Mathematical and Statistical Resources

Statistical and mathematical analyses lay at the core of most of the work we produce as neuroscientists. Hence, it is not a surprise that, since undergraduate training, there is an emphasis on properly understanding concepts from these two disciplines. However, it still happens that we come across new analysis or methods that require us to expand our mathematical knowledge. Fortunately, the internet is full of great tutorials that can help us fill these gaps in knowledge.

This page provides a collection of resources we think are very useful for learning some of these skills:

Statistics

  • Statistics and Data Analysis in MATLAB by Kendrick Kay - Great comprehensive tutorial to get up to speed on statistics using MATLAB. It teaches you the core of statistics through interactive MATLAB exercises. Kendrick Kay is a very respected neuroscientist in the field of vision.

  • Statistical Concepts via Matlab by Jill O’Reilly - Similar to the one above. It provides an alternative on a comprehensive tutorial to navigate core statistical concepts using MATLAB.

  • Discovering Statistics Using R (Andy Field) - There is probably not a better book to learn the core statistical analysis performed in Experimental Psychology than Andy Field’s book. Clear explanations, together with exercises, will ensure you master all these skills in no time.

  • Multivariate analysis for the behavioral sciences (Vehkalahti) - Taking it a step further, this book covers statistical concepts in more depth, providing you with the necessary knowledge to flexibly adjust these concepts to your own analysis. It requires familiarity with statistical analysis to be understood.

Bayesian Focused

  • A Student’s Guide to Bayesian Statistics (Lambert) - If you want to expand your knowledge beyond frequentist statistics, this book is the perfect introduction to Bayesian statistics.
  • JASP Tutorials - JASP is a statistical analysis software focused on allowing you to do Bayesian statistics in an intuitive fashion. The creators of it, provide multiple explanations and tutorials on the different types of Bayesian (and frequentist) analysis you can perform using their software. It is also a great starting point if you are not looking to completely master Bayesian statistics.

EXTRA

Mixed Effects Models

This is a statistical analysis that focuses on more complex data structures. The main advantage of these models is that they can represent hierarchical dependencies in the data (e.g. datapoints from the same participant, but also participants from different groups, etc.). We have a page dedicated to this type of model in case you want to use it for your data. See here

Good Old Machine Learning

  • An Introduction to Statistical Learning - This book provides an accessible overview of the field of statistical learning, an essential toolset for making sense of the vast and complex data sets. Topics include linear regression, classification, resampling methods, shrinkage approaches, tree-based methods, support vector machines, clustering, and more. Highly recommended. They also have a version for applications in R and a version for Python.
    • The Elements of Statistical Learning - If you are mathematical savvy and want to dive deeper into the underlying mathematical equations behind some of the algorithms mentioned in the previous book, the same authors created a more advanced version of it to get the nitty gritty of what goes behind every statistical technique you use.
  • Pattern Recognition and Machine Learning - If you want to go even a step further, this is considered by many (especially in the AI field) as the best introduction to machine learning. It does require you to have a good mathematical foundation. Hence, if you want to dive into the field but not feel yet fully confident, we recommend trying one of the other two alternatives.

Mathematics

Linear Algebra

  • Mike Cohen’s Linear Algebra - Amazing resource to master linear algebra without any mathematical training. The link provided includes a large discount on the course
  • 3 Blue 1 Brown - Their series of linear algebra videos will help you develop a intuitive geometric understanding of core topics in linear algebra. We recommend their Youtube channel to understand mathematical concepts in general
  • Khan Academy - They are at the forefront of mathematical tutorials online. They provide clear explanations on a variety of topics, including linear algebra.
  • Mathematical Tools for Neuroscience by Ella Batty - a Python Jupyter notebook including interactive exercises to master the important concepts in linear algebra for neuroscience

Calculus

Probability Theory

  • MCMC sampling for dummies - amazing, hands-on Python tutorial on Markov Chain Monte Carlo with very clear explanations on the topic.

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