Sunday, February 22, 2015

Reading List on The Foundations of Probability and The Origins of Statistics

I have finished reading Willful Ignorance from Herbert Eisberg. From this book I got an interesting reading list in the subject of probability and the challenges that statistical techniques are now facing in the era of Big Data.

The reading list is composed of the following books:

  1. Laplace - Theorie Analytique des Probabilities. Considered by many as the first modern author in the field of probability, this book introduces the classical notion of probability as the measure of our uncertainty, but more important, solidifies the idea that a probability is the ratio between the successes and the total number of occurrences (good or bad) instead the old notion (from before the XVIII century) that used the odds ratio. 
  2. Keynes - A Treatise on Probability. An interesting approach on the epistemological basis of probability. 
  3. Andrei Kolmogorov - Foundations of The Theory of Probability. THE Text if you want to delve deeper in the mathematical foundations of probability. I noticed that he establishes his theory based on set theory and presents several of his ideas with Lebesgue Integrals. Both subjects are a must if you want to understand modern quantitative financial theory. 
  4. Student (1908). The probable error of a mean. Biometrika, 6: 1–25; - Very important paper, because it establishes the mathematical basis for the so called Student Distribution. It is interesting specially from a methodological perspective, for a researcher so it can be understood how a continuous probability distribution was discovered.
  5. Student, Probable error of a correlation coefficient. Biometrika, 6: 302–310 - Same as above. On the other hand I was not able to easily locate this paper like the previous one that can be downloaded from a myriad of sites.
  6. Stephen M. Stigler (1986a). The History of Statistics: The Measurement of Uncertainty before 1900. Cambridge: Harvard University Press, Part 1, pp. 1–139. - It gives an important view on the development of Gauss ideas that lead to the least square method and the gaussian (normal) curve. I will try fqllowing the presentation in this book to better understand the mathematical foundations of the gaussian curve. In other words: how it was discovered. 
  7. Ronald A. Fisher (1925). Statistical Methods for Research Workers. - Very important because it gives an idea on the origin of the p-value and the so called factorial designs.
  8. Karl Pearson (1900). On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philosophical Magazine Series 5, 50: 157–175. - It provides an understanding on the Chi-Squared distribution and the research problems that leaded to it.
  9. John W. Tukey (1977). Exploratory Data Analysis. Reading, MA: Addison–Wesley.
  10. John P. A. Ioannidis (2005). Why most published research findings are false. PloS Medicine,
  11. Gary King (1995). Replication, replication, replication. Political Science and Politics, 28: 443–499
The order for me will be 1st) Kolmogorov, 2nd) Stiegler, 3rd) Pearson, 4th) Student, 5th) Fisher

So far so good.

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