The two examples you give (Bayesian statistics and calculus) are very good ones, I would definitely recommend becoming familiar with these. I am not sure how much is covered by the 'calculus' label, but I would recommend trying to understand on a gut level what a differential equation means (this is simpler than it might sound. Solving them, on the other hand, is hard and often tedious). I believe vector calculus (linear algebra) and the combination with differential equations (linear ODE's of dimension at least two) are also covered by 'calculus'? Again having the ability to solve them isn't that important in most fields (in my limited experience), but grasping what exactly is happening is very valuable.
If you are wholly unfamiliar with statistics then I would also advice looking into frequentist statistics after having studied the Bayesian statistics - frequentist tools provide very accurate and easily computable approximations to the Bayesian inference, and being able to recognise/use these is useful in most sciences (from social science all the way to theoretical physics).
I would advise looking into frequentist statistics before studying Bayesian statistics. Inference done under Bayesian statistics is curiously silent about anything besides the posterior probability, including whether the model makes sense for the data, whether the knowledge gained about the model is likely to match reality, etc. Frequentist concepts like consistency, coverage probability, ancillarity, model checking, etc., don't just apply to frequentist estimation; they can be used to asses and justify Bayesian procedures.
If anything, Bayesian statistics ...
I have started to put together a sort of curriculum for learning the subjects that lend themselves to rationality. It includes things like experimental methodology and cognitive psychology (obviously), along with "support disciplines" like computer science and economics. I think (though maybe I'm wrong) that mathematics is one of the most important things to understand.
Eliezer said in the simple math of everything:
I want to have access to outlook-changing insights. So, what math do I need to know? What are the generally applicable mathematical principles that are most worth learning? The above quote seems to indicate at least calculus, and everyone is a fan of Bayesian statistics (which I know little about).
Secondarily, what are some of the most important of that "drop-dead basic fundamental embarrassingly simple mathematics" from different fields? What fields are mathematically based, other than physics and evolutionary biology, and economics?
What is the most important math for an educated person to be familiar with?
As someone who took an honors calculus class in high school, liked it, and did alright in the class, but who has probably forgotten most of it by now and needs to relearn it, how should I go about learning that math?