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Well, it's less of a conundrum in the case of the die because it's easier to estimate the priors. I agree, but in the case of a die, "estimating the priors" is

by nkurz 10y ago

Well, it's less of a conundrum in the case of the die because it's easier to estimate the priors. I agree, but in the case of a die, "estimating the priors" is the same thing as "knowing the probability of a 6". So you are saying (correctly) that once we have a model that we believe in, we can assign a probability because we believe we know the probability in advance. I was pointing more to the author's emphasis on "either it does or it doesn't". One view is that probability requires replication, and we can only speak of probabilities in the long run of many trials. The other view (Bayesian to my limited understanding) is that probability can also be used to measure appropriate degree of belief in a proposition. While it's hard to quantify, and dependent on one's assumptions, I do think it's possible to speak of "the probability that the earth revolves around the sun", much as I think it's meaningful to talk about "the probability of anthropogenic warming" even though we only have a single Earth to study. I don't really understand how classical statistics disallows discussion of the first while allowing discussion of the second. Maybe it doesn't?

bbctol 10y ago
I'd say classical statistics lets you deduce, based on some knowledge that something is the case, the probability of an event. It doesn't let you induce the probability of something being the case (that's why we have all this indirect dodging with p-values.) So I think there is a fundamental difference between "What are the odds of rolling a six" as "What are the odds of that event happening," and "What are the odds the Sun revolves around the Earth" as a question about whether or not something is true. That's what the author seems to mean by "either it does or it doesn't," though it isn't worded that well. Even if the die has already been rolled, we know that it could have been a 4 or a 5, and have good knowledge of the probabilities of those events. This is more like looking at a picture of the top of a die and seeing a six: what are the odds that it's a standard die, vs. a die with sixes on each face? I don't think it's meaningful to talk about that, or the sun going around the Earth, without using a Bayesian prior.
- duneroadrunner 10y ago
  > So I think there is a fundamental difference between "What are the odds of rolling a six" as "What are the odds of that event happening," and "What are the odds the Sun revolves around the Earth" as a question about whether or not something is true. Right, using Bayes makes the difference not a "fundamental" one, but just a practical one of coming up with the Bayesian prior. Even if it would be hard to establish a consensus on the most appropriate complete set of factors determining the Bayesian prior, there are clearly some examples of meaningful inputs. Like, for example, if you somehow had information about how many of the researcher's previous hypotheses on the subject failed to obtain a "p-value of significance". But perhaps more practically, you could consider things like the (Kolmogorov) complexity of the hypothesis. Since the number of "low complexity" hypotheses are finite, they are less susceptible to "p-value mining"[1]. The challenge being deciding which inputs to use to evaluate the complexity. This seems to me like an area where machine learning should be applicable. Rather than lament about the impracticality of determining an appropriate, tractable set of (quantifiable) criteria for determining a Bayesian prior, why not just include every potentially relevant piece of information and let Deep Thought[2] figure out which are actually relevant? So what we really need is unified data about all published results that have been confirmed and discredited. [1] obligatory xkcd: https://www.xkcd.com/882/ https://www.xkcd.com/882/ [2] for the youngsters: https://en.wikipedia.org/wiki/List_of_minor_The_Hitchhiker%27s_Guide_to_the_Galaxy_characters#Deep_Thought https://en.wikipedia.org/wiki/List_of_minor_The_Hitchhiker%2...

by nkurz 10y ago

bbctol 10y ago

I'd say classical statistics lets you deduce, based on some knowledge that something is the case, the probability of an event. It doesn't let you induce the probability of something being the case (that's why we have all this indirect dodging with p-values.) So I think there is a fundamental difference between "What are the odds of rolling a six" as "What are the odds of that event happening," and "What are the odds the Sun revolves around the Earth" as a question about whether or not something is true. That's what the author seems to mean by "either it does or it doesn't," though it isn't worded that well. Even if the die has already been rolled, we know that it could have been a 4 or a 5, and have good knowledge of the probabilities of those events. This is more like looking at a picture of the top of a die and seeing a six: what are the odds that it's a standard die, vs. a die with sixes on each face? I don't think it's meaningful to talk about that, or the sun going around the Earth, without using a Bayesian prior.

duneroadrunner 10y ago
> So I think there is a fundamental difference between "What are the odds of rolling a six" as "What are the odds of that event happening," and "What are the odds the Sun revolves around the Earth" as a question about whether or not something is true. Right, using Bayes makes the difference not a "fundamental" one, but just a practical one of coming up with the Bayesian prior. Even if it would be hard to establish a consensus on the most appropriate complete set of factors determining the Bayesian prior, there are clearly some examples of meaningful inputs. Like, for example, if you somehow had information about how many of the researcher's previous hypotheses on the subject failed to obtain a "p-value of significance". But perhaps more practically, you could consider things like the (Kolmogorov) complexity of the hypothesis. Since the number of "low complexity" hypotheses are finite, they are less susceptible to "p-value mining"[1]. The challenge being deciding which inputs to use to evaluate the complexity. This seems to me like an area where machine learning should be applicable. Rather than lament about the impracticality of determining an appropriate, tractable set of (quantifiable) criteria for determining a Bayesian prior, why not just include every potentially relevant piece of information and let Deep Thought[2] figure out which are actually relevant? So what we really need is unified data about all published results that have been confirmed and discredited. [1] obligatory xkcd: https://www.xkcd.com/882/ https://www.xkcd.com/882/ [2] for the youngsters: https://en.wikipedia.org/wiki/List_of_minor_The_Hitchhiker%27s_Guide_to_the_Galaxy_characters#Deep_Thought https://en.wikipedia.org/wiki/List_of_minor_The_Hitchhiker%2...