“Regression to the mean: what it is and how to deal with it” (International Journal of Epidemiology 2005;34:215–220 [ doi:10.1093/ije/dyh299])is a very instructive paper.
I have taken the example and illustrated to demonstrate effect of between and within group variance and number of sample measurements.
This is an excellent book. It is extremely well written. It fits well with “Black Swan” and “Thinking fast and slow” in importantly making us aware of underlying statistical considerations in interpreting coincidence, clusters, extreme value or apparently extremely low probability events. The author gathers these considerations under the “improbability principle” and through real examples and instructive toy examples beautifully explains very important biases and limitations. He provides helpful labels such: “law of truly large numbers”, “laws of selection”, :law of probability leverage” covering topics such as: hindsight bias, lead time bias, base rate fallacy, prosecutots fallacy, the effects of fat tailed distributions.
I enjoyed this book and sadly (but wonderfully) it exposed some of my own hidden biases and misconceptions. It is always good to be shaken out of complacent lazy and convenient thinking.
It has been a challenging time of late…the evanescence of life, I am a speck of dust floating aimlessly on a turbulent sea. Using some code from the talented MSE users( @RahulNarain and @MichaelE2) I digitized my handwritten ambigram and with Mathematica produced the animated gif…
This is a wonderful textbook that complements Professor Blitzstein’s Harvard STAT10 course.
I was very much looking forward to this textbook. I was not disappointed. The book follows closely the course. The concepts are clearly explained and the use of story and the examples work very well. The concepts accumulate gradually but steadily to increasingly complex subjects.
The book affirms Professor Blitzstein’s aphorism: “conditioning is the soul of statistics” and helps to use this principle in tackling a broad and deep swathe of problems.
It has been a very difficult time of late. The sudden unexpected passing of the person who has had the most significant developmental influence on my life continues to cast a long shadow over my life (as it should). My thoughts and focus has been poor. I still learn a lot and derive a lot of satisfaction from Mathematica Stackexchange.
This post is to share a beautiful answer by user ybeltukov that converts the problem to a simpler spherical one and exploits the symmetry. The answer is here (beautiful).
This is a readable book. I enjoyed it. It makes a valliant attempt to explain quantum theory. The click analogy is useful. However, I was less convinced by the style and approach than I thought I would. The authors are clear and deliberate and try to focus on concepts and use the minimum amount of Mathematics required to get their aim across.
I have consistently enjoyed Philip Ball’s books. I particularly enjoy his rich writing style. I did find this book, however, difficult to engage with. The book does provide a comprehensive and detailed exploration of the mergence of scientific thinking and empirical science from the medieval period. It is largely focussed (therefore) on the 16 th and 17 th century. The cultural, religiious and individual personalities interacting to reveal a more interesting and complex emergence of science from “Natural Magick” and curiosity (the theme of the book) is interesting and edifying.
The book’s length and detail did exceed my concentration. Perhaps, this reflects more about me and my time constraints, but it was less enjoyable than Ball’ other wonderful works.