Advanced Data Analysis Techniques

Instructor:	R. Balaji
Office:		ECOT-541
Phone:		2-5698
e-mail:		balajir@spot.colorado.edu

Timings:	Tuesdays and Thursdays : 12:30 - 1:45
Location:	ECCR 1B08

Course:		CVEN 5833

Objective: 

The objective of the course is to provide exposure to a variety of traditional
and recent data analysis techniques for solving "typical" problems in
hydrology and hydroclimatology. The techniques are general in nature
that they could be easily applied to data analysis problems in other
fields.

Pre-requisites:

Basic course in probability and statistics, calculus, differential

equations, linear algebra.


Topics proposed:

1. Scenario generation:
   (for decision making models)

    Parametric and Nonparametric fitting of probability
    density/distribution functions
      Univariate
      Multivariate

    Re-sampling from distribution functions.
    	(Monte-Carlo methods, Bootstrap techniques)

    Risk theory/application
   
    Regionalization issues/scaling - stable laws	


2. Time Series Problems 

	General Time series frameworks
		-ARMA
		-State Space/Non-linear Dynamics/Chaos/Predictability
		-Bootstrap

	Stationarity/trends
		Spectral analysis
		Long memory issues and scaling/Hurst phenomenon

	
3.  Multivariate data analyses
    (identifying patterns/signal from multivariate data set such as
    spatial rainfall, spatial streamflow, etc.)
    Also identifying relationships between two sets of multivariate data
    e.g. spatial rainfall and global Sea Surface Temps.,

      Principal Component Analysis
      SVD analyses
      Canonical Correlation Analyses
      Singular Spectrum Analyses



References:

Visualizing Data by William S. Cleveland  - Hobart Press, Summit, NJ

Density Estimation for Statistics and Data Analysis by B. W. Silverman -
Chapman and Hall

Multivariate Density Estimation Theory, Practice, and Visualization by
David W. Scott - John Wiley & Sons.

Local Regression and Likelihood by Clive Loader - Springer

Smoothing Techniques with implementation in S by Wolfgang Hardle -
Springer

Analysis of Observed Chaotic Data by Abarbanel - Springer
       
Nonlinear Time Series Analysis by Holger Kantz and Thomas
Schreiber - Cambridge

Statistical Methods in Water Resources by D.R. Helsel, R.M. Hirsch 
- Elsevier

The Analysis of Time Series: An Introduction  by Chris Chatfield
CRC Press, Inc.


Singular Spectrum Analysis: A New Tool in Time Series Analysis
by  James B. Elsner (Editor)  Anastasios A.  Tsonis (Editor)


Statistical Methods in the Atmospheric Sciences: An Introduction
 by Daniel S. Wilks - Academic Press

Probability and Statistics for Engineers and Scientists by R. E. Walpole
and R. H. Myers, Macillan Publishing and Co.