/sci/ - Science & Math

>>14681198

>>14535436
>elementary school interpretation of probability aka frequentist
ngmi

>>9304007
>>9304119
This is the problem with frequentist statistics. It does NOT represent probability, even though it really sounds like it should. It regularly confuses even experts. It was designed for a world that didn't have computers and doing the mathematically ideal calculations was impossible.

The problem is you are just assuming an arbitrary prior. Usually a VERY convenient prior that gives your hypothesis a high probability to start with.

Let's say you have a hypothesis that "green jelly beans cause cancer". Let's give this hypothesis a prior probability of 1 in 1 100,000. Why? Because the vast majority of random assertions like that are wrong. If more than 1% of random foods caused cancer, we would all be dead by now. And if you really believed that the probability was higher than 1% you would probably avoid eating them.

So a study is done and comes back with a p value of 0.05. Is there now a 5% that green jelly beans cause cancer? Let's do the calculation.

In 1 hypothetical world, green jelly beans cause cancer and in 99,999 hypothetical worlds they don't. Now in 5% of those 99,999 worlds, the same study comes back positive. And lets say it also does in the 1 jelly-beans-cause-cancer world. Now out of all the hypothetical worlds that have a positive study, 1 actually has jelly beans that cause cancer and 5,000. So the probability you exist in the world where jelly beans actually cause cancer is 0.02%.

This is why possibly the majority of scientific research is wrong. Certainly the majority of research with large p values.

The correct thing to do is report Bayesian likelihood ratios. In my example above, that would be 20:1. That is, it increases the odds of the hypothesis by a factor of 20 (20 times 1:99,999 is 1:5,000, same as we calculated above.) It DOES NOT depend on any prior and does not pretend to be a probability. It also means you can chain together multiple studies easily just by multiplying their likelihood ratios together.

Can someone tell me the details of this comic? I'm not that knowledgeable in statistics but what is the real joke to be told here?

Ok, lets do this.

What is /sci/s opinion. Bayesian or frequentist?

http://en.wikipedia.org/wiki/Quantum_Bayesianism

Quantum Bayesianism applies the Bayesian approach to the fundamentals of quantum mechanics. The Bayesian approach is a mode of statistical inference which is itself derived from information theory. It introduces the concept of "degree of belief".[12] Quantum bayesianism is used in quantum computer science for Quantum Bayesian networks, which find applications in "medical diagnosis, monitoring of processes, and genetics".[13] A Bayesian framework is also used for neural networks.[14]
An interpretation of quantum mechanics, Quantum Bayesianism attempts to find compatibility between different understandings of quantum mechanics and their respective implications on metaphysics and philosophy. Mainly, it attempts to answer questions about the nature of the universe and the observer effect.[citation needed]
When the wavefunction of a system is written as a linear combination of the eigenstates of an observable such as position, the square of the coefficient corresponding to the eigenstate also corresponds to the probability of the system being in that eigenstate with the particular observable value. Since this is probabilistic, this leads to the question of whether the universe is deterministic and how this is consistent with events being described probabilistically. Another idea which Quantum Bayesianism tries to address is whether quantum mechanical probabilities are objective or subjective, and the implications of the Born rule on either.

>TL;DR schrodinger's cat IS dead OR alive. The wave function is a description of the observer's mental state. The superposition applies to the mental state and nothing more.

What do you crackheads think?

Does this picture depict the difference between frequentists and bayesians correctly? The POV of the frequentist seems wrongfully depicted to me, but my knowledge on statistics is still fairly limited.

You meet a mathematician on the street, and the mathematician is pushing two babies in a carriage. They’re so swaddled up that you can’t tell what gender the babies are, but the mathematician says, "At least one of my children is a boy." What is the probability that both children are male?

>>5282088
http://xkcd.com/