El Posterior bayesiano refers to the revised probability of a certain hypothesis after considering new evidence or data. In estadística bayesiana, we start with a prior probability, which reflects our initial belief about the hypothesis before observing any data. When we gather nuevos datos, we can update our belief using Bayes’ theorem, leading us to the posterior probability.
Matemáticamente, la posterior bayesiana puede expresarse como:
P(H | D) = (P(D | H) * P(H)) / P(D)
Donde:
- P(H | D) es la probabilidad posterior de la hipótesis H dada la data D.
- P(D | H) es la probabilidad de observar la data D dado que la hipótesis H es verdadera.
- P(H) es la probabilidad previa de la hipótesis H.
- P(D) is the probabilidad marginal de la data D.
This formula illustrates how we can adjust our beliefs about a hypothesis in light of new evidence. The Bayesian posterior is crucial in many fields, including aprendizaje automático, where it is used to update models based on incoming data, making it a foundational concept in Inferencia Bayesiana.