## ST3454: Stochastic Processes in Space and Time

Hilary Term 2017

Lecturer: Rozenn Dahyot

### Timetable

- Tuesday 1-3pm (Room 1.07 Lloyd Building)
- Thursday 9-10am (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, Orntein-Uhlenbeck 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 978-90-9024981-0
- Gaussian Markov Random Fields - Theory and Applications , H. Rue & L. Held, 2005.

### 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
- semi-variogram:nugget-range-sill
- 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.