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SYLLABUS
Prof. Emanuele Di Lorenzo
phone 404-894-3994, web
office ES&T 3252
email edl@eas.gatech.edu
Andrew Davis
phone 864-357-6761
office ES&T 3162
email
andrew.davis@gatech.edu |
ESM 210,
MW 3:05 -
4:25
PM
Discrete Inverse and State Estimation Problems
Carl Wunsch, Cambridge Press.
Class notes on Objective Analysis
Dennis Hartmann, Web Notes
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: This
course is an advanced introduction to environmental data analysis. It is
intended for first year graduate students and senior undergraduates. The
goal of this class is to provide a deeper understanding of the theory
underlying the statistical analysis of environmental data, both in the
space, time and spectral domain, and to provide the students with a
hands on experience. Ideally at the end of this class you will have
developed a series of computer programming tool boxes and theoretical
skills that should immediately be available for analyzing and modeling
data in your own research.
Although some previous knowledge of
probability and statistics is required, a background review will be
provided. Concepts and notation will be reintroduced as needed. In this
class you will learn (A) how to combine models, which quantify
statistical or dynamical relationships, with observations, (B) time
series analysis, (C) forecasting and extrapolation and (D) signal
decomposition. A more detail description of these topics is appended in
the
below.
:
There will be a homework assignment
approximately every two weeks. You will be required to learn some
computer programming skills with either MATLAB or the R –software
(http://www.r-project.org/) or IDL or anything you
wish. If you do not have access to a computer with these software
you will be provided with an account at the beginning of the semester.
The type of data to be analyzed in the homeworks will vary depending on
the interest of the attending students.
:
There is going to be a short MIDTERM and a FINAL
presentation.
:
To help you put into practice your data analysis skills you will be
asked to choose a data analysis project, possibly involving your own
research data, that you will present at the end of the semester. The
project is to be chosen based on a set of questions that you would like
to answer rather than the type of data analysis technique you would like
to apply, and it may require the use of one or more data analysis
techniques.
:
50% Homework, 25% Midterm,
25% Presentation.
:
* :
Matrix and Vector Algebra, Fundamental Statistical Measures,
Multivariable Probability Densities, Sample Estimates, Correlation and
Covariance, Function and Sums of Random Variables, Central Limit
Theorem.
(3 lectures)
* :
Interpolation and Function Fitting, Least Square modeling and
Singular Vector Expansion, Uncertainties in Estimates, Inverse Methods,
Statistical vs. Dynamical Constraints.
(7 lectures)
* :
Time and Frequency Domain Models, Stationarity, Auto-Regression Models,
Spectral Analysis and Coherence, Trend Analysis and Significance,
Estimating errors in time series reconstruction.
(8 lectures)
* :
Statistically Optimal Linear Estimators, Regression models, space and
time models, objective mapping (multivariate regression), covariance
modeling.
(7 lectures)
* :
Multivariate eigenfunction analysis, EOFs, PCA, CCA, and Wavelet
analysis
(5 lectures)
* :
2-3 lectures |
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