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Stochastic Hydrology

IISc Bangalore Course , Prof. P. P. Mujumdar       Subscribe to feed

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Lecture 32: Mod-07 Lec-32 Regression on Principal Components

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Lecture Details :

Stochastic Hydrology by Prof. P. P. Mujumdar, Department of Civil Engineering, IISc Bangalore For more details on NPTEL visit http://nptel.iitm.ac.in

Course Description :

The objective of this course is to introduce the concepts of probability theory and stochastic processes with applications in hydrologic analysis and design.
Modeling of hydrologic time series with specific techniques for data generation and hydrologic forecasting will be dealt with.
Case study applications will be discussed.
Contents:
Introduction to Random Variables (RVs).
Probability Distributions - One dimensional RVs.
Higher Dimensional RVs - Joint Distribution.
Conditional Distribution; Independence.
Properties of Random Variables.
Parameter Estimation.
Parameter Estimation.
Hydrologic Data Generation.
Introduction to Time Series - stationarity; ergodicity.
Purely stochastic Models; Markov Processes.
Spectral Density; Analysis in the Frequency Domain.
Auto Correlation and Partial Auto Correlation.
Auto Regressive Moving Average Models (Box - Jenkins models - model identification; Parameter estimation ; calibration and validation; Simulation of hydrologic time series ; Applications to Hydrologic Forecasting - case studies).

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  1. Mod-01 Lec-01 Introduction
  2. Mod-01 Lec-02 Bivariate Distributions
  3. Mod-01 Lec-03 Independence ; Functions of Random Variables
  4. Mod-01 Lec-04 Moments of a Distribution
  5. Mod-02 Lec-05 Normal Distribution
  6. Mod-02 Lec-06 Other Continuous Distributions
  7. Mod-03 Lec-07 Parameter Estimation
  8. Mod-03 Lec-08 Covariance and Correlation
  9. Mod-03 Lec-09 Data Generation
  10. Mod-04 Lec-10 Time Series Analysis - I
  11. Mod-04 Lec-11 Time Series Analysis - II
  12. Mod-04 Lec-12 Time Series Analysis-III
  13. Mod-04 Lec-13 Frequency Domain Analysis - I
  14. Mod-04 Lec-14 Frequency Domain Analysis - II and ARIMA Models - I
  15. Mod-04 Lec-15 ARIMA Models-II
  16. Mod-04 Lec-16 ARIMA Models - III
  17. Mod-04 Lec-17 ARIMA Models-IV
  18. Mod-04 Lec-18 Case Studies - I
  19. Mod-04 Lec-19 Case Studies - II
  20. Mod-04 Lec-20 Case Studies -III
  21. Mod-04 Lec-21 Case Studies- IV
  22. Mod-05 Lec-22 Markov Chains - I
  23. Mod-05 Lec-23 Markov Chains-II
  24. Mod-06 Lec-24 Frequency Analysis - I
  25. Mod-06 Lec-25 Frequency Analysis-II
  26. Mod-06 Lec-26 Frequency Analysis - III and Probability Plotting - I
  27. Mod-06 Lec-27 Probability Plotting - II
  28. Mod-06 Lec-28 Goodness of Fit
  29. Mod-06 Lec-29 IDF Relationships
  30. Mod-07 Lec-30 Multiple Linear Regression
  31. Mod-07 Lec-31 Principal Component Analysis
  32. Mod-07 Lec-32 Regression on Principal Components
  33. Mod-07 Lec-33 Multivariate Stochastic Models - I
  34. Mod-07 Lec-34 Multivariate Stochastic Models - II
  35. Mod-07 Lec-35 Multivariate Stochastic Models - III
  36. Mod-08 Lec-36 Data Consistency Checks -I
  37. Mod-08 Lec-37 Data Consistency Checks - II
  38. Mod-08 Lec-38 Data Consistency Checks - III
  39. Mod-09 Lec-39 Recent Applications: Climate Change Impact Assessment
  40. Mod-09 Lec-40 Summary of the Course