Bayesian methods in statistics – article review –

Abstract

    A basic substitute for conventional iterative models, Bayesian statistics gives a thorough intellectual framework. Instead of only reflecting the proportional frequency of events, this method redefines probability as a statement of individual certainty. The philosophical underpinnings of Bayesian statistics are first examined in this methodical research, with a focus on the cognitive updating process. In order to create updated views expressed through subsequent distributions, this approach relies on the methodical integration of previous beliefs (expressed through initial distributions) with fresh data obtained from real-world experiments (using a probability function). In sophisticated computations, Bayesian statistics presents difficulties despite its many benefits. However, these difficulties have been largely overcome because to developments in simulation methods like the Markov Monte Carlo Chain (MCMC). The Metropolis-Hastings algorithm, Gibbs sampling, Monte Carlo Hamiltonian, and the Nuclear-Inverted Sampling (NUTS) technique are the four main algorithms that are examined in this paper within the MCMC framework. It explains how they developed historically and examines their theoretical and practical traits. The study compares the benefits of the Bayesian approach, such as model design flexibility and uncertainty management, with its drawbacks, such as initial distribution selection and computational complexity. In view of the increased usage of artificial intelligence technologies and large data, the study also examines the prospects for the Bayesian approach in the future. In order to help researchers and professionals in the field stay up to date with the latest advancements in this quickly growing field, the review finishes with practical advice. These recommendations include identifying interesting research directions.