The inverse Gaussian distribution has been shown to he potentially useful in modelling positively skewed data (see Chikarra and Folks,1989). Tweedie (1957) in his landmark paper, studying the sampling properties of this distribution, developed parallel procedure to ANOVA and called it ANOREE (analysis of reciprocals). This has been subsequently generalized to the two way model by Schuster and Miura (1973) and Miura (1978). Fries and Bhattacharyya (1983) proposed to model the reciprocal of the cell means distribution in two factor experiments involving failure times following inverse Gaussian distribution. The reciprocal mean parametrization was earlier used by Banerjee and Bhattacharyya (1979) in carrying out a Bayesian analysis in a single sample. The present paper generalizes this set-up to one-way data following inverse Gaussian distribution. The resulting posterior distributions exhibit some interesting properties.