16 September 2011 Bayesian big bang
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Abstract
We show that the flow of particles corresponding to Bayes' rule has a number of striking similarities with the big bang, including cosmic inflation and cosmic acceleration. We derive a PDE for this flow using a log-homotopy from the prior probability density to the posteriori probability density. We solve this PDE using the gradient of the solution to Poisson's equation, which is computed using an exact Green's function and the standard Monte Carlo approximation of integrals. The resulting flow is analogous to Coulomb's law in electromagnetics. We have used no physics per se to derive this flow, but rather we have only used Bayes' rule and the definition of normalized probability and a loghomotopy parameter that could be interpreted as time. The details of this big bang resemble very recent theories much more closely than the so-called new inflation models, which postulate enormous inflation immediately after the big bang.
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Fred Daum, Fred Daum, Jim Huang, Jim Huang, } "Bayesian big bang", Proc. SPIE 8137, Signal and Data Processing of Small Targets 2011, 81370P (16 September 2011); doi: 10.1117/12.894898; https://doi.org/10.1117/12.894898
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