Special Mathematics Lecture
Contact:
Serge Richard (richard@math.nagoyau.ac.jp), Rm. 247 in Sci. Bldg. A
Introduction to data assimilation (Spring 2022)
Registration code : 0053621
Schedule : Wednesday (18.30  20.00) in room 207 of Science Building A and on Zoom

Class dates :
April 13, 20, 27
May 11, 18, 25
June 1, 8, 15, 22, 29
July 6, 13, 20

Program :
1) Motivation
2) Mathematical background
3) Basic algorithms of data assimilation
4) Variants and extensions of the Kalman filter

Weekly summaries :
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13

Study sessions :
Are organized on an individual basis by some students.
For any information, contact
Hiep,
Qi,
Vic,
Tom.

For the evaluation, you need to submit the solutions of some exercises and/or the proofs of some statements.
These submissions can take place at any time during the semester.
If you have any question, contact me
or Qiwen Sun.

Student's reports :
A minimization problem, by Sirawich Saranakomkoop
Proof of Woodbury Matrix Identity and the Kalman Update Formula, by Vic Austen
Forecast: data driven, by Nguyen Minh Diep
Best Linear Unbiased Estimator, by Ethan Dowley
Marginal and conditional pdfs, and various exercises about the normal distribution, by Nguyen Hoang Hiep and Jotaro Kobayashi
On Monte Carlo quadrature, by Taichi Kato
The Kalman filter, by Hla Hany Mohamed Helmy Ahmed
Monte Carlo method: an application for the determination of pi, by Miki Satoshi
An example of Bayesian inference, by Peng Qi
Another approach for the Kalman filter, by Nguyen Duc Thanh
Several results with the normal distribution, by Malak Hamed Mokhtar
Least squares, by Qiuling Low

References:
[ABN] Data Assimilation, methods, algorithms, and applications, by M. Asch, M. Bocquet, M. Nodet
[Ev] Data Assimilation, the ensemble Kalman filter, by G. Evensen
[HE] Introduction to hidden SemiMarkov models, by J. van der Hoek, R. Elliott
[LSZ] Data Assimilation, a mathematical introduction, by K. Law, A. Stuart, K. Zygalakis
[RC] Probabilistic Forecasting and Bayesian Data Assimilation, by S. Reich, C. Cotter
[Roh] Multivariate localization methods for ensemble Kalman filtering, S. Roh et al.
[Sa] Bayesian filtering and smoothing, by S. Sarkka
[SRMT] Analysis of COVID19 spread in Tokyo through an agentbased model with data assimilation, C. Sun, S. Richard, T. Miyoshi, N. Naohiro
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