Another person said that, if the probability that X is true is below your detection threshold or your digits of accuracy, you should assign P(X) = 0, since any other number is just made up.
This immediately struck me as so very wrong. The worse you can measure, the more events you feel justified assigning zero probability?
It’s strange that such claims make it out into the wild. Maybe there was additional context that made it make sense for someone once upon a time, and they generalized to an ill fitting context.
My own response to this is “P(X) = 0 is made up, too. If I want to avoid using a made-up value, I should stop thinking about P(X) altogether. Alternatively, if I want to think about P(X), I should assign it a made-up value that works well. In many contexts epsilon works far better than zero.”
I think Phil’s experience suggests a reasonable way to attack these problems.
Do the analysis for a series of epsilons, starting with your measurement delta and working down, and see if it makes any difference to the results.
Also, in one of Jaynes’ paper on the marginalization “paradox” he suggested that ignoring the existence of a variable gives you a different result than applying an ignorance prior (showing yet again that the term “ignorance prior” is a stupefying oxymoron).
Re: ignoring the existence of a variable… yes, absolutely. I meant in the more sweeping, less useful sense of “go work on a different problem altogether, or perhaps just have a beer and watch telly.”
Re: seeing how results vary for different possible values of an unknown variable… yup, agreed.
This immediately struck me as so very wrong. The worse you can measure, the more events you feel justified assigning zero probability?
Assigning more events zero probability leaves you worse off compared to someone who makes accurate estimates, but it doesn’t necessarily leave you worse off compared to someone else who measures as poorly as you and makes poorly estimated measurements..
It’s a way of mitigating the damage by not being able to measure well. You’re still worse off than a person who can measure well, you’re just not as worse off.
No. If you’d only ever seen TAAGCC, period, you would NOT have any sort of license to completely rule out the possibility of anything else. Indeed, the probabilities should be nearly even with a little more weight given to that particular observation.
Applying the Sunrise formula seems appropriate here.
This immediately struck me as so very wrong. The worse you can measure, the more events you feel justified assigning zero probability?
It’s strange that such claims make it out into the wild. Maybe there was additional context that made it make sense for someone once upon a time, and they generalized to an ill fitting context.
My own response to this is “P(X) = 0 is made up, too. If I want to avoid using a made-up value, I should stop thinking about P(X) altogether. Alternatively, if I want to think about P(X), I should assign it a made-up value that works well. In many contexts epsilon works far better than zero.”
I think Phil’s experience suggests a reasonable way to attack these problems.
Do the analysis for a series of epsilons, starting with your measurement delta and working down, and see if it makes any difference to the results.
Also, in one of Jaynes’ paper on the marginalization “paradox” he suggested that ignoring the existence of a variable gives you a different result than applying an ignorance prior (showing yet again that the term “ignorance prior” is a stupefying oxymoron).
Re: ignoring the existence of a variable… yes, absolutely. I meant in the more sweeping, less useful sense of “go work on a different problem altogether, or perhaps just have a beer and watch telly.”
Re: seeing how results vary for different possible values of an unknown variable… yup, agreed.
Assigning more events zero probability leaves you worse off compared to someone who makes accurate estimates, but it doesn’t necessarily leave you worse off compared to someone else who measures as poorly as you and makes poorly estimated measurements..
It’s a way of mitigating the damage by not being able to measure well. You’re still worse off than a person who can measure well, you’re just not as worse off.
No. If you’d only ever seen TAAGCC, period, you would NOT have any sort of license to completely rule out the possibility of anything else. Indeed, the probabilities should be nearly even with a little more weight given to that particular observation.
Applying the Sunrise formula seems appropriate here.