STAT 775 — Fall 2021 · Colin Grudzien
Colin Grudzien

STAT 775 — Fall 2021

A schematic of the observation-analysis-forecast cycle.

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.

Introduction

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.

Course syllabus

Modules, assignments and grades will be posted through Web Campus.

Course information

There are no required books for this class but the following books are suggested for further readings. The course will loosely follow Chapters 1 - 5 and 7 from Stochastic processes, estimation, and control and Chapters 1 - 3 and 6 - 11 of Data assimilation: methods, algorithms, and applications. Other sources of material will include relevant journal articles and surveys.

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 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 Gauss-Markov models Part I Supplementary materials: Stochastic processes and discrete Gauss-Markov models Part II Supplementary materials:
09/20 - 09/26 Continuous-time models and stochastic calculus Part I Supplementary materials: Continuous-time 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 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