# Introduction

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.