A schematic of the recursive observationanalysisforecast 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 uptodate class schedule.
The uptodate schedule is in the table below.
Week  Day 1  Day 2  Day 3 

08/23  08/29  Course introduction  A review of random variables Supplementary materials:  A review of sampling distributions and the univariate Gaussian Supplementary materials: 
08/30  09/05  A review of inner product spaces and matrix algebra Supplementary materials:  A review of linear transformations Supplementary materials:  A review of vector calculus and concepts in optimization Supplementary materials: 
09/06  09/12 
No class 09/06 — Labor Day  A review of random vectors Supplementary materials:  A review of covariances and the multivariate Gaussian Supplementary materials: 
09/13  09/19  Conditional expectations and Bayesian inference Supplementary materials:  Stochastic processes and discrete GaussMarkov models Part I Supplementary materials:  Stochastic processes and discrete GaussMarkov models Part II Supplementary materials: 
09/20  09/26  Continuoustime models and stochastic calculus Part I Supplementary materials:  Continuoustime models and stochastic calculus Part II Supplementary materials:  Elementary numerical solution to ODEs and SDEs Part I Supplementary materials: 
09/27  10/03  Elementary numerical solution to ODEs and SDEs Part II Supplementary materials: 
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 leastsquares Part I

10/11  10/17 
Variational leastsquares Part II

Joint stateparameter estimation

Filtering, smoothing and sequential smoothing

10/18  10/24  Review day 
Particle filters Part

MetropolisHastings Part I

10/25  10/31 
MetropolisHastings Part II

Review day  No class 10/29 — Nevada Day 
11/01  11/07  The 3DVAR and the extended Kalman filter  Review day  Review day 
11/08  11/14  4DVAR and generalized nonlinear leastsquares  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 