인지 베이지안 모델

The core of this approach is Bayes’ rule: [latex]P(H|D) = frac{P(D|H)P(H)}{P(D)}[/latex], where [latex]H[/latex] is a hypothesis and [latex]D[/latex] is observed data. The posterior probability [latex]P(H|D)[/latex] (belief in the hypothesis after seeing data) is proportional to the product of the likelihood [latex]P(D|H)[/latex] (how well the hypothesis explains the data) and the prior probability [latex]P(H)[/latex] (initial belief in the hypothesis). This framework provides a normative standard for how a rational agent should update its beliefs.

In cognitive science, this is applied by assuming that the mind implicitly performs these calculations. For example, in perception, the brain combines noisy sensory input (the data) with prior knowledge about the world to form a stable percept (the posterior). This can explain many visual illusions, where prior expectations override sensory data. In language learning, a child might use Bayesian inference to figure out the meaning of a new word by considering which potential meaning best explains the contexts in which the word was used. The approach is powerful because it provides a unifying mathematical framework for diverse cognitive phenomena and connects cognition directly to statistics and machine learning.