Entering Maximum Likelihood Meltdown
It's not good, I've learned, when I substack, as venting is highly correlated to my frustration
So, I think that Maximum Likelihood Estimation stands to be a very challenging class. It is putting R at the center of comprehension, in part because simulations are more accurate than actual worked-out math, but also because the heart of estimation is these simulations. So I can't pretend the coding is happening in the background because it's part of the conceptual proof of concept (we're forgoing the analytical proofs, which I am weirdly sad about). Today, I spent a solid thirty minutes trying to debug my code below that I had copied*directly*from*the*textbook* - I had spelled “denom” wrong in one place, and so the code wasn’t working and it took me forever to figure this out.
I think I'd rather get ace on taking anti-derivatives under integrals than have to run simulations with logic games. Luckily, I have a tutor (yay Zayne!) so that should maybe help, but honestly, I need to be on top of the work to be able to be tutored, and if my head starts swimming… I shut down, and … well…wouldn’t you shut down?
Here's the issue for me with probability, generally. I’m just not a linear thinker in a mathy logic sense. Think the LSAT logic games - total bust for me. Everything else? Winner, winner, chicken dinner. Ask me why I didn’t go to law school? (Actually, I did, for five days, but a hurricane happened and I ran away to a PhD program, really).
So take this basic concept - let's take the classic birthday problem.
The goal is to see the number of people in the room where you've got a more than 50% likelihood of having two people with the same birthday. That is basically Maximum Likelihood in a nutshell - we have a sense of the likelihood but what are the elements needed to actually create that output? What number would give us the best chance of having two people in a room with the same birthday (~23).
In my universe, I see the probability as:
How many people (k) in one room have the same birthday?- so, like, the 1/365 and 1/365 would have to be the SAME 1/365 -> and then I get stuck. And then now you're asking me to program some simulation in R? I might collapse.
This is a question about factorials and sampling with replacement, but the hard part for me is the right way to set this up, which is the following:
P (at least two have the same bday) = 1 - P(nobody has same bday)
WHAT IS THIS BRAIN VOODOO??? I CAN'T SEE IT OR HEAR IT, I'M TOMMY PLAYING PINBALL BUT HAVE NO GAME! Also conditional probability expressed in formula terms makes my head hurt. I need it in English, not notation, but somehow the english (above) also doesn't make sense. Somehow, we get to this plot, which in turn, tells us something about probabilities of the birthday problem. And then I cry a little bit because I get confused reading the graph at first and initially am not sure why I now see a negative probability (nope, that’s just a cut line tricking my fragile brain). Anyway, onwards and upwards. Now seems like a GREAT time to do all the journal reviews I’ve promised to my friends ….