Archaeological digs discovered Hominid remains at three different sites. The remains were clearly of the same species. The geological structures within which they were found were similar, coming from...

Archaeological digs discovered Hominid remains at three different sites. The remains were clearly of the same species. The geological structures within which they were found were similar, coming from about the same period. Geologists estimate this period to be about 8 million years ago, plus or minus 1 million years. A radiocarbon dating technique, used on the three remains, gave ages of 8.5 million, 9 million, and 7.8 million years. The technique is known to give a result which is normally distributed, with mean 8 = true age, and standard deviation 600,000 years. It is desired to estimate

is the true age of the ith remains) under a quadratic loss. The radiocarbon dating technique is considered much more reliable than the geological information, so the geological information is to be considered vague prior information, namely the specification of a prior mean and standard deviation for each 8i Estimate 8 using (4.102), and give the percentage increase in Bayes risk that would be suffered, compared to using the conjugate prior Bayes estimator, if a normal prior were correct. Also, calculate the conjugate prior Bayes estimate, and judge if concern for robustness in using (4.102) has caused any decline in Bayesian performance from a conditional perspective.