Abstract
The most essential process in statistical image and signal processing is the parameter estimation of probability density functions (PDFs). The estimation of the probability density functions is a contentious issue in the domains of artificial intelligence and machine learning. The study examines challenges related to estimating density functions from random variables. Based on minimal predictions regarding densities, the study discusses a framework for evaluating probability density functions. During the Bayesian approach, which is to generate correct samplings that reflect the probability aspect of the variables, sampling is widely used to estimate as well as define the probabilistic model of unknown variables. Because of its effectiveness and extensive application, the generalized likelihood uncertainty estimation (GLUE) method has earned the most popularity among the various methodologies. The Bayesian technique allows parameters of the model to be estimated using prior expertise in the parameter results and experimental observations. The study uses a number of engineering issues that were lately looked into to illustrate the effectiveness of the upgraded GLUE. As the focus is on the examination of sampling effectiveness in view of engineering components, only a brief summary is provided to describe every challenge. The suggested GLUE method's outcomes are contrasted with those obtained using MCMC. Nevertheless, using the GLUE approach, the model's mean squared error of prediction is substantially higher than that of the previous algorithms. The methods' results are affected by the assumptions being made on parameter values in advance. The concepts of prediction accuracy, as well as the utility of geometric testing, are presented. Such notions are valuable in demonstrating that the GLUE approach defines an inconsistent and incoherent statistical inference process.