Appendix A — Further reading
Throughout this handout, I provide references to papers that might be of interest to those of you who are more interested in a particular topic. I also mention some of the books below, which I think are of general interest. Reading some, or all, of the books below would be an excellent next step if you wish to further your statistical knowledge.
A course in the ‘advanced fundamentals’ of statistics, in the approximate order in which you should read them:
Bulmer MG, Principles of Statistics, Dover Books on Mathematics (1979).
This book covers the fundamentals of statistics in a remarkably approachable way. I cannot recommend it highly enough, and is the one you should start with. It contains no R code, or really anything practical that you can use in everyday statistics. Instead, it contains fundamental information about the bases of the methods you use. If you want a tutorial, go to Youtube, if you want understanding, read this.
Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A, and Rubin DB, Bayesian Data Analysis, CRC Press (2010).
The book on Bayesian statistics. Simply reading and truly understanding the first 100-ish pages would be sufficient to put you above the majority of ecologists who loudly profess to be Bayesians. An alternative that is more approachable might be Gelman and Hall’s similar book on hierarchical modeling, which expands less material into a similar page count but contains more pictures.
Edwards AWF, Likelihood, Johns Hopkins University Press (1992).
An opinionated (i.e., angry) and difficult read, but one that will reward you with a fundamental understanding of statistics. Do not read this first: it’s difficult, so come to it when you have a reasonable understanding of calculus and are feeling strong. Spend time understanding every page in depth: half an hour staring at an equation until it ‘clicks’ is worth the effort here.
…If you have made it this far, I would strongly encourage you to look into classical machine-learning methods in detail, since you will now be able to appreciate the extent to which they are often deeply routed in fundamental theory.
A set of books to dip into for ‘those tricky problems’:
Faraway JJ, Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models, CRC Press (2005).
My secret weapon while a graduate student: this book is a pot-luck of approaches that you can dip through to find an entry-point into many a difficult problem. Always worth having a copy on-hand somewhere ‘just in case’…
Zuur A, Leno EN, Walker N, Saveliev AA, and Smith GM, Mixed Effects Models and Extensions in Ecology with R, Springer (2009).
If you ever need to get a mixed-effects (or temporal, or spatial) model past a reviewer, simply crack this open, follow the algorithm it suggests, and cite the book. Invaluable for that, although you know by now how I feel about mixed effects models…
Crawley MK, The R Book, Wiley (2012).
Everything’s in here, and everything has remarkably succinct R code showing how to use it. This is the only one of the books above that I take down from the shelf in my office.
A course in advanced machine learning is a bit trickier to recommend because, as outlined in your course, there really isn’t such a thing as machine learning. For the classical methods, there is no better source than ‘The Elements of Statistical Learning’ Hastie, Tibshirani, and Friedman; 2008 Springer. Amazingly, the authors have also released the book online for free 1 and so you can download it guilt-free right now. It is an intimidating book, and so if you want a slightly gentler introduction (and I would not blame you!) many of the same authors have written ‘An Introduction to Statistical Learning’ (James, Witten, Hastie, and Tibshirani; 2013 Springer with a new edition coming soon) which has chapters that are directly analogous to its parent book such that you can flip between them at will (perhaps leaning on the latter for more R examples). This second book is also released online for free 2.
Artificial neural networks are covered very nicely in the above books, but they don’t go into as much detail about deep learning as might be ideal. There are very few good books on deep learning, in part because the field is expanding so rapidly, but also because there are so many expanding software packages and most resources focus on those rather than the actual underlying concepts. With those pieces of software changing so rapidly, it can be difficult to make headway. ‘Deep Learning (Adaptive Computation and Machine Learning Series)’ (Goodfellow et al. 2017 MIT Press) is very popular, and is notable for covering a lot of concepts in linear algebra (which you now already know), but I personally find it to be very long and very unclear. I much prefer ‘Neural Networks and Deep Learning’ (Charu Aggarawal; 2018 Springer); it’s shorter, denser, and covers more (I think) than other books but is up-to-date and is much more intelligible. Personally, I think there are enough tutorials of how to use TensorFlow to be found online so your focus should be on concepts in books. The tutorials and examples on the website of the Keras website are brilliant and I think are superior to most other articles I’ve seen online; I hate learning from YouTube so I can’t recommend any videos I’m afraid.
In terms of practical examples of the use of ML methods, I strongly recommend ‘Machine Learning for Ecology and Sustainable Natural Resource Management’ (Eds. Humphries, Magness, and Huettmann; 2018 Springer) which you have available in the library. It’s an edited volume and has lots of examples; they’re obviously mixed in terms of quality, but broadly are good. ‘Methods in Ecology & Evolution’ (December 2020) also had a fantastic special issue recently on ML, which outlines techniques and their uses 3. There is also the symposium that I organised in 2021, whose recordings are shared on your course website.