Homework Set 16, Due Wednesday November 23, 2016.
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Assigned 11/14/2016, due 11/23
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Consider the simulated dataset Y_1,...,Y_30    located in 
"http://www.math.umd.edu/~slud/s705/Homework/HW16dat.txt"

Analyze the data in Bayesian fashion using the model that Y_i ~ Normal(mu,1)
with (conjugate) prior density making  mu ~ N(0,16)  (ie variance =16).

Based on the posterior density g(mu) you find, simulate 1000 batches 
of new parameters mu^(*r) and "posterior-predictive" datasets Y^(*r)  
of 30 observations each.

Using whatever descriptive statistics S(Y) you choose, assess the fit of the 
Normal model for Y's by examining whether the observed descriptive statistics 
S(Y) fall within estimated credible intervals for those statistics. Those 
credible-interval endpoints will generally be quantiles of the posterior 
predictive values S(Y^(*r)), r=1,...1000 generated from posteriors and pseudo-data.

Choices for S(Y) will generally be of the form (1/30) * sum( h(Yvec)) 
where Yvec is the vector of Y_1,...Y_30  and  h  is often either a power of 
the Y_i arguments or something like the indicator that Y_i > a.