estimation. Estimation of variance when mean is unknown If the mean is not known, the most uninformative prior that can be taken for it is arguably the translation-invariant prior p(μ|I) ∝ const., which gives the following joint posterior distribution for μ and σ2, The marginal posterior distribution for σ2 is obtained from the joint posterior distribution by integrating out over μ, This is again a scaled inverse chi-squared distribution, with parameters and . Related distributions If then If (Inverse-chi-squared distribution) then If then (Inverse-chi-squared distribution) If then (Inverse-gamma distribution) Scaled inverse chi square distribution is a special case of type 5 Pearson distribution References Gelman A. et al (1995), Bayesian Data Analysis, pp 474–475; also pp 47, 480 Continuous distributions Exponential family distributions