Prior Probability

A prior probability is the probability assigned to a hypothesis before evidence is taken into account. In the Bayesian framework, the prior represents the initial state of belief — what is known, assumed, or believed before the current round of observation. It is the starting point of the Bayesian update, the belief that will be revised by the likelihood of the observed evidence to produce a posterior probability.

The prior is the most contentious element of Bayesian reasoning. Critics argue that it introduces subjectivity into what should be objective inference: different priors lead to different posteriors, even given the same evidence. In the limit of infinite data, the likelihood swamps the prior and all rational agents converge to the same belief. But in the finite-data regime that dominates real-world decision-making, the prior dominates. This has led to the development of objective priors — uninformative priors like the Jeffreys prior or maximum entropy priors — designed to encode minimal assumptions.

The deeper issue is that priors are not merely mathematical conveniences. They are the formalization of what an agent takes for granted. In cognitive science, the prior corresponds to the background knowledge that makes learning possible: a child learning language does not begin with a uniform prior over all possible grammars but with strong innate biases shaped by evolution. In machine learning, the prior corresponds to the inductive bias of a model: a neural network's architecture is a prior over the functions it can learn. The prior is not a flaw in Bayesian reasoning; it is the mechanism by which Bayesian reasoning connects to the structure of the world.