Refertothepreviousexercise,regardingestimating when y = 0 in n = 25 trials. (a) Withuniformpriordistribution,findthe95%highestposteriordensity(HPD)interval, and comparewiththe95%equal-tailposteriorinterval,usingthe2.5and97.5percentiles. Whyaretheydifferent? (b)

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Refertothepreviousexercise,regardingestimating π when y = 0 in n = 25 trials.

(a) Withuniformpriordistribution,findthe95%highestposteriordensity(HPD)interval, and comparewiththe95%equal-tailposteriorinterval,usingthe2.5and97.5percentiles.

Whyaretheydifferent?

(b) When y = 0, explainwhythelowerBayesianequal-tailposteriorintervallimitfor π cannot be0,unliketheBayesianHPDinterval.WhyistheHPDintervalmoresensibleinthis case? (Seealsothediscussionin Section A.4.6 of the R Appendix.)

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