Observational data about human behavior is often heterogeneous, i.e., generated by subgroups within the population under study that vary in size and behavior. Heterogeneity predisposes analysis to Simpson's paradox, whereby the trends observed in data that has been aggregated over the entire population may be substantially different from those of the underlying subgroups. I illustrate Simpson's paradox with several examples coming from studies of online behavior and show that aggregate response leads to wrong conclusions about the underlying individual behavior. I then present a simple method to test whether Simpson's paradox is affecting results of analysis. The presence of Simpson's paradox in social data suggests that important behavioral differences exist within the population, and failure to take these differences into account can distort the studies' findings.
In the sixteenth and seventeenth centuries, gamblers and mathematicians transformed the idea of chance from a mystery into the discipline of probability, setting the stage for a series of breakthroughs that enabled or transformed innumerable fields, from gambling, mathematics, statistics, economics, and finance to physics and computer science. This book tells the story of ten great ideas about chance and the thinkers who developed them, tracing the philosophical implications of these ideas as well as their mathematical impact. Persi Diaconis and Brian Skyrms begin with Gerolamo Cardano, a sixteenth-century physician, mathematician, and professional gambler who helped develop the idea that chance actually can be measured. They describe how later thinkers showed how the judgment of chance also can be measured, how frequency is related to chance, and how chance, judgment, and frequency could be unified. Diaconis and Skyrms explain how Thomas Bayes laid the foundation of modern statistics, and they explore David Hume’s problem of induction, Andrey Kolmogorov’s general mathematical framework for probability, the application of computability to chance, and why chance is essential to modern physics. A final idea―that we are psychologically predisposed to error when judging chance―is taken up through the work of Daniel Kahneman and Amos Tversky. Complete with a brief probability refresher, Ten Great Ideas about Chance is certain to be a hit with anyone who wants to understand the secrets of probability and how they were discovered.
We discuss properties of the "beamsplitter addition" operation, which provides a non-standard scaled convolution of random variables supported on the non-negative integers. We give a simple expression for the action of beamsplitter addition using generating functions. We use this to give a self-contained and purely classical proof of a heat equation and de Bruijn identity, satisfied when one of the variables is geometric.
The U.S.C./Los Angeles Times poll has consistently been an outlier, showing Donald Trump in the lead or near the lead.
Alone, he has been enough to put Mr. Trump in double digits of support among black voters. He can improve Mr. Trump’s margin by 1 point in the survey, even though he is one of around 3,000 panelists.
He is also the reason Mrs. Clinton took the lead in the U.S.C./LAT poll for the first time in a month on Wednesday. The poll includes only the last seven days of respondents, and he hasn’t taken the poll since Oct. 4. Mrs. Clinton surged once he was out of the sample for the first time in several weeks.
This is the signal for the second.
How can you not follow this twitter account?!
Now I’m waiting for a Shannon bot and a Weiner bot. Maybe a John McCarthy bot would be apropos too?!Syndicated copies to:
In catching up on blogs/reading from the holidays, I’ve noticed that physicist Sean Carroll has a forthcoming book entitled The Big Picture: On the Origins of Life, Meaning, and the Universe Itself (Dutton, May 10, 2016) that will be of interest to many of our readers. One can already pre-order the book via Amazon.
Prior to the holidays Sean wrote a blogpost that contains a full overview table of contents, which will give everyone a stronger idea of its contents. For convenience I’ll excerpt it below.
I’ll post a review as soon as a copy arrives, but it looks like a strong new entry in the category of popular science books on information theory, biology and complexity as well as potentially the areas of evolution, the origin of life, and physics in general.
As a side bonus, for those reading this today (1/15/16), I’ll note that Carroll’s 12 part lecture series from The Great Courses The Higgs Boson and Beyond (The Learning Company, February 2015) is 80% off.
Syndicated copies to:
THE BIG PICTURE: ON THE ORIGINS OF LIFE, MEANING, AND THE UNIVERSE ITSELF
* Part One: Cosmos
- 1. The Fundamental Nature of Reality
- 2. Poetic Naturalism
- 3. The World Moves By Itself
- 4. What Determines What Will Happen Next?
- 5. Reasons Why
- 6. Our Universe
- 7. Time’s Arrow
- 8. Memories and Causes
* Part Two: Understanding
- 9. Learning About the World
- 10. Updating Our Knowledge
- 11. Is It Okay to Doubt Everything?
- 12. Reality Emerges
- 13. What Exists, and What Is Illusion?
- 14. Planets of Belief
- 15. Accepting Uncertainty
- 16. What Can We Know About the Universe Without Looking at It?
- 17. Who Am I?
- 18. Abducting God
* Part Three: Essence
- 19. How Much We Know
- 20. The Quantum Realm
- 21. Interpreting Quantum Mechanics
- 22. The Core Theory
- 23. The Stuff of Which We Are Made
- 24. The Effective Theory of the Everyday World
- 25. Why Does the Universe Exist?
- 26. Body and Soul
- 27. Death Is the End
* Part Four: Complexity
- 28. The Universe in a Cup of Coffee
- 29. Light and Life
- 30. Funneling Energy
- 31. Spontaneous Organization
- 32. The Origin and Purpose of Life
- 33. Evolution’s Bootstraps
- 34. Searching Through the Landscape
- 35. Emergent Purpose
- 36. Are We the Point?
* Part Five: Thinking
- 37. Crawling Into Consciousness
- 38. The Babbling Brain
- 39. What Thinks?
- 40. The Hard Problem
- 41. Zombies and Stories
- 42. Are Photons Conscious?
- 43. What Acts on What?
- 44. Freedom to Choose
* Part Six: Caring
- 45. Three Billion Heartbeats
- 46. What Is and What Ought to Be
- 47. Rules and Consequences
- 48. Constructing Goodness
- 49. Listening to the World
- 50. Existential Therapy
- Appendix: The Equation Underlying You and Me
- Further Reading
While browsing through some textbooks and researchers today, I came across a fantastic looking title: Probability Models for DNA Sequence Evolution by Rick Durrett (Springer, 2008). While searching his website at Duke, I noticed that he’s made a .pdf copy of a LaTeX version of the 2nd edition available for download. I hope others find it as interesting and useful as I do.
I’ll also give him a shout out for being a mathematician with a fledgling blog: Rick’s Ramblings.Syndicated copies to: