3 ms·

How is this statement false at all? Conditioning on sigma-algebras, which are the objects at the base of probability theory and which further function as a reas

by ves 10y ago

How is this statement false at all? Conditioning on sigma-algebras, which are the objects at the base of probability theory and which further function as a reasonable model of "knowledge," is at the heart of how we understand probability today. The experimenter and the subject mentioned by the GP both hold different information and we can model that by constructing different sigma-algebras for each, F_e and F_s respectively. It's not at all absurd to think that P(E | F_e) != P(E | F_s) where E is the event in question. This idea holds in general, as you might imagine. I won't address your latter point but the former is definitely not true.

kordless 10y ago
I believe that, under certain circumstances, the probability of something occurring can be well known to one aggregate and completely different or unknown to the other. To illustrate this, that little island in the South Pacific that has no outside contact is still likely to experience rising ocean levels due to global warming based on current calculated probabilities. Just because they don't know the chances doesn't mean the external chances aren't still valid based on current knowledge somewhat within their scope of perception (i.e. they live on the planet but choose not to know the knowledge about the levels rising). There likely exist other probability based variables we cannot see because of our own dissonance on matters under scrutiny. An opposition to global warming which got funding cut on a program which was starting to be able to refine the probabilities a bit further would result in us "knowing" the probabilities were wrong but not "knowing" what they actually were because we didn't do the work to figure them out. My whole point is that "probabilities" can be internally or externally represented and that stating the probability of an "event" occurring depends on "your" knowledge about that event is inaccurate at best.

by ves 10y ago

kordless 10y ago

I believe that, under certain circumstances, the probability of something occurring can be well known to one aggregate and completely different or unknown to the other. To illustrate this, that little island in the South Pacific that has no outside contact is still likely to experience rising ocean levels due to global warming based on current calculated probabilities. Just because they don't know the chances doesn't mean the external chances aren't still valid based on current knowledge somewhat within their scope of perception (i.e. they live on the planet but choose not to know the knowledge about the levels rising). There likely exist other probability based variables we cannot see because of our own dissonance on matters under scrutiny. An opposition to global warming which got funding cut on a program which was starting to be able to refine the probabilities a bit further would result in us "knowing" the probabilities were wrong but not "knowing" what they actually were because we didn't do the work to figure them out. My whole point is that "probabilities" can be internally or externally represented and that stating the probability of an "event" occurring depends on "your" knowledge about that event is inaccurate at best.