5 ms·

it sounds like the strength of the bayesian model is completely dependant on the ability of experts to provide accurate statistical guesses

thearn4 13y ago
Bayesian inference is definitely only as good as the quality of the chosen prior, if the number of samples is low.
- ajtulloch 13y ago
  I don't think this is technically correct - as Bernstein-Von Mises guarantee under certain conditions that the posterior is independent of the prior after sufficient data is observed. http://en.m.wikipedia.org/wiki/Bernstein%E2%80%93von_Mises_theorem http://en.m.wikipedia.org/wiki/Bernstein%E2%80%93von_Mises_t...
  - XFrequentist 13y ago
    It was actually "technically correct" - he said "if the number of samples is low". You're correct about the general case, of course.
    - ajtulloch 13y ago
      The previous comment was edited - the comment I replied to said something along the lines of 'especially when the number of samples are low'
    - thearn4 13y ago
      In fairness, I actually edited my reply for clarity, what I had in mind were small samples where the prior ends up dominating.
- Houshalter 13y ago
  But what's the alternative? The same experts making the same guesswork with the same information.
- oscardelben 13y ago
  I'd like to disagree with that. If your priori are particularly bad then you should expect your estimates to change quickly based on new evidence.
  - 001sky 13y ago
    Completess of the state space seems relevant.
    - varelse 13y ago
      And unfortunately 4-dimensional. They could have landed the plane, taken it apart and melted it for scrap, killed all the passengers and crew, and burned the bodies by now. Unless of course, they have a lot more data than they're saying. My chief worry here is that this was a dress rehearsal for how to make a jet disappear. If so, then the media is doing a fantastic job enumerating the mistakes they made so they can refine the technique so down the road they can make it last just enough to ram a bunch of jets into skyscrapers again. Sigh...
- varelse 13y ago
  Consider an ideal black spherical 777, hilarity ensues... But seriously, the strength of Bayes is in coping with an initially craptastic prior by updating probabilities (the posteriors) as (potentially noisy) evidence comes in. Now based on that data as it arrives, build an evolving model for the location with confidence intervals and probabilities. Now refine your search to emphasize locations with both emerging high probability and high variance and hope the noise in the data isn't so pathological as to make the process worthless. It's worth a shot.
- jwr 13y ago
  While technically true, another way to say the same thing is "Bayesian reasoning helps you draw reasonable conclusions if the number of samples is low, while converging on the objective solution as the number of samples grows". Which has an entirely different ring to it.
tokenadult 13y ago
For any model of statistical analysis, it's difficult for an inference to be accurate if the data are poor.
shill 13y ago
It probably helps, but having experts may not be necessary in all cases. http://en.wikipedia.org/wiki/The_Wisdom_of_Crowds http://en.wikipedia.org/wiki/The_Wisdom_of_Crowds

thearn4 13y ago

Bayesian inference is definitely only as good as the quality of the chosen prior, if the number of samples is low.

ajtulloch 13y ago
I don't think this is technically correct - as Bernstein-Von Mises guarantee under certain conditions that the posterior is independent of the prior after sufficient data is observed. http://en.m.wikipedia.org/wiki/Bernstein%E2%80%93von_Mises_theorem http://en.m.wikipedia.org/wiki/Bernstein%E2%80%93von_Mises_t...
- XFrequentist 13y ago
  It was actually "technically correct" - he said "if the number of samples is low". You're correct about the general case, of course.
  - ajtulloch 13y ago
    The previous comment was edited - the comment I replied to said something along the lines of 'especially when the number of samples are low'
  - thearn4 13y ago
    In fairness, I actually edited my reply for clarity, what I had in mind were small samples where the prior ends up dominating.
Houshalter 13y ago
But what's the alternative? The same experts making the same guesswork with the same information.
oscardelben 13y ago
I'd like to disagree with that. If your priori are particularly bad then you should expect your estimates to change quickly based on new evidence.
- 001sky 13y ago
  Completess of the state space seems relevant.
  - varelse 13y ago
    And unfortunately 4-dimensional. They could have landed the plane, taken it apart and melted it for scrap, killed all the passengers and crew, and burned the bodies by now. Unless of course, they have a lot more data than they're saying. My chief worry here is that this was a dress rehearsal for how to make a jet disappear. If so, then the media is doing a fantastic job enumerating the mistakes they made so they can refine the technique so down the road they can make it last just enough to ram a bunch of jets into skyscrapers again. Sigh...
varelse 13y ago
Consider an ideal black spherical 777, hilarity ensues... But seriously, the strength of Bayes is in coping with an initially craptastic prior by updating probabilities (the posteriors) as (potentially noisy) evidence comes in. Now based on that data as it arrives, build an evolving model for the location with confidence intervals and probabilities. Now refine your search to emphasize locations with both emerging high probability and high variance and hope the noise in the data isn't so pathological as to make the process worthless. It's worth a shot.
jwr 13y ago
While technically true, another way to say the same thing is "Bayesian reasoning helps you draw reasonable conclusions if the number of samples is low, while converging on the objective solution as the number of samples grows". Which has an entirely different ring to it.

tokenadult 13y ago

For any model of statistical analysis, it's difficult for an inference to be accurate if the data are poor.

shill 13y ago

It probably helps, but having experts may not be necessary in all cases. http://en.wikipedia.org/wiki/The_Wisdom_of_Crowds http://en.wikipedia.org/wiki/The_Wisdom_of_Crowds