Probability and Conditional Expectation
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A reader's letter about the book "Probability and Conditional Expectation"

Dear Prof. Steyer,

I hope you are doing well. I am writing this email to you in order to express my gratitude for writing your book titled "Probability and Conditional Expectation - Fundamentals for the Empirical Sciences". I cannot tell you how much this book has helped me in my quest to better understand statistical inference.

As a software engineer working towards a career in applied statistics and without a rigorous research background, I have always found there to be a gap between Probability Theory and Statistics. Most books focus on one of the two areas but don't really illuminate the connection between the two domains. I found that your book does this masterfully. There have been so many instances while reading your book when I have marveled at the simplicity with which you disentangle topics that I have historically found difficult to understand. (E.g. the way you explain conditional expectations with the help of sigma algebras). I also think that the arrangement of the book (with the initial chapters dedicated to Measure Theory) is particularly well suited for gaining a solid understanding of the material.

I want to congratulate you on writing a wonderful book that I am sure many have found (and will continue to find) helpful. I, for one, will definitely do my best to let this book be known among my peers.

I currently work as a Data Scientist in San Francisco. As part of my work (and also for the pure joy of acquisition of knowledge), I am required to read literature and learn new ideas in the fields of Statistical Inference and Machine Learning. While I do have a fairly quantitative background (BS in Civil Engineering, MS in Operations Research and work experience in Software Engineering), my official training in statistics has been rather superficial, with more focus on application rather than understanding of the underlying principles. I have always felt that this approach was backwards. I was looking to strengthen my grasp of theoretical foundations of probability before jumping to applications.

When scouring the internet searching for the right sources of information, I found that a lot of literature is dedicated to estimation of model parameters under some conditions. But it doesn't talk about what it is that we are estimating, precisely. I felt like the idea of Conditional Expectations needed a more complete treatment from a theoretical standpoint before applying it to any kind of estimation. I was specifically searching the internet for a text that was accessible without compromising on mathematical rigor. That is how I found your book on I read the blurb and had a very strong feeling that the book would provide exactly what I needed. And I was not disappointed!

After completing your book, I am now reading Alan Agresti's book on Generalized Linear Models (that you recommend in your book). I cannot tell you how natural and accessible everything in that book seems, now that I have a decent grasp of E(Y | X). In the past, I have picked up many a book on estimation only to feel frustrated and quit. After reading your book, this is no longer the case!

Thank you again,
Ayush Bharadwaj

Probability and Conditional Expectation

Book "Probability and Conditional Expectation"

Rolf Steyer & Werner Nagel

Wiley, April 2017