(2 points) The US Geological Survey (USGS) monitors occurrences of earthquakes a

Question

(2 points) The US Geological Survey (USGS) monitors occurrences of earthquakes across the world (see, for example, http:/learthquake.usgs.govlearthquakes/search/). Suppose a USGS researcher is interested in the annual number of earthquakes worldwide that are between 6.0 and 6.9 on the Richter scale, and considers a Poisson model with some mean to be appropriate for this variable. The researcher takes a random sample of twenty years for which reliable data exist, and observes the following numbers of counts of earthquakes of interest on those years: 128,137, 122,123,123, 127, 139,124,151,127, 132, 126, 144,124, 118,139, 126, 130, 133,136 The mean of the above counts is 130.45. In performing a Bayesian analysis, the researcher takes as a prior distribution for a density function proportional to 266-,-0.5 (266A)266-1 e-0.5 Part a) Use R to compute a two-sided 95% Bayesian credibility interval for , giving your answers to two decimal places. Lower bound: Upper bound: Part b) Suppose in the above analysis the researcher chose a Gamma prior distribution, Ga (, , and let 0 and to find the asymptotic two-sided 95% Bayesian credibility interval for , giving your answers to two decimal places. 0. In this limit, use R Lower bound: Upper bound:

Explanation / Answer

Part A) 95 % Basyesian Confidance Interval :

Lower bound : 125.39

Upper bound : 126.19

Part B ) : 95 % Basyesian Confidance Interval :

Lower bound : 114.08

Upper bound : 146.81

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