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Comment by RobertRoberts | Hacker News Reader

Thanks for this explanation, it certainly expels some of my confusion.

It seems then based on your reply that my friend is possibly wrong for invoking Bayesian theory regarding the Monty Hall problem for the exact reason he claimed it was the only answer? (note, my friend is a brilliant person and dedicated engineer who understands math far above my level. I only program with statistics and the PhD's tell me what to do.)

In other words, his argument is incorrect in his assessment because we actually _do_ have previous knowledge? (He pointed out that Bayes theorum was used for analysing insurance premiums for new kinds of insurance because there was no previous data to work with, which fits with your statement.)

This seems like too easy an answer for him to have missed, which makes me suspect of my understanding of your reply.

(yes, my initial question was serious, I appreciate you replying)

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Not only do we have previous knowledge, we know basically everything about what's going on. You only use Bayesian inference if there is something you don't know which can't be computed from the things you do know. Then, after doing an experiment, you work backwards to figure out the value of the things you didn't know.

Don't confuse Bayesian inference with Bayes' theorem, which is a theorem that doesn't have any philosophy attached to it. Bayesian inference makes use of this theorem on top of some philosophical assumptions, which may be questionable depending on how you use them.

Bayesian inference also requires you to give your "prior" beliefs, which are the beliefs you have before you do the experiment. If these beliefs are strongly biased away from the right answer, you will get Garbage Out.

Ok, that is really neat. I need to read more about this. I just did some searching on bayesian interference solution for the monty hall problem. And I am guessing they are applying the math whilst pretending to not have foreknowledge of the outcome?

https://sc5.io/posts/how-to-solve-the-monty-hall-problem-usi...

I certainly don't expect you to research this or explain every detail for me, I may have to take a class on this subject after I retire to satisfy my need to grasp this. Thank you for time, this was enlightening.

just to chime in. The monty-hall problem is a pure math (probability-theory) and not statistics-excersize, since we know all the probabilities beforehand and don't estimate.

It's very important to distinguish between bayesian inference and the bayesian theorem. The bayesian theorem can be proven and therefore must be true (if we accept the axioms). Bayesian inference has some real philosophical problems, since we often have no way to choose a justified prior. Frequentists approaches may also use the Bayesian theorem.

I always like the blog-posts of the angry statistician and he also has one about the monty-hall problem: http://angrystatistician.blogspot.com/2012/06/bayes-solution...

The important difference is that one is the probability of P(x == car), which is 1/3, and one is P(x == car | y == goat). Just apply the bayes theorem and calculate it yourself!

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