Bayesian Analysis, Multilinear Regression and Modern Machine Learning Algorithms Applied for Soil Probabilistic Characterization

Modern engineering problems are facing the growing demand to deal with huge amount of data and their intrinsic uncertainties. This exigence has led us to unprecedented insights and developments in the machine learning field. To date, the healthcare and financial sectors has been the precursor of practical application of machine learning approaches. In geotechnics and rock mechanics, the materials we deal with are characterized by a large amount of data, various levels of uncertainty and often a prior knowledge, therefore they lend themselves well to this type of analysis. This article aims to present Bayesian methods and machine learning algorithms applied for geotechnical characterization of soil and rocks. Once the test sample has been properly filtered and classified, we will demonstrate the potentiality of multivariate Bayesian linear regression as a main tool for dealing with multivariate data and uncertainty. In addition to frequentist approaches, we will make use of Bayesian models where the regression parameters, based on a prior distribution, will be calculated in terms of mean and variance.