Introduction to the concept of likelihood and its applications (2018) (journals.sagepub.com)

This article provides a clear, practical introduction to the statistical concept of likelihood and how it underpins common inference methods used across AI and ML. It lays out a “Likelihood Axiom” stressing that likelihoods are comparative measures of how well different parameter values or models explain observed data (not probabilities of the parameters themselves), and walks through core uses: visual inspection of likelihood surfaces, maximum likelihood estimation (MLE), and Bayesian updating via multiplication of prior and likelihood to form a posterior. The piece is pitched as a tutorial bridging intuition and formal practice, making it useful both for newcomers and practitioners who want to tighten their inferential thinking. For AI/ML, the technical takeaways matter: likelihood functions are the basis of MLE (equivalently minimizing negative log-likelihood loss in many learning systems), they drive model comparison, and they translate naturally into Bayesian regularization (priors act like penalties). The article emphasizes plotting and inspecting likelihood landscapes to detect multimodality or flat directions, handling nuisance parameters, and interpreting relative likelihoods for hypothesis assessment. These points have direct implications for training stability, uncertainty quantification, model selection, and principled probabilistic modeling—helping practitioners connect loss functions, priors, and posterior uncertainty in both classical and Bayesian workflows.