Bayes

The word Plurinational represents in South America the coexistence of our local cultural diversities. This vision is particularly appropriate for a community working with Bayesian methods because, unlike ad-hoc procedures that select a single hypothesis (e.g. by maximum likelihood), the strict application of probability rules (Bayesian approach) forces us to consider each and every hypothesis. Just as Bayesian methods adapt to uncertainty by believing in mutually contradictory hypotheses, a plurinational society adapts to life through the coexistence of our diversities.

Science has a claim to truth: to reach intersubjective agreements with universal validity. Formal sciences (mathematics, logic) reach these agreements by deriving theorems within closed axiomatic systems. However, the empirical sciences (from physics to the social sciences) must validate their propositions in open systems that always contain some degree of uncertainty. Is it then possible to reach intersubjective agreements ("truths") in empirical sciences in which it is inevitable to say "I don't know"? Yes. We can avoid lying: by maximizing uncertainty (not asserting more than what is known) given the available information (without hiding what is known).

The rules of probability have been known since the end of the 18th century and have since been adopted as a system of reasoning in all empirical sciences. They are conceptually intuitive: preserve the prior belief that remains compatible with the data (product rule) and predict with the contribution of all hypotheses (sum rule). Although nothing better has been proposed in the meantime, the computational cost associated with the evaluation of the entire hypothesis space has in fact limited its applicability. Therefore, over time, partial solutions were developed, such as statistical physics in the 19th century and the frequentist approach in the 20th century. Only with the enormous growth in computing power, on the eve of the 21st century, did it become possible for the first time to strictly apply the rules of probability in all fields of science.

After overcoming these obstacles, historical inertia now appears as one of the main limitations. Although the growth of the Bayesian approach is currently an accelerating worldwide phenomenon, its development is still in its early stages. Although knowledge under uncertainty is "plural and conditional", the traditional language of the empirical sciences is presented as "singular and definitve". Just as selecting a single hypothesis has known negative consequences in probability (overfitting), the massive loss of cultural diversity caused by the imposition of a single type of society during colonial-modernity is having ecological consequences that metropolitan science is unable to compensate for.