#### MA8001 Autumn 2016

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

## Messages

- 13.9.2016: First lecture. At 08:30-10:00. Room 656 (6 floor) Central building II.

## Lecture plan

13.09 | Inverse problems | Hand-out report (Kolbjørnsen, 2002) | Project,Data,Some code |

20.09 | Hidden Markov models | Parts of Ch 2.3-4 + Appendix A.3.1, or Hand-out report (Lindberg, 2014) | Project,Some code |

27.09 | Spatial regression model | Ch 4.1-4 | Project,Some code |

04.10 | NO LECTURE | ||

11.10 | Ensemble Kalman filter | Hand-out report (Myrseth and Omre, 2011) | Project,Some code,code for exact solution,Data |

18.10 | Decision analysis and value of information | Ch 3 | Project,Some code |

25.10 | Spatial decision making and value of information | Ch 5.1-4 & 6.1-6.2.1 | Project,Some code |

08.11 | Value of information and design of experiments | Ch 5.5-6 and 5.9 & 6.3.2 / 6.4.1 | Project and some code |

## Curriculum

Topics from lectures and projects. 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.
- Eidsvik et al., 2015, Value of information in the Earth sciences (Chapters 1-3, 4.1-4, 5, 6.1, 6.2.1, 6.3.2, 6.4.1) 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