ST3454: Stochastic Models in Space and Time
Hilary Term 2017
Lecturer: Rozenn Dahyot
Timetable
 Tuesday 13pm (Room 1.07 Lloyd Building)
 Thursday 910am (Room 1.07 Lloyd Building)
Forewords
This module is a 5 ECTS module which corresponds to about 100+ hours of study time (including the 30+ hours of lectures organised on campus). As part of your independent personal work, you are asked to learn to use the software R. Other sources of information are available to help you (e.g. online ressources such as webpages, videos, MOOCs, and books in TCD libraries). Be creative and independent to build up your skills!
R Software
Playing with data is an important part of Statistics modules. Help is given on this webpage for using R.
Course content and Lecturenotes
This course introduces different statistical modelling used for analysing stochastic processes defined in the spatial and/or time domains. These have many applications (e.g. engineering, finance). Contents include Kalman Filter, State Space Models, Brownian motion, OrnteinUhlenbeck Process, geostatistics (Kriging), functional data analysis. It is advised to come to class and take notes: only short notes will be given online.
Exam/Assessment
 Exam (100%)
References
 Linear Models for Multivariate, Time Series, and Spatial Data, R. Christensen, Springer 1991.
 Multivariate Geostatistics  An Introduction with Applications, H. Wackernagel, Springer 2003
 Statistics fo Spatial Data, Noel Cressie, Wiley 1993
 Geostatistics for Environmental Scientists, R. Webster and M.A. Oliver, John Wiley and Sons 2001
 Time series Analysis with Applications in R, J. D. Cryer and K.S. Chan, Springer 2008
 Functional Data Analysis, J.O. Ramsay and B. W. Silverman, Springer.
 A Practical Guide to Geostatistical Mapping, T. Hengl (free online book), ISBN 9789090249810
 Gaussian Markov Random Fields  Theory and Applications , H. Rue & L. Held, 2005.
 The Fourier Transform and its Applications, Brad Osgood, Stanford University
Weekly timeline
 W1: lecturenotes: Introduction  linear smoothing
 Dirac function (slides)
 lecturenotes: Time series
 Dirac function (wikipedia)
 Laurent Schwartz (wikipedia) (Field m. 1950)
 Paul Dirac (wikipedia) (Nobel Physics 1933)
 W2: lecturenotes: Filters
 W3: lecturenotes: State Space Models
 no lecture on Thursday 02/02/2017
 W4: lecturenotes: Interpolation & Kriging
 W5: lecturenotes: Stationarity
 W6: variograms, periodogram
 Tutorial: Variogram fitting
 semivariogram:nuggetrangesill
 lecturenote: periodogram
 tutorial: periodogram applied to time series 'beer' and 'airpass' (taken from R fma package, c.f. ST3010 R Lab notes)
 R lab: Finding period(s) in noisy time series
 Answers for lecturenote slide 132
 W7: Reading week

W8: Recap, Questions and feedback.
 Tutorial: State Space models with solutions
 Exercises: slides 47 and 102
 Lecture: Fourier Transform
 Example of the importance of Convolution and Fourier transform in AI : Fast Convolutional Nets With fbfft: A GPU Performance Evaluation (2015)
 Hybrid images
 White noise (wikipedia)

W9: Functional Data Analysis
 Lecturenote: Introduction FDA and Linear Smoothing
 R lab: NadarayaWatson
 R lab: Regression on basis of functions
 Suggested Reading: (chapter 1 of ) Functional Data Analysis, J.O. Ramsay and B. W. Silverman, Springer.
 Tutorial: histograms, kernel density estimate and NadarayaWatson estimators

W10: Linear Smoothing: Conclusion and Extensions
 Tutorial: Bsplines basis of functions inspired from this webpage
 Tutorial: Regularised basis approach
 Lecturenotes: Regularised basis approach
 Matrix_calculus (wikipedia)

W11: Functional PCA, Radon transform & Conclusions
 Lecturenotes: FPCA
 Extra suggested reading: Functional data clustering: a survey, J. Jacques and C. Preda (2014)
 Lecturenotes: Radon transform
 Exercise: Dirac Function and Radon transform.
 Tutorial: ODE and time series
 W12: Exam revisions.