Calendar · Lecture Notes
MIT OpenCourseWare
Inference from Data and Models
- Instructor
- Carl Wunsch
- Term
- Spring 2005
- Level
- Graduate
- What's inside
- 1 lecture note · 96 other files · 4 web pages
- Materials open
- MIT OCW
About this course
Source: MIT OpenCourseWare 12.864 Inference from Data and Models, Spring 2005, Carl Wunsch — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.
Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.
Before you start
Prerequisites are not listed here. Check MIT's own syllabus for this course.
How this course was organized
What's here, and what isn't
- A lecture sequence of 12 items is confirmed. It stays as organized materials rather than a full course order.
Not included here
1 item from the source could not be safely included:
- MIT's page format for this item wasn't recognized clearly enough to place it safely.
Materials by section
Grouped by section, as MIT organized them. Not sequenced or ordered.
Lecture Notes
35 files
- This resource includes the different contents captures in course notes (tabl_of_contents.pdf) Download
- Table of Contents Download
- Preface Download
- Chapter 1 - Frequency Domain Formulation Download
- 1.1 Fourier Transforms and Delta Functions Download
- 1.2 Fourier Series and Time-Limited Functions Download
- 1.3 The Sampling Theorem Download
- 1.4 Discrete Observations Download
- 1.5 Aliasing Download
- 1.6 Discrete Fourier Analysis Download
- 1.7 Identities and Difference Equations Download
- 1.8 Circular Convolution Download
- 1.9 Fourier Series as Least-Squares Download
- 1.10 Stochastic Processes Download
- 1.11 Spectral Estimation Download
- 1.12 The Blackman-Tukey Method Download
- 1.13 Colored Processes Download
- 1.14 The Multitaper Idea Download
- 1.15 Spectral Peaks Download
- 1.16 Spectrograms Download
- 1.17 Effects of Timing Errors Download
- 1.18 Cross-Spectra and Coherence Download
- 1.19 Simulation Download
- Chapter 2 - Time Domain Methods Download
- 2.1 Representations-1 Download
- 2.2 Geometric Interpretation Download
- 2.3 Representations-2 Download
- 2.4 Spectral Estimation from ARMA Forms Download
- 2.5 Karhunen-Loève Theorem and Singular Spectrum Analysis Download
- 2.6 Wiener and Kalman Filters Download
- 2.7 Gauss-Markov Theorem Download
- 2.8 Trend Determination Download
- 2.9 EOFs, SVD Download
- Chapter 3 - Examples of Applications in Climate Download
- 3.1 References Download
Assignments
15 problem sets
- Assignments for 2005 · Problem Set 1 Download
- Assignments for 2005 · Problem Set 2 Download
- Assignments for 2005 · Problem Set 3 Download
- Assignments for 2005 · Problem Set 4 Download
- Assignments for 2005 · Problem Set 5 Download
- 2004 Problem Sets · Problem Set 1 Download
- 2004 Problem Sets · Problem Set 2 Download
- 2004 Problem Sets · Problem Set 3 Download
- 2004 Problem Sets · Problem Set 4 Download
- 2004 Problem Sets · Problem Set 5 Download
- Problem Set 6 Download
- 2003 Problem Sets · Problem Set 1 Download
- 2003 Problem Sets · Problem Set 2 Download
- 2003 Problem Sets · Problem Set 3 Download
- 2003 Problem Sets · Problem Set 4 Download
Other materials from this course
46 files
- This resource includes notes and solutions of problems using Gauss-Markov type method (adaptive_5_7.pdf) Download
- This resource contains the appendix for chapter 2- Basics Machinary (appendix1_2_10.pdf) Download
- This resource contains the appecdix for chapter 2 - Basics Machinary (appendix2_2_11.pdf) Download
- This resource contains the appexdix for chapter 2 -Basics Machinary (appendix3_2_12.pdf) Download
- This resource has been primarily devoted to the principles underlying various state estimation… (approximate_5_3.pdf) Download
- The purpose of this resource is to record a number of results which are useful in finding and… (background_2_1.pdf) Download
- This file contains notes on the time dependent inverse problem: state estimation (background_4_1.pdf) Download
- This resource contains the following topics: Differential Equations, Partial Differential… (chap1.pdf) Download
- The purpose of this chapter is to record a number of results which are useful in finding and… (chap2lg.pdf) Download
- This resource includes introduction of left and right eigenveectors, model nonlinearity, the… (chap3.pdf) Download
- chap4.pdf Download
- This resource includes the following topics: Ensemble Methods and Particle Filters, Monte… (chap5.pdf) Download
- This file contains notes on Lagrange Multipliers and Adjoints, and the control riccati problem (contrl_estim_4_4.pdf) Download
- This file contains notes on controllability and observability (contrl_obser_4_6.pdf) Download
- This resource mainly discusses about the differential equations which are often used to describe… (differen_eq_1_1.pdf) Download
- This file contains notes on duality and simplification: The steady-state filter and adjoint (duality_4_5.pdf) Download
- eigenvector_3_1.pdf Download
- This file contains the notes on empirical orthogonal functions using matrices (empirical_3_5.pdf) Download
- This file contains notes on model and data consistency, and estimation (estimation_4_3.pdf) Download
- This resource includes the following examples: A Tracer Box Model, A Tomographic Problem, A Second… (examples_1_3.pdf) Download
- This resource contains exercises for second chapter - Basics Machinary (exercise_2_13.pdf) Download
- This resource includes the the importance of the Forward Model (forward_modl_1_4.pdf) Download
- This file contains notes on forward models (forward_modl_4_8.pdf) Download
- This file contains notes for basic ideas and notation, models and how to find an inverse matrix A… (ideas_nota_4_2.pdf) Download
- This resource contains the following topics: Least-Squares, and Minimum Variance Recursive… (improv_recur_2_8.pdf) Download
- This file contains the notes for the topic inequality constraints and nonnegative least squares (inequality_3_3.pdf) Download
- This file contains notes for Kriging and other variants of Gauss-Markov estimation (kriging_3_6.pdf) Download
- This resource contains the following topics: Exact Constraints, and Relation to Green Functions (least_sq_adj_2_6.pdf) Download
- This resource contains the following topics: Basic Formulation, Weighted and Tapered Least-Squares… (least_square_2_4.pdf) Download
- linear_3_4.pdf Download
- This resource includes a brief results of equations solved using matrix and vector algebra (matrix_vectr_2_2.pdf) Download
- This resource incldues the followig topics: The Fundamental Result, Linear Algebraic Equations… (min_variance_2_7.pdf) Download
- This resource includes some equations based on Ensemble Methods and Particle Filters (monte_carlo_5_1.pdf) Download
- This file contains notes on total least squares, method of total inversion, variant nonlinear… (nonlinear_3_7.pdf) Download
- This file contains notes on nonlinear models using matrices (nonlinear_4_7.pdf) Download
- This resource includes the solutions of equations by non-normal systems (nonnormal_5_6.pdf) Download
- This resource includes the following topics: Meteorological Assimilation, and Nudging and Objective… (numerical_5_2.pdf) Download
- This resource explaines the use of Partial Differential Equations (partial_eq_1_2.pdf) Download
- This resource includes the preface of 1 part and a large extent the second edition of The Ocean… (preface_1.pdf) Download
- This resource includes some summary of what has been accomplished may be helpful from lecture 2… (recapitul_2_9.pdf) Download
- This resource includes the solutions of the equations using Reduced State Methods (reduced_5_4.pdf) Download
- This file contains notes on the sampling, one dimensional interpolation, higher dimensional… (sampling_3_2.pdf) Download
- This resource includes the following topcis: Simple Vector Expansions, Square-Symmetric Problem… (sing_vector_2_5.pdf) Download
- This resource includes the following topics: Probability Densities, Moments, Sample Estimates… (statis_regr_2_3.pdf) Download
- This file contains notes on the summary of the course (summary_4_9.pdf) Download
- This resource includes the advantages and disadvantages of solving the equations using Lagrange… (uncertainty_5_5.pdf) Download
Course outline
Calendar · Lecture Notes
Lecture 2: Examples of Inverse Problems, Static and Time Dependent
Calendar · Lecture Notes
Lecture 3: Basic Vector/Matrix Notation Algebraic Formulation
Calendar · Lecture Notes
Lecture 7: Basic Statistics Concepts and Notation
Calendar · Lecture Notes
Lecture 8: Variances/Covariances Biases of Solutions
Calendar · Lecture Notes
Lecture 9: Special Case of Eigenvector Solutions
Calendar · Lecture Notes
Lecture 14: Time-dependent Models Whole Domain Least-Squares
Calendar · Lecture Notes
Lecture 18: Stationary Processes Numerical Fourier Series/Transforms; Delta Functions
Calendar · Lecture Notes
Lecture 19: Statistics of Fourier Representations Sampling Periodograms
Calendar · Lecture Notes
Lecture 20: Convolution Power Density Spectral Estimates
Calendar · Lecture Notes
Lecture 21: Coherence; Multiple Linear Regression
Calendar · Lecture Notes
Lecture 22: Filtering, Prediction Problems
MIT OpenCourseWare, Carl Wunsch, 12.864 Inference from Data and Models, Spring 2005.
License: CC BY-NC-SA 4.0 · Edition: Spring 2005 · Open the original course on OCW ↗
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