Observations y; for i = -m, -m + 1, ... , m are available which satisfy the regression model 

Transcribed Image Text:

yi~ N(a + Bu; + yvi, d), where u = i and v₁ = i² — m(m + 1). Adopting the reference prior p(a, b, y, 0) x 1/0, show that the posterior distribution of a is such that a-y s/√n ~ tn-3, where n = 2m + 1, s² = See/(n-3) and See = Syy - Suy/Suu - Sy/Svv in which Syy, Suy, etc., are defined by Syy = (y₁ - y)² and Suy = [(u₁-u))(y₁ - y). [Hint: Note that Σui = [vi = Eu¡v; = 0, and hence u = v= 0 and Suy = 0.]