HW 9 due 11/18
1. Pick an example from your own research or general interest where statistical data are
used. Don’t pick any application discussed in class. In the context of your example,
do the following:
(a) Define Nature, Design and Measurement, and DATA.
(b) Write down a statistical model for {Nature + Design and Measurement} that you
are willing to assume produces the DATA in your study.
(c) Identify a particular parameter θthat is part of your statistical model you identified
in (b). Explain why you are interested in this parameter.
(d) Draw a graph, by hand, of your prior distribution of θfor your example. Explain
your logic.
2. Look at the document called "My introductory document describing the necessity of
Bayesian models for learning, and the Bayesian method in general" that is on our class
web page. Suppose the survey that got separated from the pile had the response
"2" instead of "4". Find the posterior distribution of Company, assuming a uniform
prior. Write tutorial-style, so that people other than your professor may understand.
Interpret your result.
3. Repeat 2., but assume that there were five surveys that got separated from the pile,
with responses 2, 1, 1, 2, 4. You may assume that they all came from the same
company and that they are the result of an independent sampling. Find the posterior
distribution of Company, assuming a uniform prior. Write tutorial-style, so that people
other than your professor may understand. Interpret your result. (Big picture alert:
Data reduce the uncertainty. More data, more reduction.)
4. Consider the EXCEL spreadsheet from my web document "Graphs of Likelihood Func-
tions," under the tab "Ex 2. Uniform, 1 obs".
(a) Find the posterior distribution of θassuming a uniform (0,10) prior.
(b) Find the posterior probability that θis greater than 4.0.
5. Consider the EXCEL spreadsheet from my web document "Graphs of Likelihood Func-
tions,"under the tab "Ex 2. Uniform, sample".
(a) Find the posterior distribution of θassuming a uniform (0,10) prior.
(b) Find the posterior probability that θis greater than 4.0.
(Big picture alert: Data reduce uncertainty. More data, more reduction.)
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