Apply the Poisson dispersion test to the data on gamma-ray counts—Problem 42 of Chapter...

Apply the Poisson dispersion test to the data on gamma-ray counts—Problem 42 of Chapter 8. You will have to modify the development of the likelihood ratio test in Section 9.5 to take account of the time intervals being of different lengths.

Reference

The file gamma-ray contains a small quantity of data collected from the Compton Gamma Ray Observatory, a satellite launched by NASA in 1991 (http://cossc.gsfc.nasa.gov/). For each of 100 sequential time intervals of variable lengths (given in seconds), the number of gamma rays originating in a particular area of the sky was recorded. Assuming a model that the arrival times are a Poisson process with constant emission rate (λ = events per second), estimate λ. What is the estimated standard error? How might you informally check the assumption that the emission rate is constant? What is the posterior distribution of if an improper gamma prior is used?