ABSTRACT
Bayes estimates provide another class of asymptotically efficient estimates. We assume that θ is chosen from Θ an open subset of ℝ k according to a prior density g(θ) with respect to Lebesgue measure, d θ, and that g(θ) is continuous and positive on Θ. The posterior density of θ, given a sample X 1,…, X n from f(x|θ), is https://www.w3.org/1998/Math/MathML"> g ( θ | x 1 , … , x n ) = ( ∏ 1 n f ( x j θ ) ) g ( θ ) ∫ Θ ( ∏ 1 n f ( x j θ ) ) g ( θ ) d θ = L n ( θ ) g ( θ ) ∫ Θ L n ( θ ) g ( θ ) d θ . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315136288/c12c5089-77f8-4e14-84a1-364a5e26ae30/content/eq1012.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
