“A Bayesian, in contrast, believes that the realization is the primary thing … the flipping of the coin yields the property of having 50% probability of coming up heads as you flip it.”
Thanks for trying to explain the difference, but I have no idea what this means.
What I was thinking about was this: Bayesians and frequentists both agree that if a fair coin is tossed n times (where n is very large) then a string of heads and tails will result and the probability of heads is .5 in some way related to the fact that the number of heads divided by n will approach .5 for large n.
In my mind, the frequentist perspective is that the .5 probability of getting heads exists first, and then the string of heads and tails realize (i.e., make a physical manifestation of) this abstract probability lurking in the background. As though there is a bin of heads and tails somewhere with exactly a 1:1 ratio and each flip picks randomly from this bin. The Bayesian perspective is that there is nothing but the string of heads and tails—only the string exists, there’s no abstract probability that the string is a realization of. No picking from a bin in the sky. Inspecting the string, a Bayesian can calculate the 0.5 probability … so the 0.5 probability results from the string. So according to me, the philosophical debate boils down to: what comes first, the probability or the string?
I definitely get the impression that the Bayesians in this thread are skeptical of this description of the difference, and seem to prefer describing the difference of the Bayesian view as considering probability a measure of your uncertainty. However, probability is also taught as a measure of uncertainty in classical probability, so I’m skeptical of this dichotomy. (In favor of my view, the name “frequentist” comes from the observation that they believe in a notion of “frequency”—i.e., that there’s a hypothetical distribution “out there” that observed data is being sampled from.)
Perhaps the difference in whether the correct approach is subjective or objective better gets to the heart of the difference. I am leaning towards this hypothesis because I can see how a frequentist can confuse something being objective with that something having an independent “existence”.
I have a little difficulty with the notion that the probable outcome of a coin toss is the result of the toss, rather like the collapse of a quantum probability into reality when observed. Looking at the coin before the toss, surely three probabilities may be objectively observed - H, T or E, and the likelihood of the coin coming to rest on its edge dismissed.
Since the coin MUST then end up H or T ; the sum of both probabilities is 1, both outcomes are a priori equally likely and have the value1/2 before the toss. Whether one chooses to believe that the a priori probabilities have actual existence is a metaphysical issue.
“A Bayesian, in contrast, believes that the realization is the primary thing … the flipping of the coin yields the property of having 50% probability of coming up heads as you flip it.”
Thanks for trying to explain the difference, but I have no idea what this means.
What I was thinking about was this: Bayesians and frequentists both agree that if a fair coin is tossed n times (where n is very large) then a string of heads and tails will result and the probability of heads is .5 in some way related to the fact that the number of heads divided by n will approach .5 for large n.
In my mind, the frequentist perspective is that the .5 probability of getting heads exists first, and then the string of heads and tails realize (i.e., make a physical manifestation of) this abstract probability lurking in the background. As though there is a bin of heads and tails somewhere with exactly a 1:1 ratio and each flip picks randomly from this bin. The Bayesian perspective is that there is nothing but the string of heads and tails—only the string exists, there’s no abstract probability that the string is a realization of. No picking from a bin in the sky. Inspecting the string, a Bayesian can calculate the 0.5 probability … so the 0.5 probability results from the string. So according to me, the philosophical debate boils down to: what comes first, the probability or the string?
I definitely get the impression that the Bayesians in this thread are skeptical of this description of the difference, and seem to prefer describing the difference of the Bayesian view as considering probability a measure of your uncertainty. However, probability is also taught as a measure of uncertainty in classical probability, so I’m skeptical of this dichotomy. (In favor of my view, the name “frequentist” comes from the observation that they believe in a notion of “frequency”—i.e., that there’s a hypothetical distribution “out there” that observed data is being sampled from.)
Perhaps the difference in whether the correct approach is subjective or objective better gets to the heart of the difference. I am leaning towards this hypothesis because I can see how a frequentist can confuse something being objective with that something having an independent “existence”.
I have a little difficulty with the notion that the probable outcome of a coin toss is the result of the toss, rather like the collapse of a quantum probability into reality when observed. Looking at the coin before the toss, surely three probabilities may be objectively observed - H, T or E, and the likelihood of the coin coming to rest on its edge dismissed.
Since the coin MUST then end up H or T ; the sum of both probabilities is 1, both outcomes are a priori equally likely and have the value1/2 before the toss. Whether one chooses to believe that the a priori probabilities have actual existence is a metaphysical issue.