#### MA8001 Autumn 2019

# Methods for spatial and spatio-temporal data and value of information analysis

## Messages

- Exam dates: 20 Nov (Henrik, Håkon, Mina), 4 Dec (Andreas, Dennis, Jorge) and 11 Dec (Alberto, Faiga, Kwaku, Martin, Silius, Susan)
- Exam will be 15 min presentation (one of projects 1-7) and then questions. This questioning will mainly be focused around some key questions you receive 45 min before your exam. You will then prepare answers to these questions sitting on your own in a separate room.
- No lecture on Oct 18!
- I put lecture notes online.
- Lectures will from now on (13 Sept) be Friday 1215-14. Lectures are in Room 656, 6th floor, Central building II.
- First lecture is 29 Aug (Inverse Problems). The second lecture is 13 Sept (Hidden Markov models).
- This course is intended for MSc or PhD students working on spatial / spatio-temporal data and methods for data assimilation or design of experiments in this setting. MSc students can do this course as modules in course TMA4505. PhD students can do it as part of their training. Email jo.eidsvik@ntnu.no if you are interested in taking the class.

## Lecture plan

29 Aug | Inverse problems | Hand-out report (Kolbjørnsen, 2002) | Project,Data |

13 Sept | Hidden Markov models | Parts of Ch 2.3-4 + Appendix A.3.1, Hand-out report (Lindberg, 2014), Lecture notes: PDF | Project |

20 Sept | Spatial Gaussian process regression and spatio-temporal Gaussian processes | Ch 4.1-4, Sigrist et al., Lecture notes: PDF | Project |

27 Sept | Work on projects in class | ||

4 Oct | Ensemble Kalman filter | Hand-out report (Myrseth and Omre, 2011), Katzfuss et al. paper. Lecture notes PDF | Project,Data |

11 Oct | Decision analysis and value of information | Ch 3. Lecture notes PDF | Project |

18 Oct | Work on projects in class | ||

25 Oct | Spatial decision making and value of information | Ch 5.1-4 & 6.1-6.2.1 Lecture notes PDF | Project |

1 Nov | Value of information computations, design and sequential information | Ch 5.5-9. Lecture notes PDF | Project |

## Curriculum

Topics from lectures and projects, and the following literature:

- Kolbjørnsen, 2002, Fundamentals of inverse problems (PhD introduction);
- Lindberg, 2014, Inference and categorical Bayesian inversion of convolved hidden Markov models applied to geophysical observations (PhD introduction);
- Myrseth and Omre, 2011, The ensemble Kalman filter and related filters, In: Biegler, L., Large-scale Inverse Problems and Quantification of Uncertainty. Wiley series in Computational statistics.
- Katzfuss et al. Understanding the ensemble Kalman filter https://www.tandfonline.com/doi/full/10.1080/00031305.2016.1141709
- Eidsvik et al., 2015, Value of information in the Earth sciences (Chapters 1-3, 4.1-4, 5, 6.1, 6.2.1) http://www.cambridge.org/9781107040267

## Learning outcomes

1. Knowledge. The student has knowledge about statistical models for spatial and spatio-temporal phenomena, and methods for fitting such models from data. The student has acquired fundamental understanding of inverse problems and regularisation methods for large-scale models. The student has solid understanding of Gaussian process models, hidden Markov models and the ensemble Kalman filter, which are very important tools for extracting insight from spatial and spatio-temporal data. The student also has knowledge about conditioning spatial and spatio-temporal models, and in quantifying the effect of various data gathering schemes for evaluating spatial designs. The student has knowledge about decision theoretic concepts, in particular the value of information, and has acquired solid understanding of spatial decision problems, and the value of information in this context.

2. Skills. The student understands the assumptions underlying important spatio-temporal models, and can use the models and methods to do inference and predictions from spatio-temporal data. The student can use a workflow to conduct value of information analysis in spatial decision situations.

## Exam

Oral exam at the end of the semester. Project presentation and questions from curriculum.

## Responsible

Jo Eidsvik, room 1034, Sentralbygg II, jo [dot] eidsvik [at] math [dot] ntnu [dot] no