Recent Advances in Statistical Inference: From Classical Paradigms to Bayesian and Likelihood-Based Approaches

Abstract Statistical inference forms the backbone of data-driven decision-making and has evolved significantly beyond traditional frequentist frameworks. Classical approaches based on hypothesis testing, confidence intervals, and p-values have been widely used but face many challenges and limitations when dealing with complex data structures and uncertainty. This review summarizes recent advances in statistical inference, emphasizing the shift toward likelihood-based and Bayesian methodologies. A bibliometric analysis based on Scopus and VOSviewer indicates the top published authors and countries contributing on statistical inference research from 2014 to 2024. This review also highlights the philosophical foundations and methodological developments of these paradigms, highlighting their strengths and practical relevance. Key topics include modern likelihood inference, Bayesian hierarchical models, prior specification, and computational techniques such as Markov Chain Monte Carlo and variational inference. Hybrid approaches, including empirical Bayes methods and information-theoretic criteria, are also discussed as efforts to unify inferential perspectives. The review critically addresses ongoing challenges such as model misspecification, computational scalability, and interpretability, while identifying emerging research directions. In conclusion, the review provides a balanced synthesis of contemporary inferential methods for both theoretical and applied statisticians.