What is Reddit's opinion of Regression Modeling Strategies: With Applications to Linear Models, Logistic and Ordinal Regression, and Survival Analysis (Springer Series in Statistics)?

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That's only one area of nonparametric. Nonparametric models are important for small data too where you don't or can't assume a distribution.

But I do agree with your sentiment that having a CI for your prediction is important.

To be fair to ML, there are area where they are very good at and that's data with low noises (images, NLP, etc..). I believe Frank Harrell's book Regression Modeling Strategies talk about this and his view on ML.

I also believe ASA have talk about how to augment ML with statistic for their goal for 2020.

If I can find ASA's post I'll update this post.

I don't know if this fall under nonparametric models but bootstrap get the distribution from data and not some assume distribution. It's certainly nonparametric technique at least. There are situation where bootstrap would be better than it's parametric counterpart.

A couple of initial questions to better inform recommendations:

1. Have you ever taken a probability/statistics course, or are you planning to entirely self-study?
2. Which programming languages do you know and use at a proficient level? I ask because this will be crucial for finding a biostats/stats job. Ideally, you should aim to gain some experience with R, Python, SQL, SAS etc. The choice of which programming language(s) you should focus on depends on the types of jobs you are targeting. SAS gets a lot of hate on this subreddit, but it is quite commonly the tool of choice for biostats. Stata is also used in some biostats teams too, albeit not nearly as common as SAS and R. You should start searching for biostats/stats job to gain a better sense of the common requirements, as they typically list the desired programming applications.

Yes, I think Casella/Berger would be a good start. However, this just scratches the surface... Again, depending on the specific jobs you are targeting, that would help inform which books to read. For biostats, I would recommend Regression Modeling Strategies by Frank Harrell. In general, it would be helpful to also read through an applied regression textbook, such as Kutner et al. Honestly, there are so many books which could be recommended. Once you provide some additional details (more specifics on your background in stats and target jobs), I am happy to follow-up with more recommendations.

I really like the Gelman text as well but honestly, I have begun to prefer Regression Modeling Strategies from Harrell, Jr. This book focuses on the "Hmisc" package and the 2nd edition was released within the last couple of years.