Goodness of estimators: Ensemble properties - bias, variance, mean square error, efficiency, Cramer-Rao inequality Asymptotic (large sample) properties - asymptotic bias and consistency ĭistribution of parameter estimates and confidence regions: Sampling distributions of estimators Central limit theorem Confidence regions Significance testing
Information metrics for estimation: Notion of information in estimation Fisher’s information, Bayesian information measures. Review of mathematical and statistical essentials: Optimization and linear algebra basics Random variables and probability distributions Random signals, correlation functions and spectral density White- and coloured noiseįoundational concepts: Formal introduction to estimation Types of estimation problems Classification of estimators Soft introduction to goodness of estimators, concepts of significance testing and confidence regions Introduction: Overview of estimation Importance and value of estimation in inferencing, modelling, prediction, control, monitoring and all other fields of data-driven process analysis Course overview. The objectives of this course are three-fold: (i) to provide foundational concepts on parameter and state estimation for dynamical systems including theory and methods (ii) equip the students with the concepts of information metrics in estimation and (iii) train the students in applying these concepts to estimation problems in engineering, biological and other systems of interest using modern tools of data analysis (e.g., MATLAB).
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