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The Bayesian believes that probability represents our beliefs about the world. The Frequentist believes that probabilities merely represent the long term frequ
by platz 8y ago
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 (for a given 'population').
- analog31 8y agoIs either of these universally true? Or is it possible that a "belief" associated with a given math tool can be chosen as appropriate to the problem being solved du jour? When I learned Bayes' theorem in college stats class, there was no mention of beliefs. It was just a straightforward theorem related to conditional probability.
- platz 8y agoYou don't need belief to write a theorem. You need it in order to use/apply it - the theorem doesn't tell you where your prior comes from.
- Koshkin 8y ago> The Frequentist believes The frequentists do not "believe," they measure.
- platz 8y agoThey still non-trivially define/demarcate what the population actually is. That is kind of a belief because it is a choice not given by nature, and there are infinitely many choices one could choose.
- Koshkin 8y agoNature does not give you choice, it gives you the frequency (say, in the form of the intensity of a spectral line of an atom), and it is the base of the scientific method to listen to what nature is trying to tell you. There is nothing subjective in this process. Arguing otherwise is like saying that atheists “believe” in the non-existence of god.
- platz 8y agoNature is telling you an infinite number of things, the process of selecting what to measure and what to exclude in the measurement is a choice. In terms of frequentism, how you define what the population distribution you are sampling from is exactly, is a choice. You are limiting the discussion to what happens after you've chosen how and what the population distribution consists of.. that part is itself a nontrivial and subjective process.
- akvadrako 8y agoNo. They believe you can measure an infinite number of trials (say # of heads vs tails) and whatever ratio you get is the probability of heads. However it's problematic because you can measure a million coin flips and get heads every time. It's not possible to actually measure an infinite number of trials - you need to imagine it.