In this paper, Bayesian estimation using diffuse (vague) priors is carried out for the parameters of a two parameter Weibull distribution. Expressions for the marginal posterior densities in this case are not available in closed form. Approximate Bayesian methods based on Lindley (1980) formula and Tierney and Kadane (1986) Laplace approach are used to obtain expressions for posterior densities. A comparison based on posterior and asymptotic variances is done using simulated data. The results obtained indicate that, the posterior variances for scale parameter obtained by Laplace method are smaller than both the Lindley approximation and asymptotic variances of their MLE counterparts.
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