Interval Analysis. The interval number. The interval arithmetic. The fundamental theorem of Interval Analysis for solving problems. The interval arithmetic for problems with many variables. Convergence of interval methods. Termination criteria. Basic interval methods. Basic characteristics of interval methods for global optimization problems. Acceleration devices. Basic interval methods for finding all global solutions of an objective function.
Data Science. Simple linear regression using interval arithmetic. Non-linear and multiple regression using intervals. Auto-regressive and/or moving average models for interval arithmetic. Principal Component Analysis (PCA) and Factor Analysis (FA) using interval variables. Statistical modelling. Structural Equation Modelling.
Applications. Application on real data, i.e. satisfaction questionnaires or financial (stock-market) data. Respondents profile. Application of Regression recursive trees in order to approximate statistical models