Introduction to mathematical statistics

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1. luhbegMay 2022
   High-school dropout with a phd in a social science here. My grades weren’t good enough to study math during undergrad and I was dealing with a chronic illness that meant I didn’t have my shit together enough to transfer into a useful degree either. I’m a machine learning scientist at a company you’ve heard of and probably spent money on (not FAANG). Math is a big part of my day job.

   Here’s what I did to learn math. I wouldn’t recommend this path. You will have a much easier time getting a job with a quantitative degree. You’re only 26, so you can go back to school without really losing much time. If you must do it this way, do the exercises, do the exercises, do the exercises, build a portfolio, and do the exercises.

   Calculus/Analysis

   Stewart single var calculus, then the multivar book. These are easy starters

   Real analysis: Series, Functions of Several Variables, and Applications. Miklós Laczkovich, Vera T. Sós

   Spivak Calc and Calc on Manifolds books

   Bonus: Advanced Calculus A Geometric View, Callahan. This is what I turn to when I want to punish myself or remind myself how certain analysis proofs go.

   Linear Algebra

   Strang, Intro to LA is great. Start with this one

   Strang, LA and learning from data. Will be tough without the first book

   Stats

   Hogg, Introduction to Mathematical Statistics

   Gelman et al, BDA3 for Bayes

   ML

   Bishop PRML and Elements of statistical learning. Do the exercises. Build the algos in Python.

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2. _eigenfooJul 2018
   If you're looking for just mathematical statistics, I liked Hogg McKean and Craig's "Introduction to Mathematical Statistics" (4th edition was much better than the ones after it, imo).

   But if you're looking to learn prob/stats for applications to ML, most ML textbooks have a chapter or two reviewing the relevant stuff. I liked the first two chapters of Bishop's PRML for that.

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3. stanleydrewAug 2009
   I highly recommend Hayashi's book on Econometrics. It's what we used in the first year of my PhD program in Economics. But it's probably worth starting with a basic probability and statistics book, preferably one that's pretty mathematical. I've used Hogg McKean and Craig's Introduction to Mathematical Statistics and it's really good.
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4. disgruntledphd2May 2025
   Basically all of the Andrew Gelman books are also good.

   Data Analysis... https://sites.stat.columbia.edu/gelman/arm/ Regression and Other Stories: https://avehtari.github.io/ROS-Examples/

   Wasserman's All of Statistics is a really good introduction to mathematical statistics (the Gelman stuff above are more practically and analytically focused).

   But yeah, it would probably be easier to find a good statistics course at a local university and try to audit it or do it at night.

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5. gololMar 2024
   I feel like you must be a using a wrong approach to searching for mathematics. In your case I would search for a script or book with title "Introduction to probabilify theory" or "Introduction to mathematical statistics". Then you skim through it to see if you can find an analysis of your problem. If not, you can hopefully find out what the right keywords are to then find a more advanced script or book for the specific subfield your problem needs.
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6. LesabotsyAug 2020
   So I never really found a practical use for mathematics while I was in school, so I never really paid attention to it, basically just studied for grades. Now that I have some interest in ML, I have come to realize that I suck at math. Help me fix that, my ultimate goal being the ability to work through Bishop's Pattern Recognition and Machine Learning or being able to understand ML papers. I know I mostly need Probability, Statistics, Calculus and Linear Algebra. For now I'm studying precalc (Stewart). Next steps are:

   Probability: Introduction to Probability - Blitzstein & Hwang.

   Statistics: Introduction to Mathematical Statistics - Hogg & al.

   Calculus: Calculus, Early Transcendentals - James Stewart & al.

   Linear Algebra: Introduction to Linear Algebra - Gilbert Strang.

   What are your picks in those subject? Are these enough?

   Edit: preferably books that use the metric system.

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