Statistical inference
=====================

This page is a draft.


Some discussions about a good book: 

   - [Math Overflow: Statistics for Mathematicians](https://mathoverflow.net/questions/31655/statistics-for-mathematicians)
   - [Stack Exchange: What to learn after Casella/Berger](https://stats.stackexchange.com/questions/91863/what-to-learn-after-casella-berger)

Topics
------

Review of probability:

- random variables, outcomes, probability
- distributions, pdf/cdf

Mathematic statistics itself:

- idea: learn about data generating process (DGP) from a sample
- sample/realisation as a random vector 
- statistic as a function of sample 
- parameter inference: 
   - point estimation and methods (estimators)  
   - estimator quality (bias, consistency, efficiency)
- confidence intervals (CI)
- hypothesis testing (HT), types of errors
- analysis of variance and regression 


See an example of [stated learning objectives](http://comet.lehman.cuny.edu/owen/teaching/mat327/syllabus_mat327_782_2018fa.pdf)


<!--

https://www.amazon.com/Statistical-Inference-Monographs-Statistics-Probability-ebook/dp/B076M4Q3WH/ref=sr_1_fkmrnull_1?keywords=S.D.+Silvey&qid=1557747351&s=gateway&sr=8-1-fkmrnull

----------

May buy:

https://www.amazon.com/gp/offer-listing/052100618X/ref=dp_olp_all_mbc?ie=UTF8&condition=all

----------

Programming:

- [R infer package](https://infer.netlify.com/): 
- [Julia - Statistical Primer]https://people.smp.uq.edu.au/YoniNazarathy/julia-stats/exploring-julia-a-statistical-primer-DRAFT.pdf

----------

Modern Applied Statistics with S. Venables & Ripley.
http://www.bagualu.net/wordpress/wp-content/uploads/2015/10/Modern_Applied_Statistics_With_S.pdf

+ MASS package.

----------

http://greenteapress.com/thinkstats/thinkstats.pdf

I  also  used  two  books,  David  MacKay’sInformation  Theory,  In-ference, and Learning Algorithms, which is the book that got me hooked onBayesian statistics, and Press et al.’sNumerical Recipes in C. But both booksare available online, so I don’t feel too bad
-->

Key textbook
------------

Casella, Berger. Statistical Inference.   
   - [link](https://fsalamri.files.wordpress.com/2015/02/casella_berger_statistical_inference1.pdf)


Other choices
-------------

Larry Wasserman. All of Statistics: A Concise Course in Statistical Inference 
    - [text 1](https://www.ic.unicamp.br/~wainer/cursos/1s2013/ml/livro.pdf)
    - [text 2](http://static.stevereads.com/papers_to_read/all_of_statistics.pdf)
    - [Amazon](https://www.amazon.com/All-Statistics-Statistical-Inference-Springer/dp/0387402721) 


Efron, Hastie. Computer Age Statistical Inference: Algorithms, Evidence and Data Science.
    - https://web.stanford.edu/~hastie/CASI_files/PDF/casi.pdf


Supplements
-----------

[James Gentle. A theory of statistics.](https://mason.gmu.edu/~jgentle/books/MathStat.pdf)

[De Groot and Shervish](http://professor.ufabc.edu.br/~nelson.faustino/Ensino/IPE2016/Livros/Morris%20H%20DeGroot_%20Mark%20J%20Schervish-Probability%20and%20statistics-Pearson%20Education%20%20(2012)%20(1).pdf)

[Herman J. Bierens. Introduction to the Mathematical and Statistical Foundations of Econometrics](https://bit.ly/2zWyyff)


Aris Spanos. Probability Theory and Statistical Inference: Econometric Modeling
with Observational Data.   
    - [link](https://wilfridomtz.files.wordpress.com/2014/08/cambridge-university-press-probability-theory-and-statistical-inference-842pg.pdf)


[Probability and Statistics for Engineers and Scientists (PSES)][PSES]

[PSES]: https://fac.ksu.edu.sa/sites/default/files/probability_and_statistics_for_engineers_and_scientisst.pdf

<!--
Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, Keying Ye
-->

Other reading
-------------

Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars   
    - [Amazon](https://www.amazon.com/Statistical-Inference-Severe-Testing-Statistics/dp/1107664640)
    - very philosophic reading

Peter M. Aronow, Benjamin T. Miller. Foundations of Agnostic Statistics. 
    - [Google Book (fragments)](https://books.google.ru/books?id=u1N-DwAAQBAJ&printsec=frontcover&hl=ru&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false)
    - [book proposal](http://aronow.research.yale.edu/aronowmillerproposal.pdf)
    - simplictic


Papers
------

[Statistical Inference:  The Big Picture. Robert E. Kass (2006)](http://static.stevereads.com/papers_to_read/statistical_inference_the_big_picture.pdf)

[A short history of probability theory and its applications.
International Journal of Mathematical Education. January 2015. Kanadpriya Basu.](https://www.researchgate.net/publication/271856948_A_short_history_of_probability_theory_and_its_applications)


Video
-----

Placeholder:

- [Andrew Gelman - Theoretical Statistics is the Theory of Applied Statistics: How to Think About What We Do](https://www.youtube.com/watch?v=cuE9eHSbjNI)
- [Andrew Gelman - Solve All Your Statistics Problems Using P-Values](https://www.youtube.com/watch?v=ZmbrsbYwRWw)
- [Andrew Gelman - Barcelona Data Science Meeting](https://www.youtube.com/watch?v=K7e7IHdU1Q4)
- [Andrew Gelman - Crimes against data, Professor Andrew Gelman](https://www.youtube.com/watch?v=KS3yPw91iC0)

In Russian
----------

[Cramer, 1946, Russian translation](http://cyber.sibsutis.ru:82/Monarev/docs/nauka/MV_Probability/MVsa_Statistics%20and%20applications/0417.Kramer-Matem_Metodi_Statistiki.pdf), timeless! also has dataset if wheat yeilds.

Also concise version of lectures [here (in Russian)](http://math.csu.ru/new_files/students/lectures/teor_ver/solovev_teor_ver.pdf)