Statistics Seminars: On the limitations of classical Bayesianism for parameter estimation problems
9 November 2015 14:00 in CM221Objective Bayesian methods are being increasingly employed for parameter estimation problems in physics, chemistry and engineering. They often (directly or indirectly) involve the use of a uniform prior probability distribution with respect to some parametrisation, following the Principle of Indifference(POI). The most frequent objection to the POI is its inability to provide a prior distribution uniform over all possible reformulations of the parameters. There does not appear to be, however, any discussion of an equally (and perhaps even more) significant problem: favouring a model incompatible with measurements over one closely fitting them. A numerical example belonging to the field of chemical kinetics is presented here. Frequentist methods well adapted to chemical kinetics (Feasible Set approach) correctly identified the realistic model while Bayesian methods based on the POI led to its rejection. The reason for this is that traditional Bayesianism cannot appreciate the difference between two irreducible notions, namely experimental implausibility and ignorance. Imprecise Bayesianism was shown to be a promising approach having the potential to overcome this problem. These techniques were applied to an estimation problem related to the reaction CO + OH → CO2 + H. It could be shown that in this case, the results are robustly insensitive to the choice of the prior distribution.
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