Final answer:
Prior probability is the initial estimate of an outcome's likelihood, likelihood is the probability of observing the data given a model, and marginal likelihood is the probability of the data under all possible parameter values, serving as a normalizing factor in Bayes' theorem.
Step-by-step explanation:
Prior probability, likelihood, and marginal likelihood are important concepts in the context of the Naive Bayes algorithm, which is a probabilistic classifier based on applying Bayes' theorem with strong independence assumptions between features. Prior probability refers to the probability of an event before new data is taken into account. In the context of Naive Bayes, it is the initial estimate of the likelihood of an outcome. This can be established based on previous knowledge or assumptions about the data. The likelihood is the probability of the observed data under a specific model or hypothesis. It measures how well the model explains the observed data. In Naive Bayes, it reflects how probable the observed features are, assuming the model is true.
Bayes' theorem is a mathematical formula used to update the probability estimate for a hypothesis as more evidence or information becomes available. The theorem is expressed as:
P(Hypothesis|Data) = (P(Data|Hypothesis) × P(Hypothesis)) / P(Data)
The marginal likelihood, also known as the evidence, is the probability of the observed data under all possible values of the model parameters. This serves as a normalizing constant in Bayes' theorem and ensures that the resulting posterior probabilities sum up to one.