A Pathway from Bayesian Statistical Analysis to Superstatistics

TL;DR

This paper interprets superstatistics within Bayesian analysis, extends it using Mathai's pathway model, and explores its applications in statistical physics, connecting various integrals and functions through Fox's H-function.

Contribution

It introduces a generalized superstatistics framework using Mathai's pathway model, linking it to diverse mathematical functions and applications in physics.

Findings

Superstatistics interpreted via Bayesian analysis.

Extension using Mathai's pathway model.

Connections to Fox's H-function and various integrals.

Abstract

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.