Applications of Bayesian Statistics. A closer look at Bayesian Inference

Summary

Τhe aim of this thesis is to analyze known Bayesian inference problems via different kind of algorithms, demonstrating the power of Bayes’ Theorem. A range of Bayesian estimators under conjugate probability distributions can simplify parameter estimation problems and provide solutions under specific conditions. The Markov Chain Monte Carlo (MCMC) techniques solve big problems with un- known/latent variables. Extensive details are given on algorithms of the MCMC family such as the Metropolis as well as the Metropolis-Hasting and the Gibbs Sam- pling methods. It is very interesting how a linear regression model, based on Gibbs sampling method, can predict an outcome variable depending on some predictor variables. In addition to explaining the flow of each algorithm, this thesis also measures their performance including performance metrics under the corresponding chapters. Decision-making is a process that allows professionals to solve problems by weighing evidence, examining alternatives and choosing the right model based on data and facts. Bayesian networks are directed probabilistic graphs which aid in decision- making when there is uncertainty. They can describe conditionally dependent and conditionally independent relationships between events and they can also represent their probability distributions. Decision trees is another very useful technique which can express problems in terms of a tree of decisions, helping to answer a variety of questions. Decision trees, like Bayesian networks assist in making decisions. Big telecommunications organisations could take advantage of Bayes’ Theorem and Bayesian Inference and create more efficient networks. MCMC sampling methods could find application in order to estimate the most convenient placement of the network resources that lead to better network performance, less delay when transmitting network services to the end users and as a result, better customer experience.