Marginal likelihood, also known as the model evidence, is a crucial component in Bayesian model comparison, representing the probability of observing the data under a specific model, integrated over all possible parameter values. It is used to weigh different models against each other, with higher marginal likelihoods indicating a better fit to the observed data while inherently penalizing model complexity.

Marginal Likelihood

Marginal likelihood

Model evidence, also known as the marginal likelihood, is a crucial component in Bayesian model comparison as it quantifies how well a model explains the observed data, balancing fit and complexity. It is used to compute the Bayes factor, which helps in selecting the most probable model among a set of candidates by considering both the data likelihood and prior information.

model evidence

Bayesian model comparison

probability of observing the data

specific model

possible parameter values

weigh different models

higher marginal likelihoods

better fit to the observed data

penalizing model complexity

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