Statistical foundations/theory book recommendation(s)

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After what feels like an eternity helping out at the intensive care unit with Covid-19 patients, I now get a long break, both from clinical and having completed my medical studies.

I am very lucky to have 2 months break and I want to use that period to invest in my statistical knowledge, or specifically, foundations/theories of medical Statistics - I know I shall not be a statistician, but I want to understand the basics (maths was never a problem for me, and I find formulas beautiful).

I am currently not sure which of these two books to buy and hence I thought that it might be better to tap into the collective expertise from this wonderful group (are there perhaps better books, in which case am very open to your suggestion). Would you recommend any? or perhaps others?

Introduction to Mathematical Statistics

The Foundations of Statistics

PS: I have read and own a copy of the RMS book.

Thank you and have a nice weekend!

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The perspective you take will impact what you need in a foundation. Think about David Spiegelhalter’s Art of Statistics, Richard McElreath’s Statistical Rethinking, and Richard Royal Statistical Evidence. For an introduction to the latter, go to Blume’s blog.

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I found the book “Foundations of agnostic statistics” very useful in terms of its emphasis on assumptions underlying frequentist inference

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this looks interesting as a general reference: Table of Contents | The Book of Statistical Proofs, "Purpose of the project is to build “a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences”
re books for stats in medicine with equations, there are so many eg https://www.amazon.co.uk/Mathematical-Statistics-Data-Analysis-John/dp/0534209343, I can’t think of a stand out, definitely benefit in reading multiple books/authors

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You will likely need to re-teach yourself the underlying math if you have never had a mathematical analysis course, but the text by Mark Schervish titled Theory of Statistics would seem to cover any topic you could possibly need. Both Bayesian and Frequentist perspectives are presented.

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