Okay, so this isn’t much of a battle either as many statisticians nowadays adopt principles of both. Like when I started grad school, I was a frequentist with Bayesian tendencies but by working under my advisor who was a Bayesian with frequentist tendencies, I became a Bayesian with frequentist tendencies. So what is the difference between a frequentist and a Bayesian and is it like being Team Aniston vs. Team Jolie? Or Team Edward vs. Team Jacob? Or Team Randy vs. Team Anton? What? You’re not familiar with the last one? Well, you will be in a few years. Or at least just make my day and pretend you will be. That’d be terrific, thanks. Anyway, a frequentist bases his or her inferences on the data at hand and assumes that the parameters related to the data, i.e., values such as the mean, median, mode, and so on remain fixed, although the data could change. But a Bayesian might believe that the data will stay the same, although parameters might change, depending on how much more information we can gain from our data. So let’s say I go to bed and happen to have a Multiverser (a black box device that can transport me into any dimension as featured in Order of The Dimension, Revised Orders, and Final Orders) in my room and I want to determine the probability of me sleep walking into the black box and waking up in a dimension in Bermuda. I know … if only, right?
A frequentist will tell you that if I haven’t sleep walked into the black box yet, the probability is very small if not zero that I ever will. But if I do walk into that box in the future, he or she would argue that a higher probability of me doing so was always there. It was just underestimated because I’ve never done it before. But a Bayesian would say that if I was destined to sleep walk into the black box and wake up in Bermuda, I will sleep walk into the black box and wake up in Bermuda. And if that ever does happen, we can update the probability of that happening once it happens. So who’s right? Well, maybe they both are right and both are wrong. Maybe both data and parameters change or on the other hand, maybe they both stay the same. Take the discovery of gravitional waves as an example. Have the data pertaining to the waves changed or have modifications in our parameter estimations pertaining to cosmic data allowed us to discover them? Personally, I’ve come to the realization that although both data and parameters can be updated, it might be easier for us to observe changes in the parameters, thus leading me to become a Bayesian with frequentist tendencies. So that’s the current stance of Bayesian vs. frequentist thinking in a nutshell. Not really like Team Randy vs. Team Anton, but sort of. Although who would want to be Team Anton since he’s the villain? Well, I did have one reviewer who gave me a positive review (YAY!), who was definitely Team Anton. At one point, she also compared Anton to Pinky and The Brain. Which lead me to this HAWT image of these deep, dark, sexy hunks:
Well, anyway, join me next time when I discuss the Bayesian inference involved in Monte Carlo Marko chains and how they could be also used to create different dimensions. Just still hoping one chain takes me to a realm in Bermuda. Hey, sorry to sound like a broken record about that but have you heard about the winter in Chicago this year? Seriously, if you lived through it, don’t tell me you wouldn’t be obsessed with walking into a box and walking out on a tropical island. Really now.