  Superstatistics and Tsallis statistics in statistical mechanics is given an
interpretation in terms of Bayesian statistical analysis. Subsequently
superstatistics is extended by replacing each component of the conditional and
marginal densities by Mathai's pathway model and further both components are
replaced by Mathai's pathway models. This produces a wide class of
mathematically and statistically interesting functions for prospective
applications in statistical physics. It is pointed out that the final integral
is a particular case of a general class of integrals introduced by the authors
earlier. Those integrals are also connected to Kraetzel integrals in applied
analysis, inverse Gaussian densities in stochastic processes, reaction rate
integrals in the theory of nuclear astrophysics and Tsallis statistics in
nonextensive statistical mechanics. The final results are obtained in terms of
Fox's H-function. Matrix variate analogue of one significant specific case is
also pointed out.
