Statistics is a big field. At the highest level, we can organize concepts under the frequentist or Bayesian schools of thought, but the concepts that we might typically use to differentiate the two aren't the aims of performing an analysis. Instead, the differences tend to be philosophical. At the most fundamental level, for example, frequentists interpret the probability of an event as being an expression of the relative proportion of times that an event occurs if the "experiment" is repeated an infinite number of times. Alternatively, Bayesians view probability as measuring one's beliefs that an event will occur---how we quanity this precisely is difficult, I think, and might be an interesting topic to explore in another post.
To return to the idea that the aim of an analysis is not what differentiates frequentist from Bayesian statistics, I think it's natural to ask the following two questions. First, how can we match or equate procedures in the two camps that are essentially answering the same inferential questions? And second, how do the philosophical differences that I outlined above affect the mathematical analyses that support the procedures, and what assumptions are we implicitly accepting as a result? In this essay, I'll be exploring these two questions, and at the end I'd like to reflect on which set of assumptions are more appropriate for problems typically solved by computer scientists working in machine learning. This will be a living document, and will be updated as I continue to read and reevaluate my understanding.