Bayesian Methods in Biomedical Systems

Abstract

ABSTRACT newlineBayesian inference is the process of fitting a probability model to a set of data and summarizing the result by a probability distribution on the parameters of the model and on unobserved quantities such as predictions for new observations. newlineBayesian prediction plays an important role in different areas of applied statistics. Bayesian inference has a number of advantages in statistical modelling and data analysis. It provides a way of formalising the process of learning from data to update beliefs in accord with recent notions of knowledge synthesis. Bayesian methods usually require less sample data to achieve the same quality of inferences than methods based on sampling theory, which become extremely important in the case of expensive testing procedures. Bayesian inference has been used in various fields such as computer science, reliability analysis, etc. newlineThe major objective of a typical Bayesian statistical analysis is to get the posterior distribution of model parameters. The posterior distribution is the weighted average between knowledge about the parameters before data are observed and the information about the parameters contained in the observed data. newlineIn Bayesian estimation prior distribution, posterior distribution and the loss function are the most important ingredients. newlineStudies have been done vigorously in the literature to determine the best method in estimating its parameters. Recently, much attention has been given to the Bayesian estimation approach for parameter estimation under different loss functions which is in contention with other estimation methods. Loss functions lie in the heart of statistical decision theory, which is commonly recognized as a coherent foundational framework for inferential problems and comparison of procedures. newlineBased on the above concepts, the Thesis entitled Bayesian Methods in Biomedical Systemsand#8223; has been developed. newlineIn this thesis, Bayesian inference has been studied using the Poisson model, the Gompertz model, the Conditional Autoregressive model and the var