I took one course in statistics. I didn't enjoy it, though the ideas in it could have been interesting, the presentation of them was not.
I came across a video by Cassie Kozyrkov that asks "What if I told you I can show you the difference between Bayesian and Frequentist statistics with one single coin toss?" Cassie is a data scientist and statistician. She founded the field of Decision Intelligence at Google, where she serves as Chief Decision Scientist. She has another one of those jobs that didn't exist in my time of making career decisions.
Most of probably had some math teacher use a coin toss to illustrate simple probability. I'm going to toss this quarter. What are the odd that it is heads-up? 50/50. The simple lesson is that even if it has come up tails 6 times in a row the odds for toss 7 is still 50/50.
But after she tosses it and covers it, she asks what is the probability that the coin in my palm is up heads now? She says that the answer you give in that moment is a strong hint about whether you’re inclined towards Bayesian or Frequentist thinking.
The Frequentist: “There’s no probability about it. I may not know the answer, but that doesn’t change the fact that if the coin is heads-up, the probability is 100%, and if the coin is tails-up, the probability is 0%.”
The Bayesian: “For me, the probability is 50% and for you, it’s whatever it is for you.”
Cassie's video about this goes much deeper - too deep for my current interests. However, I am intrigued by the idea that if the parameter may not be a random variable (Frequentist) you can consider your ability to get the right answer, but if you let the parameter be a random variable (Bayesian), there's no longer any notion of right and wrong. She says, "If there’s no such thing as a fixed right answer, there’s no such thing as getting it wrong."
I'll let that hang in the air here for you to consider.
If you do have an interest to go deeper, try:
Frequentist vs Bayesian fight - your questions answered
An 8 minute statistics intro
Statistical Thinking playlist
Controversy about p-values (p as in probabllity)
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