CVEN 5454 (Quantitative Methods)
PROBABILITY & STATISTICAL METHODS FOR NATURAL AND ENGINEERED SYSTEMS
  Fall 2025
Instructor: Prof. R. Balaji
Office Location: ECOT-452
Phone: (303)-492-5968
E-mail: balajir@colorado.edu
Lectures: Tue. and Th. 12:30 - 2:00 in ECCE 1B 41 & Zoom
Office Hours: Anytime on E-mail, by appointment and Walk-in

Course Material & Resources                                                      
R-sessions Resources
        Homeworks                

Information

"Text" (Montgomery, Runger)
"Probability Applications Text" (Ang and Tang)
 Online Books
 Springer books
Basic Probability & Bayesian Rules
 Random Variables, PMF/PDF/CDF

Extreme Value Distribution Resources

Joint Distributions and Functions
of Random Variables

  • Chapter 5
  • Ang-n-Tang-Chap4 -PDFs-of-Joint RVs
  • Ang-n-Tang-Chap4-Moments-of- Joint RVs

Point and Interval Estimation

Hypothesis Testing

Regression

Nonparametric Density Estimation

Bayesian Modeling
Bayes resources - notes, presentations, etc.

Copula

  R-links

Data Files for R-practice:
 Leeferry-mon-data.txt – Lee’s Ferry Data
Note: col1 = year, col2 = Jan… col13 = Dec
Units: acre-feet; divide by 10^6 to get MAF (Million Acre-Feet) or;
 (X 0.0004691 to get cubic meters per second (i.e., cms))
Leeferry-annual-maximum.txt
 aismr.txt – All Indian monthly rainfall total (in mm)
 nino3-index.txt – Nino3 Index of ENSO
annual-peak-clark-fork.txt – Annual Flood Data at Clark Fork River, near Missoula, Montana (cubic feet / second)
 
R-Tutorials - Sean-Billy-etc
R - Mikaela - lecture and Commands

R-Session #1 
  •  Data Reading
  • Compute basic statistics - including robust measures
  • Line and boxplots - including multiple plots
  • Quantile plots
  • Source Functions
R-Session #2

R-Session #3

  • Linear Combination of Random Variables - Using Monte Carlo
  • 2d-histogram and Kernel density PDF
  •  2d and Conditional Kernel Density Estimation
  • Copula
  • Bayesian parameter estimation
  • Correlation
  • Mutual Information

R-Session #4

  • Confidence Interval for sample mean and variance
  • Hypothesis test of sample means and variances
  • Nonparametric tests
  • Bootstrap-based confidence intervals and consequently, hypothesis test
R-Session #5
 Bayesian Estimation - Installing R-JAGS
R-JAGS Manual
Intro to Bayesian Reasoning (including RJAGS)
R-Session Bayes & Bayes Regression