Genetic Creutzfeldt-Jakob Disease (gCJD) is a very rare disease, and the number of deaths caused by gCJD each year in the United Kingdom can be modeled using a Poisson distribution with unknown parameter 8. Numbers of gCJD deaths for the period 2005-9 are given in Table 12. A Gamma(11, 2) was selected as a prior for 8. Year Number of deaths Table 12 2005 2006 9 13 2007 2008 9 5 2009 8 (a) State the posterior for parameter 8, given the data and prior above. (b) Calculate the posterior mode for 8, giving your answer to 2 decimal places. (c) Figure 11 shows the prior, likelihood and posterior for 8. Figure 11 Prior Likelihood -Posterior 15 Comment on the relative contributions of the prior and data to the posterior, justifying your opinion. How have the data affected opinion about 8?

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Genetic Creutzfeldt-Jakob Disease (gCJD) is a very rare disease, and the number of deaths
caused by gCJD each year in the United Kingdom can be modeled using a Poisson
distribution with unknown parameter 0. Numbers of gCJD deaths for the period 2005-9
are given in Table 12. A Gamma(11, 2) was selected as a prior for 0.
Year
Number of deaths
Table 12
2005 2006
13 9
2007 2008 2009
9 5 8
(a) State the posterior for parameter 0, given the data and prior above.
(b)
Calculate the posterior mode for 8, giving your answer to 2 decimal places.
(c) Figure 11 shows the prior, likelihood and posterior for 8.
Figure 11
10
Prior
Likelihood
Posterior
15
Comment on the relative contributions of the prior and data to the posterior,
justifying your opinion. How have the data affected opinion about ?
Transcribed Image Text:Genetic Creutzfeldt-Jakob Disease (gCJD) is a very rare disease, and the number of deaths caused by gCJD each year in the United Kingdom can be modeled using a Poisson distribution with unknown parameter 0. Numbers of gCJD deaths for the period 2005-9 are given in Table 12. A Gamma(11, 2) was selected as a prior for 0. Year Number of deaths Table 12 2005 2006 13 9 2007 2008 2009 9 5 8 (a) State the posterior for parameter 0, given the data and prior above. (b) Calculate the posterior mode for 8, giving your answer to 2 decimal places. (c) Figure 11 shows the prior, likelihood and posterior for 8. Figure 11 10 Prior Likelihood Posterior 15 Comment on the relative contributions of the prior and data to the posterior, justifying your opinion. How have the data affected opinion about ?
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