A schematic of the recursive observation-analysis-forecast cycle of sequential, Bayesian filtering. Estimates of the density are squentially forecasted with the dynamical model and conditioned with the likelihood of incoming observations.
This is the course web page for Data Assimilation and Estimation Theory, STAT 775 FALL 2021 – Section 1001. Please see the menus below for class resources and the up-to-date class schedule.
The up-to-date schedule is in the table below.
|Week||Day 1||Day 2||Day 3|
|08/23 - 08/29||Course introduction||A review of random variables||A review of sampling distributions and the univariate Gaussian|
|08/30 - 09/05||A review of inner product spaces and matrix algebra||A review of linear transformations||A review of vector calculus and concepts in optimization|
| 09/06 -
|No class 09/06 — Labor Day||A review of random vectors||A review of covariances and the multivariate Gaussian|
|09/13 - 09/19||Conditional expectations and Bayesian inference||Stochastic processes and discrete Gauss-Markov models Part I||Stochastic processes and discrete Gauss-Markov models Part II|
|09/20 - 09/26||Continuous-time models and stochastic calculus Part I||Continuous-time models and stochastic calculus Part II||Elementary numerical solution to ODEs and SDEs Part I|
|09/27 - 10/03||Elementary numerical solution to ODEs and SDEs Part II||Minimum variance and maximum likelihood estimation Part I||Minimum variance and maximum likelihood estimation Part II|
|10/04 - 10/10||The Kalman filter Part I||The Kalman filter Part II||Variational least-squares Part I|
|10/11 - 10/17||Variational least-squares Part II||Joint state-parameter estimation||Filtering, smoothing and sequential smoothing|
|10/18 - 10/24||Review day||Particle filters Part||Metropolis-Hastings Part I|
|10/25 - 10/31||Metropolis-Hastings Part II||Review day||No class 10/29 — Nevada Day|
|11/01 - 11/07||The 3D-VAR and the extended Kalman filter||Review day||Review day|
|11/08 - 11/14||4D-VAR and generalized nonlinear least-squares||The ensemble Kalman filter and smoother Part I||The ensemble Kalman filter and smoother Part II|
|11/15 - 11/21||No new material – work on term project||No new material – work on term project||No new material – work on term project|
|11/22 - 11/28||No new material – work on term project||No new material – work on term project||No class 11/26 — Family Day|
|11/29 - 12/05||No new material – work on term project||No new material – work on term project||No new material – work on term project|
|12/06 - 12/12||No new material – work on term project||No class 12/08 — Prep Day||Term Paper due: 12/10 5:00 PM|