Six analysis and probability diagrams

Here are a few diagrams I’ve created that summarize relationships in analysis and probability. Click on a thumbnail image to go to a page with the full image and explanatory text.

Special functions

Gamma and related functions

Probability distributions

Conjugate priors

Convergence theorems

Bessel functions


Related: Visualizing category theory concept dependencies

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3 comments on “Six analysis and probability diagrams
  1. EastwoodDC says:

    Nice work, John.

    Under Convergence theorems, near the top, “possible” should be “possibly”, I think.

    What’s the difference between the solid and the dashed arrows? I ought to remember, but it has been a long time …

    There other alternate names for some of these, such as “Almost Sure”. Including those would be helpful for people who learned them that way (me, at least).

  2. John says:

    Thanks. I fixed the typo.

    The solid arrows from A to B means that if a sequence converges with definition A, it also converges with definition B. A dashed arrow means that if a sequence converges under definition A, there exists a subsequence that converges under definition B.

    I mention probability terminology at the bottom, e.g. almost sure for almost everywhere, convergence in probability for convergence in measure, etc.

  3. Bryan says:

    I like these diagrams. I wish they had more of these sorts of things in textbooks.

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