Re: different priors (flat, uniform, etc)

Saludos Ruth!

I have a probability on several parameters and one of them is
nuisance one. I want to margizalize over it by simply
integrating the probability along the whole range of values
that such nuisance parameter is allowed to take.

Okay good. You want to "integrate out a nuisance parameter."

Doing it that way is what people call using a flat prior?

I think possibly you're combining two different issues here.
A "prior distribution" is a Bayesian term, and means, basically,
what you think the distribution of a parameter is before
(prior to) some additional data or evidence leads you to
modify your prior beliefs (i.e., produce an updated, or
posterior estimate of the distribution).

So I think we should just dispense with the word "prior"
here. It seems like all you really want to know is: given
that I don't know the shape of my nuisance parameter
distribution, what's a good guess?

Usually one looks to theory for this. Often one just assumes
a normal distribution. That follows when, for example,
the parameter reflects the joint influence of many different factors,
some positive and some negative, such that a bell-shape curve results.


I could be wrong, but I believe a "flat distribution" and a "uniform
distribution" would mean the same thing.

If you could give us some idea of the nuisance parameter, we might be
able
to make suggestions concerning its plausible shape.

Hope this helps.
--
John Uebersax PhD

.

Relevant Pages

  • Re: different priors (flat, uniform, etc)
    ... integrating the probability along the whole range of values ... that such nuisance parameter is allowed to take. ... A "prior distribution" is a Bayesian term, and means, basically, ...
    (sci.stat.math)
  • Re: different priors (flat, uniform, etc)
    ... that such nuisance parameter is allowed to take. ... A "prior distribution" is a Bayesian term, and means, basically, ...
    (sci.stat.math)
  • Re: different priors (flat, uniform, etc)
    ... that such nuisance parameter is allowed to take. ... A "prior distribution" is a Bayesian term, and means, basically, ...
    (sci.stat.math)
  • Re: different priors (flat, uniform, etc)
    ... that such nuisance parameter is allowed to take. ... A "prior distribution" is a Bayesian term, and means, basically, ... We already know Bob O'Hara isn't one. ...
    (sci.stat.math)
  • Re: different priors (flat, uniform, etc)
    ... that such nuisance parameter is allowed to take. ... A "prior distribution" is a Bayesian term, and means, basically, ... We already know Bob O'Hara isn't one. ...
    (sci.stat.math)
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