HW5.nb

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Cell["\<\
Revisit question #1 in your homework assignment #4, and read example 5.3.1 \
and exercise 5.31 on pages 130-131of CJBH\[CloseCurlyQuote]s Text carefully, \
and answer the following in the context of inferences relating to the kill \
rate, \[Theta], the average number of armadillos killed per day by men of the \
Ache tribe. You must use the Bayesian model and data as described on page \
130, adapt the code as given on page 131, and run it on OpenBUGS.\
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Cell["\<\
Solution: According to HW4,  the prior distribution is given by\
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Cell["\<\
(b) Run a single Markov Chain in OpenBUGS to find approximate answers for \
some of the following inferential questions. Set the number of burn-in \
parameter updates at 500, and set the number of total number of parameter \
updates at 5500. Note: you can set the initial value of \[Theta] to start the \
chain in any reasonable way you can.\
\>", "Item",
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Cell["\<\
\t\tmean\tsd\tMC_error\tval2.5pc\tmedian\tval97.5pc\tstart\tsample
\tpost.prob.theta1\t0.4028\t0.4905\t0.006933\t0.0\t0.0\t1.0\t501\t5000
\tpost.prob.theta2\t0.8054\t0.3959\t0.005747\t0.0\t1.0\t1.0\t501\t5000
\tpost.prob.theta3\t0.4026\t0.4904\t0.007798\t0.0\t0.0\t1.0\t501\t5000
\tpost.tau1\t-1.324\t0.3105\t0.003885\t-1.969\t-1.307\t-0.7631\t501\t5000
\tpred.prob.y39\t0.753\t0.4313\t0.006325\t0.0\t1.0\t1.0\t501\t5000
\ttau2\t0.7593\t0.06263\t8.11E-4\t 0.6276\t0.7631\t0.8705\t501\t5000
\ttheta\t0.2788\t0.08435\t0.001106\t0.1396\t0.2705\t0.4662\t501\t5000
\ty39\t0.2816\t0.5287\t0.007496\t0.0\t0.0\t2.0\t501\t5000
\
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which means the Bayesian test concludes that there is 80.58% probability the \
null hypothesis is true.\
\>", "TextNoIndent",
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Cell[TextData[{
 "v. State the meaning of the notation ",
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Cell["\<\
# SDS 384.7, Fall 2016
# Building a Bayesian Model in OpenBUGS
# pages 129-131 of CJBH

model
{
   for( i in 1 : 38 ) { kills[i] ~ dpois(theta)}
# prior distribution for theta
   theta ~ dgamma(1.11,1.61)
# Posterior prob that theta is at most 0.25
   post.prob.theta1 <- step(0.25-theta)
# Posterior prob that theta is at most 0.35
   post.prob.theta2 <- step(0.35-theta)
# Posterior prob that theta is between 0.25 and 0.35
   post.prob.theta3 <- step(0.35-theta)*step(theta-0.25)
# Posterior for tau1
   post.tau1<- log(theta)
# Posterior Predition on y39
   y39 ~ dpois(theta)
# tau2
   tau2<-exp(-theta)
# Prediction on y39
  pred.prob.y39 <- equals(y39,0)
}

#Data
list(kills=c(2,0,0,1,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,1,1,1,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0))

#inits - Chain 1
list(theta=1.0)\
\>", "TextNoIndent",
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