A Crash Course in Causality
Inferring Causal Effects from Observational Data

https://www.coursera.org/learn/crash-course-in-causality

http://bayes.cs.ucla.edu/home.htm

Take a look at below course

https://www.coursera.org/learn/crash-course-in-causality#syllabus

This course helps in analyzing observational data using ab testing concepts and some advanced techniques. Not sure if this is the path you want to take!

This might be a good place to start: https://www.coursera.org/learn/crash-course-in-causality/

Well yea the Pearl stuff but I have also seen the modern statistical literature and courses like on Coursera get into DAGs. The courses like on Coursera taught by biostat people like this one: https://www.coursera.org/learn/crash-course-in-causality don’t do the coding of DAGs but they just use them as a visual device on paper.

But on paper can only get you so far. When it comes to real data you need to represent the DAG in code and maximize the likelihood over the graph structure.

I don’t know how its done without DAGs though except in designed experiments where the DAG would be obvious anyways. In that case lm() and glm() et al would suffice.

I come from medical backgrounds and most causal inference research been done by epidemiologists (where observarional data is the only avilable evidence to guide decisions due to feasibility or ethical reasons) with strong skills in biostatistics. I found this course online and seems like a nice introduction to the subject with topics such as counterfactual outcomes and Directed Acyclic Graphs. I also couldn't recommend Miguel Hernan's book enough as other posters have stated, it is a great resource (and it's free). Since you have a pure math background you shouldn't have a problem with the book; however, I think you would get the most out of it by first reading an introductory book on epimiology to get the gist of some basic concepts as confounding, selection bias, exchangbility, etc.

https://www.coursera.org/learn/crash-course-in-causality

This can get you started:

https://www.coursera.org/learn/crash-course-in-causality

I think that's a fair thing to learn - I would probably suggest breaking it down into smaller components instead of just taking an umbrella course like this (alternatively, if you have money and time to spare, this is probably going to be a solid intro - but I think you need to take it a few steps further.)

• Experimental/Study Design/Hypothesis testing

https://www.khanacademy.org/math/statistics-probability/designing-studies

• Statistical Sampling

Don't know a good moog for this one sorry, although I always recommend the GOAT statistical course/books:

Introduction to Statistical Learning/Elements of Statistical Learning

https://lagunita.stanford.edu/courses/HumanitiesSciences/StatLearning/Winter2016/about

• Statistical Inference

https://www.coursera.org/learn/statistical-inference

• Causal Inference

https://www.coursera.org/learn/crash-course-in-causality

I think a lot this is covered in the following specialization:

https://www.coursera.org/specializations/jhu-data-science?utm_medium=listingPage#courses

https://www.youtube.com/watch?v=r5WBnAw8B4E&t=3s

video's author recommends this course in a comment: https://www.coursera.org/learn/crash-course-in-causality
and he also co-created this library: https://github.com/uber/causalml

I'm not an expert on experiments as I focus more on business and financial markets applications. For marketing we sometimes care about causality and other times more about prediction. The problem with traditional econometrics is it depends quite heavily (in undergrad course) on strong assumptions about the data generating process, which are likely not true in real life.

One of the standard books is Wooldridge, Econometric Analysis of Cross Section and Panel Data (he also has a more introductory book). There supporting websites with accompanying material in R and Python (by others, not the author).

To get away from this mindset, books like Gelman and McElreath (Statistical Rethinking) are good. Another more detailed (in terms of the math) is Shalizi's Advanced Data Analysis from an Elementary Point of View (free at http://www.stat.cmu.edu/\~cshalizi/ADAfaEPoV/). A somewhat easier, but less comprehensive book is Foundations of Agnostic Statistics (https://www.cambridge.org/core/books/foundations-of-agnostic-statistics/684756357E7E9B3DFF0A8157FB2DCECA)

Moving to more predictive models (and less causal analysis), the second edition of the classic Intro to Statistical Learning is excellent. It will allow you to handle way more cases than what you can do with the traditional econometrician's toolkit. Highly highly recommended. (The examples are in R, which will help you learn that if you don't already know it.)

https://www.statlearning.com

Another book, with a more business orientation, is Taddy's https://www.amazon.com/Business-Data-Science-Combining-Accelerate/dp/1260452778

For books specifically covering causal analysis, I would look at:

- Pearl, Book of Why (more introduction, less technical)

- Angrist, Pischke, Mostly Harmless Econometrics (excellent if you are focused on policy studies, but well worth a read for anyone interested in causal analysis)

- Morgan, Winship, Counterfactuals and Causal Inference (much more in-depth)

- Pearl, Causality (this is the bible from one of the key researchers in the field)

The causal revolution has gone mainstream in the last 20 years so there are starting to be more intro courses online. For example, https://www.coursera.org/learn/crash-course-in-causality

These should get you started.