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On Bayesian Inductive Inference & Predictive EstimationWe investigate Bayesian inference and the Principle of Maximum Entropy (PME) as methods for doing inference under uncertainty. This investigation is primarily through concrete examples that have been previously investigated in the literature. We find that it is possible to do Bayesian inference and PME inference using the same information, despite claims to the contrary, but that the results are not directly comparable. This is because Bayesian inference yields a probability density function (pdf) over the unknown model parameters, whereas PME yields point estimates. If mean estimates are extracted from the Bayesian pdfs, the resulting parameter estimates can differ radically from the PME values and also from the Maximum Likelihood values. We conclude that these differences are due to the Bayesian inference not assuming anything beyond the given prior probabilities and the data, whereas PME implicitly assumes that the given constraints are the only constraints that are operating. Since this assumption can be wrong, PME values may have to be revised when subsequent data shows evidence for more constraints. The entropy concentration previously "proved" by E. T. Jaynes is shown to be in error. Further, we show that PME is a generalized form of independence assumption, and so can be a very powerful method of inference when the variables being investigated are largely independent of each other.
Document ID
20040152058
Acquisition Source
Ames Research Center
Document Type
Preprint (Draft being sent to journal)
Authors
Cheeseman, Peter
(NASA Ames Research Center Moffett Field, CA, United States)
Stutz, John
(NASA Ames Research Center Moffett Field, CA, United States)
Smelyanskiy, Vadim
(NASA Ames Research Center Moffett Field, CA, United States)
Date Acquired
August 22, 2013
Publication Date
January 1, 2004
Subject Category
Fluid Mechanics And Thermodynamics
Funding Number(s)
CONTRACT_GRANT: NCC2-1426
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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