Radical Probabilism

What is Radical Probabilism?

Radical probabilism is a variant of Bayesian inference that states it’s impossible to have an unbiased prior probability and also proposes alternative ways to update posterior beliefs. 

Radical probabilism’s greatest practical contribution to Bayesian statistics is often considered to be in the field of “probability kinematics,” which provides techniques to update beliefs based upon uncertain (low probability) results.

Radical Probabilism Versus Standard Bayesian Probability

This probabilism theory is given the “radical” moniker primarily for its rejection of the “dynamic consistency” concept in Bayesian probability, i.e. that changing beliefs is only justified if high probability thresholds are met. Taking Cromwell’s rule a step further, this school of thought believes that no event can be considered 100% certain to occur or not, no matter how much evidence is gathered from the sample. Since any form of prior probability includes either a subjective belief or objective estimation, the posterior probability will also have a slight bias. 

Because of these unknown probability limitations, proponents of radical probabilism believe that all new information should update the belief level to some degree, even if the results of sampling aren’t statistically powerful enough to alter the probability level. So-called probability kinematics provide several different equations to update these conditional beliefs, usually based on a variation of Bayes theorem.