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Superstatistics and Tsallis statistics in statistical mechanics is given aninterpretation in terms of Bayesian statistical analysis. Subsequentlysuperstatistics is extended by replacing each component of the conditional andmarginal densities by Mathai's pathway model and further both components arereplaced by Mathai's pathway models. This produces a wide class ofmathematically and statistically interesting functions for prospectiveapplications in statistical physics. It is pointed out that the final integralis a particular case of a general class of integrals introduced by the authorsearlier. Those integrals are also connected to Kraetzel integrals in appliedanalysis, inverse Gaussian densities in stochastic processes, reaction rateintegrals in the theory of nuclear astrophysics and Tsallis statistics innonextensive statistical mechanics. The final results are obtained in terms ofFox's H-function. Matrix variate analogue of one significant specific case isalso pointed out.

A Pathway from Bayesian Statistical Analysis to Superstatistics