7. Set out the full conditionals for regression effects and precisions = 1/ 2 in a hierarchical regression model where yi are binomial

7. Set out the full conditionals for regression effects β and precisions ϕ = 1/τ 2 in a hierarchical regression model where yi are binomial or Poisson with means ηi , with logit(ηi ) = θi and log(ηi ) = θi respectively and θi ∼ N(Xiβ, τ 2). Assume a normal prior for β, namely

β ∼ N(b0, P−1 0 ) and gamma prior for ϕ, namely ϕ ∼ Ga

(a, b).