friendly controls like sliders, drop-downs, and text fields. Easily incorporate any number of outputs like plots, tables, and summaries.

No HTML or JavaScript knowledge is necessary. If you have some experience with R, you're just minutes away from combining the statistical power of R with the simplicity of a web page.

Blaze - next generation NumPy

https://speakerdeck.com/sdiehl/blaze-next-generation-numpy

Why One Statistician Buys Lottery Tickets

David Wood's discussion of the probabilities of buying lottery tickets is an entertaining read:

http://simplexify.net/blog/2012/5/6/i-am-a-statistician-and-i-buy-lottery-tickets.html

"The decision of whether to buy a lottery ticket shouldn’t be based on the probability of winning, or the expected return of a ticket, but on the entertainment value that comes from imagining a different life. If that entertainment value compares favourably with other activities with a similar price, then go for it. Plus, it has the added bonus that you might actually win; one-in-a-million events happen every day. Someone eventually wins the big prize, and you have to be in to win" - David Woods

Julia Language

Here's an interesting language for mathematical endeavors
http://julialang.org/

hat'tip to Paul Snively@psnively


From the Julia blog:

Julia is a dynamic language in the tradition of Lisp, Perl, Python and Ruby. It aims to advance expressiveness and convenience for scientific and technical computing beyond that of environments like Matlab and NumPy, while simultaneously closing the performance gap with compiled languages like C, C++, Fortran and Java.
Most high-performance dynamic language implementations have taken an existing interpreted language and worked to accelerate its execution. In creating Julia, we have reconsidered the basic language design, taking into account the capabilities of modern JIT compilers and the specific needs of technical computing. Our design includes:

• Multiple dispatch as the core language paradigm.
• Exposing a sophisticated type system including parametric dependent types.
• Dynamic type inference to generate fast code from programs with no declarations.
• Aggressive specialization of generated code for types encountered at run-time.

Julia feels light and natural for data exploration and algorithm prototyping, but has performance that lets you deploy your prototypes.

Funny: If the IRS had discovered the quadratic formula . . .

http://www.cs.amherst.edu/~djv/irs.pdf