1 / 32

Categorical Data Analysis

Categorical Data Analysis. STAT 453/653. Introduction. The probability theory begins in attempts to describe gambling (how to win, how to divide the stakes, etc.), probability theory mainly considered discrete events, and its methods were mainly combinatorial. Gerolamo Cardano

mabon
Download Presentation

Categorical Data Analysis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Categorical Data Analysis STAT 453/653 Introduction

  2. The probability theory begins in attempts to describe gambling (how to win, how to divide the stakes, etc.), probability theory mainly considered discrete events, and its methods were mainly combinatorial Gerolamo Cardano (September 24, 1501 – September 21, 1576) Author of the first book on probability “De Ludo Aleae” ~ “On the dice game” written in 1560s, published in 1663

  3. … eventually, analytical considerations motivated the incorporation of continuous variables into the theory. The foundations of modern theory of probability were laid by Andrey Nikolaevich Kolmogorov, who combined the notion of sample space, introduced by Richard von Mises, and Lebesgue measure theory and presented his axiom system for probability theory in 1933 (Grundbegrie der Wahrscheinlichkeitsrechnung, by A. Kolmogorov, Julius Springer, Berlin, 1933, 62 pp.) Andrei Kolmogorov (1903-1987): A founder of modern theory of probabilities (1933) Henri Léon Lebesgue (June 28, 1875 – July 26, 1941) Richard Edler von Mises (19 April 1883 - 14 July 1953)

  4. Karl Pearson (March 27, 1857 – April 27, 1936) established the discipline of mathematical statistics

  5. George Udny Yule (18 Feb 1871, Scotland -- 26 June 1951, England)

  6. “The only theory of correlation at present available for practical use is based on the normal law of frequency, but, unfortunately, this law is not valid in a great many cases which are both common and important. It does not hold good, to take examples from biology, for statistics of fertility in man, for measurements on flowers, or for weight measurements even on adults. In economic statistics, on the other hand, normal distributions appear to be highly exceptional; variation of wages, prices, valuations, pauperisms, and so forth, are always skew. In cases like these we have at present no means of measuring the correlation by one or more “correlation coefficients” such are afforded by the normal theory.” G.U.Yule (1897) On the theory of correlation Journal of the Royal Statistical Society, 60, 812-821

  7. Sir Ronald Aylmer Fisher (17 February 1890 – 29 July 1962)

  8. Origin of discrete data

  9. Socio-economic statistics

  10. Business statistics

  11. Patterns in complex systems

  12. El-Nino

  13. Ghil and Zaliapin (2013) El Nino, Encyclopedia of Natural Hazards.

  14. Forecast problem

  15. Complex networks

  16. Map of the blogosphere http://datamining.typepad.com/gallery/blog-map-gallery.html

  17. What is the problem?

  18. Sample problem Aspirin Placebo 0 100 Heart attack No Heart attack 100 0

  19. Sample problem Aspirin Placebo 60 40 Heart attack No Heart attack 40 60

  20. Sample problem Aspirin Placebo 60 40 Heart attack No Heart attack 4,000 6,000

  21. Finley Affair John Park Finley -- U.S. Army Signal Corps Finley, J. P., 1884: Tornado predictions. American Meteorological Journal, 1, 85 – 88. In this study tornado predictions were made for each of 18 districts in the central and eastern United States during March, April, and May. The forecasts were produced twice a day for 8-h periods beginning at 07:00 and 15:00.

  22. Finley Affair VS 5% 95%

  23. Thingness of Things Having given the number of instances respectively in which things are both thusandso, in which they are thusbutnot so, in which they are sobut not thus, and in which they are neither thus nor so, it is required to eliminate the general quantitative relativity inhering in the mere thingness of the things, and to determine the special quantitative relativity subsisting between thethusness and thesonessof the things. M. H. Doolittle, Bull. Philos. Soc. Washington, 1888

  24. Finley Affair: A Closer Look Observations Tornado No tornado 72 28 Tornado Forecasts 23 2680 No tornado

  25. Finley Affair: An ongoing challenge Finley Doolittle-Heidke Gilbert Pierce Hanssen-Kuiper Clayton Doolittle ‘‘it seems clear to me that no single numerical expression can be a proper solution of such a problem’’ M. H. Doolittle, Amer. Meteor. J., 1885

More Related