As regards 2nd problem in our homework, what I asked is similar to the way extended
beta-binomial distribution was developed in UPM.
In the book, professor King started with binomial distribution. He then relaxed the
assumption that ? (Pi) is constant, and modeled ? (Pi) by using beta distribution. He
applied beta distribution and Bayes' rule in order to update binomial distribution,
and that is how beta binomial distribution came into being.
My question here is, do we have to use multinomial distribution to model the fact that we
do not know how many banks in our data set failed (anything from 5 to 15), and then use
that multinomial distribution and Bayes' rule in order to update our binomial
distribution from the 1st problem, and reach our pdf for the 2nd problem?
Isn't there a simpler approach?
Nino Malekovic
MPA Candidate, Class 2011
Harvard Kennedy School
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Today's Topics:
1. Distribution and modeling (Lin, Eric)
2. Re: Distribution and modeling (Maya Sen)
3. Re: Model buildilng, and "the rules" (Gary King)
4. Re: Distribution and modeling (Gary King)
5. Likelihood of independent events being produced by the same
model (Miguel Solano)
6. Binomial PDF when number of "successes" is unknown
(Malekovic, Nino)
----------------------------------------------------------------------
Message: 1
Date: Sat, 6 Feb 2010 14:25:21 -0500
From: "Lin, Eric" <elin at hbs.edu>
Subject: [gov2001] Distribution and modeling
To: Class List for Gov 2001/E-2001 <gov2001-l at lists.fas.harvard.edu>
Message-ID: <C7932C51.4A5B%elin at hbs.edu>
Content-Type: text/plain; charset="iso-8859-1"
I'm a little confused on the concept of modeling using a distribution - particularly,
what is the level of analysis we are applying it to . .. .
If we have a dataset of say n=100, that is a realization of a random process. We could
plot that data and look at that distribution, but if I understand it right, that is not
the distribution of interest. I think that when we use distributions to model, we are
talking about random variables, so the distribution we pick is to model what the data
could have looked like given an underlying data generation process, right?
So , to make things simple, take one out of the 100 observations, obs_i. When we pick the
distribution, we are modeling what value that single observation could have taken given an
underlying process? We are not modeling what the collective 100 observation sample would
look like for a given sample draw?
Or is this the same thing? If it is the same thing, will the distribution we use to
characterize the potential values of a given observation always match the distribution for
the sample?
EXL