Random Sample from An Exponential Distribution
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Random Sample from An Exponential Distribution
Suppose y1 , y2, … , Yn is a random sample from an exponential distribution with mean 1/A. Further
Suppose y1 , y2, … , Yn is a random sample from an exponential distribution with mean 1/A. Further suppose that y1,y2, … . ,yk are fully observed, and Yk+ 1, … , Yn are right censored.
(a) Derive Jeffreys's prior for A. Note: Jeffrey's prior is defined to be any prior which is proportional to the square root of the Fisher information in A. (b) Derive the posterior distribution of A using the prior in part (a).
(c) Using part (b), derive the predictive distribution of a future observation z, where z is assumed to be fully observed, i.e., not
censored.
(d) Consider including a single covariate Xi in the exponential model, so that Ai = exp(xi,8). Suppose j3 “' N(f-Lo, 0″5) a priori.
Show that the posterior density of j3 is log-concave.
(e) Let () = exp(,B) from part (d), and suppose that ()”' Q(o:o, .Ao), a priori. Derive a closed form expression for the posterior distribution of().
Random Sample from An Exponential Distribution
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Average Score
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40-38 points
More depth/detail for the background and significance is needed, or the research detail is not clear. No search history information is provided.
83-76 points
Review of relevant theoretical literature is evident, but there is little integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are included. Summary of information presented is included. Conclusion may not contain a biblical integration.
52-49 points
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48-1 points
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Random Sample from An Exponential Distribution