Confidence Interval for Inverse Gamma Distribution I would like to understand if there exists any method to find confidence interval for the parameters of inverse gamma distribution.  
 A: Since inverse gamma distributions are so often used in Bayesian Inference, another approximate finite sample inference approach is to use MCMC or Gibbs sampling to draw from a posterior using an uninformative prior to obtain credible intervals. Whilst credible != confidence, most agree the approach yields approximately equivalent inference when using non-informative priors.
Using the simulation suggestion from @KjetilBHalvorsen, I generate the same X and fit a BUGS model with:
model {
  for(i in 1:200) {
    invx[i] <- 1/x[i]
    invx[i] ~ dgamma(shape, scale)
  }
    shape ~ dgamma(0.1, 0.1)
    scale ~ dgamma(0.1, 0.1)

}

To obtain the following posterior distribution samples, which have 2.5 and 97.5 quantiles given by
Inference for Bugs model at "cat.txt", fit using WinBUGS,
 2 chains, each with 5000 iterations (first 2500 discarded), n.thin = 5
 n.sims = 1000 iterations saved
            mean    sd    2.5%     25%     50%     75%   97.5%  Rhat n.eff
shape      1.070 0.096   0.887   1.009   1.067   1.129   1.280 1.000  1000
scale      1.084 0.122   0.860   1.001   1.078   1.164   1.329 1.002   790
deviance 396.018 1.994 394.100 394.600 395.400 396.800 401.800 1.005   520

For each parameter, n.eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor (at convergence, Rhat=1).

DIC info (using the rule, pD = Dbar-Dhat)
pD = 2.0 and DIC = 398.0
DIC is an estimate of expected predictive error (lower deviance is better).

Which agrees somewhat with the maximum likelihood approach used above.
