4 ms·

"Just". Pro tip, these guys work on these problems all day every day. If you think you've solved one of their major problems after 18 seconds of consideration t

"Just". Pro tip, these guys work on these problems all day every day. If you think you've solved one of their major problems after 18 seconds of consideration then you're probably missing a large amount of context.

platz 7y ago
I was inviting you to tell me why
- gzer0 7y ago
  Some care is needed when choosing priors in a hierarchical model [such as Bayesian], particularly on scale variables at higher levels of the hierarchy. The usual priors such as the Jeffreys prior [1] often do not work, because the posterior distribution will not be normalizable and estimates made by minimizing the expected loss will be inadmissible. [1] In Bayesian probability, the Jeffreys prior is a non-informative (objective) prior distribution for a parameter space; it is proportional to the square root of the determinant of the Fisher information matrix. Why is this of relevance? It has the key feature that it is invariant under a change of coordinates for the parameter vector. That is, the relative probability assigned to a volume of a probability space using a Jeffreys prior will be the same regardless of the parameterization used to define the Jeffreys prior. This makes it of special interest for use with scale parameters. Why is this an issue? Accordingly, the Jeffreys prior, and hence the inferences made using it, may be different for two experiments involving the same theta parameter even when the likelihood functions for the two experiments are the same—a violation of the strong likelihood principle.
  - Gravityloss 7y ago
    But we have a lot of statistical information and can use reasonable priors about the world. Ie objects don't spring into existence or disappear or fly around at 400 mph or change direction at 2000 gees.
    - gzer0 7y ago
      > Accordingly, the Jeffreys prior, and hence the inferences made using it, may be different for two experiments involving the same theta parameter even when the likelihood functions for the two experiments are the same—a violation of the strong likelihood principle.
- eru 7y ago
  I do appreciate your intent, but I learned that to get the intended response you need to add way more humility into your provocative question. Especially in written communication amongst strangers, where there's a lot of contexts from body language etc missing.

platz 7y ago

I was inviting you to tell me why

gzer0 7y ago
Some care is needed when choosing priors in a hierarchical model [such as Bayesian], particularly on scale variables at higher levels of the hierarchy. The usual priors such as the Jeffreys prior [1] often do not work, because the posterior distribution will not be normalizable and estimates made by minimizing the expected loss will be inadmissible. [1] In Bayesian probability, the Jeffreys prior is a non-informative (objective) prior distribution for a parameter space; it is proportional to the square root of the determinant of the Fisher information matrix. Why is this of relevance? It has the key feature that it is invariant under a change of coordinates for the parameter vector. That is, the relative probability assigned to a volume of a probability space using a Jeffreys prior will be the same regardless of the parameterization used to define the Jeffreys prior. This makes it of special interest for use with scale parameters. Why is this an issue? Accordingly, the Jeffreys prior, and hence the inferences made using it, may be different for two experiments involving the same theta parameter even when the likelihood functions for the two experiments are the same—a violation of the strong likelihood principle.
- Gravityloss 7y ago
  But we have a lot of statistical information and can use reasonable priors about the world. Ie objects don't spring into existence or disappear or fly around at 400 mph or change direction at 2000 gees.
  - gzer0 7y ago
    > Accordingly, the Jeffreys prior, and hence the inferences made using it, may be different for two experiments involving the same theta parameter even when the likelihood functions for the two experiments are the same—a violation of the strong likelihood principle.
eru 7y ago
I do appreciate your intent, but I learned that to get the intended response you need to add way more humility into your provocative question. Especially in written communication amongst strangers, where there's a lot of contexts from body language etc missing.