The Bayesian believes that probability represents our beliefs about the world. The Frequentist believes that probabilities merely represent the long term frequency counts of events.
>The Bayesian believes that probability represents our beliefs about the world.
But what if our beliefs differ?
On several occasions, while tutoring friends who were taking introductory probability, they'd be posed with a HW problem. They would compute the answer in two different ways, and occasionally get two different answers. Both methods seemed correct to them, but they were not - one was always wrong. I used to argue with them about their reasoning on the incorrect answer, but it didn't help much.
What did help? Just doing the homework problem in real life, with a reasonable number of samples. It could be literally in real life or through a computer simulation. The result would always closely agree with one of the answers.
That's why I like frequentist statistics. It gives me a way to settle the answer outside of my own belief system.
If you have different beliefs than you'll have different probability distributions. There's nothing wrong with that.
Subject to a few technical requirements (basically absolute continuity of priors), it's a theorem in that your posteriors will eventually converge as more evidence is gathered.
That's why I like frequentist statistics. It gives me a way to settle the answer outside of my own belief system.
Can you explain this? To me this makes no sense - as a Bayesian I run simulations too.
But what if our beliefs differ?
On several occasions, while tutoring friends who were taking introductory probability, they'd be posed with a HW problem. They would compute the answer in two different ways, and occasionally get two different answers. Both methods seemed correct to them, but they were not - one was always wrong. I used to argue with them about their reasoning on the incorrect answer, but it didn't help much.
What did help? Just doing the homework problem in real life, with a reasonable number of samples. It could be literally in real life or through a computer simulation. The result would always closely agree with one of the answers.
That's why I like frequentist statistics. It gives me a way to settle the answer outside of my own belief system.