This page mostly exists to collect a good selection of overview statistics introductions that are not terrible.
I’m especially interested in modern fusion methods that harmonise what we would call *statistics* and *machine learning* methods, and the unnecessary terminological confusion between those systems.

Here are some recommended courses to get started if you don’t know what you’re doing.

See also the recommended texts below. May I draw your attention especially to Kroese et al. (2019), which I proof-read for my supervisor Zdravko Botev, and enjoyed greatly? It smoothly bridges non-statistics mathematicians into applied statistics, without being excruciating, unlike layperson introductions.

There are also statistics podcasts.

Cox, D. R., and D. V. Hinkley. 2000. *Theoretical Statistics*. Boca Raton: Chapman & Hall/CRC.

Dadkhah, Kamran. 2011. *Foundations of Mathematical and Computational Economics*.

Devroye, Luc, László Györfi, and Gábor Lugosi. 1996. *A Probabilistic Theory of Pattern Recognition*. New York: Springer. http://www.szit.bme.hu/~gyorfi/pbook.pdf.

Efron, Bradley, and Trevor Hastie. 2016. *Computer Age Statistical Inference: Algorithms, Evidence, and Data Science*. Institute of Mathematical Statistics Monographs. New York, NY: Cambridge University Press.

Gelman, Andrew, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, and Donald B. Rubin. 2013. *Bayesian Data Analysis*. 3 edition. Chapman & Hall/CRC Texts in Statistical Science. Boca Raton: Chapman and Hall/CRC.

Guttman, Louis. 1977. “What Is Not What in Statistics.” *Journal of the Royal Statistical Society. Series D (the Statistician)* 26 (2): 81–107. https://doi.org/10.2307/2987957.

Guttorp, Peter. 1995. *Stochastic Modeling of Scientific Data*. 1. ed. Stochastic Modeling Series. London: Chapman & Hall.

Hastie, Trevor, Robert Tibshirani, and Jerome Friedman. 2009. *The Elements of Statistical Learning: Data Mining, Inference and Prediction*. Springer.

Kobayashi, Hisashi, Brian L. Mark, and William Turin. 2011. *Probability, Random Processes, and Statistical Analysis: Applications to Communications, Signal Processing, Queueing Theory and Mathematical Finance*. Cambridge University Press.

Kroese, Dirk P., Zdravko I. Botev, Thomas Taimre, and Radislav Vaisman. 2019. *Mathematical and Statistical Methods for Data Science and Machine Learning*. First edition. Chapman & Hall/CRC Machine Learning & Pattern Recognition. Boca Raton: CRC Press.

Lehmann, E. L., and George Casella. 1998. *Theory of Point Estimation*. 2nd ed. Springer Texts in Statistics. New York: Springer.

Lehmann, Erich L., and Joseph P. Romano. 2010. *Testing Statistical Hypotheses*. 3. ed. Springer Texts in Statistics. New York, NY: Springer.

Mohri, Mehryar, Afshin Rostamizadeh, and Ameet Talwalkar. 2018. *Foundations of Machine Learning*. Second edition. Adaptive Computation and Machine Learning. Cambridge, Massachusetts: The MIT Press.

Murphy, Kevin P. 2012. *Machine Learning: A Probabilistic Perspective*. 1 edition. Adaptive Computation and Machine Learning Series. Cambridge, MA: MIT Press.

Robert, Christian P., and George Casella. 2004. *Monte Carlo Statistical Methods*. 2nd ed. Springer Texts in Statistics. New York: Springer.

Schervish, Mark J. 2012. *Theory of Statistics*. Springer Series in Statistics. New York, NY: Springer Science & Business Media. https://doi.org/10.1007/978-1-4612-4250-5_1.

Vaart, Aad W. van der. 2007. *Asymptotic Statistics*. 1. paperback ed., 8. printing. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge: Cambridge Univ. Press.

Wasserman, Larry. 2013. *All of Statistics: A Concise Course in Statistical Inference*. Springer.