1) Το get acquainted with computational models of estimation and prediction that are based on Bayesian inference, Kalman filters, particle filters, Gaussian filtering.
2) To apply the theory to dynamical systems, e.g., stock market, weather forecasting, recommndation in the web, robotics.
Course Content (Syllabus)
Computational statistics. Dynamic systems and discrete-time Markov processes. Bayesian inference. Batch and recursive Bayesian estimation. Kalman filtering and its variations. Gaussian filtering. Data driven forecasting. Model driven forecasting and data assimilation. Applications to spatio-temporal processes (e.g., localization). Imperfect models.
Additional bibliography for study
1. Steven M.Kay Fundamentals of Statistical Signal Processing, vol. I, Estimation Theory, Prentice Hall Signal Processing Series, Upper Saddle River, NJ: Prentice Hall, 1993.
2. James V. Candy, Bayesian Signal Processing: Classical, Modern, and Particle Filtering Methods, IEEE-Wiley, Hoboken, NJ: John Wiley and Sons, 2009.
3. C. K. Hui, and G. Chen, Kalman Filtering with Real-Time Applications, 3e. Berlin: Springer Verlag, 1999.
4. S. Reich and C. Cotter, Probabilistic Forecasting and Bayesian Data Assimilation, Cambridge, U.K.: Cambridge University Press, 2015.