 Gamma prior for an inverse-gamma scale

For inverse-gamma distribution observations of known shape $k$ and scale $\Theta$, their likelihood function in $\Theta$ is proportional to ${\Theta }^{nk}\exp (-\Theta {\sum }_i{x}_i^{-1})$. A shape-$\alpha$, rate-$\lambda$ gamma distribution conjugate prior therefore gives the displayed Bayesian posterior. The Bayes estimator under squared error loss of the conditional claim expected value $\Theta /(k-1)$ is $(\alpha +nk)/[(k-1)(\lambda +{\sum }_i{x}_i^{-1})]$. It depends on reciprocals, rather than the sample mean of the claims.