7. Consider 2001 census data on religious adherence in the 33 London boroughs with K = 5 categories (Christian, Hindu and Sikh, Muslim, Other religion, No religion). The totals Sik by borough i , and the total Ui with religion not stated, are in Table 14.5. The non-response rate averages around 9%.

Consider the coding (for I = 33, K = 5)

Elicit suitable values for the prior Dirichlet weights a[1:K], and prior beta weights alpha[1:K] and beta[1:K]. Provide suitable initial values to obtain posterior probabilities of response πik specific to borough i and religion k. Is the fit improved by allowing response probabilities to be specific for religion only? How are inferences affected if the a[k] are allowed to be free parameters?

model { for (i in 1:1) {M[i]