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Question: Does anyone have a recommendation for a reference which is "the most accessible" introduction to directional statistics?

When I say "accessible", I mean that many authors are so experienced and knowledgeable in their field that they often take for granted things which are confusing for newcomers. Thus, if there is an introductory book to directional statistics (statistics of observations on compact Riemannian manifolds) which mostly avoids this pitfall I would like to know.

However, any recommendation for which the answerer can provide a 1-2 sentence explanation would be helpful, at least I imagine.

As for prerequisites, I know basic differential and Riemannian geometry, as well as basic statistics. However, I am not a complete expert, so any reference which explains any of that material again would not be problematic for me.

Also, as an ancillary question, how much does knowledge of information geometry overlap with directional statistics? I know that both involve applications of (Riemannian) geometry to statistical questions, but that's about it.

Attempt: The following (non-article) references can be found on Wikipedia -- I have no idea how useful or unhelpful they are for beginners, however:

  • Batschelet, E. Circular statistics in biology, Academic Press, London, 1981. ISBN 0-12-081050-6.
  • Fisher, NI., Statistical Analysis of Circular Data, Cambridge University Press, 1993. ISBN 0-521-35018-2
  • Fisher, NI., Lewis, T., Embleton, BJJ. Statistical Analysis of Spherical Data, Cambridge University Press, 1993. ISBN 0-521-45699-1
  • Mardia, KV. and Jupp P., Directional Statistics (2nd edition), John Wiley and Sons Ltd., 2000. ISBN 0-471-95333-4
  • Downs, (1972) Orientational statistics. Biometrika, 59, 665–676

Mardia and Jupp's book is also mentioned in this MathOverflow post.

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Batschelet is a very friendly and rich book but inevitably a little dated. It covers a lot of ground.

I find the books first authored by Fisher to have the best overall blend of statistical and scientific thinking. Fisher is best on several modern approaches, including graphics, bootstrapping and modelling.

The book by Mardia and Jupp makes stronger assumptions about readers' mathematical knowledge but does include a sprinkling of examples based on real data.

All of these books are usefully complementary.

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