On 03/17/10 11:48, Corrado wrote:
Dear Friedrik, Jaroslav, Octave,
Yes, of course it depends on the error. But you can still build a
frequency distribution with the y_j. It was additional information on
the problem, but probably not very useful, apologies.
First of all, the {p1,....,pn} and hence the {k1,....,kn} can have a few
tenths of elements (that is n could be maybe 60 in the worst case). The
problem is that for such a case we use millions of observations ;). In
the case of the 40,000 observation it would be safe to suppose we would
use a max of 20.
To me 40,000 observations seems more the enough to estimate 60
parameters. But if you are not sure on what model order to use for your
problem then there are methods available for model selection
(comparison). What you do is essentially to integrate out all parameters
of your model to get the probability for the particular model (given
your data). You do this for all model orders and you can then look at
the odds ratio, for example
p(M_1|y,I) / p(M_2|y,I)
for comparing model M_1 and M_2. So if the odds ratio is significantly
larger than one then you would prefer model M_1 over M_2.
I recommend this book:
http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521841504 but
also Larry Bretthorst's book (available for download here:
http://bayes.wustl.edu/glb/bib.html) and papers.
/Fredrik