**Professor Ke-Sheng Cheng (Email: rslab@ntu.edu.tw)**

RSLAB_BSE_NTU

No. 1, Section 4, Roosevelt Road

Bioenvironmental Syst. Eng., National Taiwan University

This course is designed to facilitate students with skills of R coding for data analysis and graphic presentation, while learning fundamental concepts of statistical methods. Students who want to register for this course should have taken an entry level statistics. Familiarity with R language is not required, although it will be helpful.

My philosophy of teaching this course is to design a list of problems, each with specific learning objectives (important concepts and theories), and to guide students to solve these problems through computer coding (using R) and in-class discussions. Such an approach will enable students to learn R quickly and gain insights into more complicated or abstract concepts of many statistical methods. Thus, this class will be conducted in an **interactive format** through the following arrangements:

- Subjects and statistical methods (
**SSMs**) to be covered will be fully explained in the beginning of the semester (the first three or four weeks). For each SSM, problems to be solved or tasks to be conducted will be given. - Students are grouped (based on their backgrounds or interests) into several groups. Each group will be assigned certain SSMs to study during the semester.
- Every week, two or more groups (depending on number of groups in the class) will present their progress and results in class, followed by discussions.
- Each group is expected to make several presentations during the semester. Hopefully, once in every 3 to 4 weeks.
- A final presentation is required for all groups in the final week.

Students will be evaluated based on their performance in the progress report and presentations, as well as their participations in class discussions.

Note: **Stochastic simulation** is an essential element of this class. Through stochastic simulation, students will observe realizations and have a better understanding of statistical theories.

**Weekly schedule of individual groups **

### R - Introduction & Graphics

### SSM1 Drought index (SPI) calculation and spatiotemporal visualization

Standardized Precipitation Index (SPI) is a measure of drought. You will learn how to calculate SPI using daily rainfalls of different rainfall stations and use the results to evaluate the spatiotemporal variation of drought occurrences.

**Data to be used:****Daily rainfall data (04/01/1995 - 03/31/2007) at 50 rainfall stations****Location (latitude, longitude) and station ID of 50 rainfall stations**

**Expected results**### SSM2 Supervised classification - the multivariate Gaussian maximum likelihood classifier

- Simulation of 2-class, 2-feature Gaussian maximum likelihood classification.
- Confusion matrix
- Uncertainty assessment of classification accuracy
- Stochastic simulation for the performance evaluation of the supervised classification (PDF)

### SSM3 Stochastic simulation of bivariate gamma distribution

### SSM4 Gamma random field simulation

- Sequential Gaussian simulation (SGS)
- Gamma random field simulation
- Potential applications

### SSM5 Model performance evaluation - Assessing the uncertainties in real-time forecasting

- Model performance evaluation criteria
- NSE (Coefficient of Efficiency, CE)
- Coefficient of Persistence (CP)
- Sample-dependent CE-CP relationship
- Model-dependent CE-CP relationship

### SSM6 Asymptotic distribution of the test statistic of the Kolmogorov-Smirnov test

### SSM7 Change detection using the Mann-Whitney-Pettitt (MWP) test

**A Non-parametric Approach to the Change-point Problem (A.N. Pettitt, Journal of the Royal Statistical Society. Series C, 1979)**### SSM8 L-moment-ratio diagram (LMRD) for GOF test

Establishing acceptance regions for L-moments basedgoodness-of-fit tests by stochastic simulation.

*Journal of Hydrology*, Vol. 355, No.1-4, 49-62. (doi:10.1016/j.jhydrol.2008.02.023).**SSM9 Rejection method for random number generation**### SSM10 Rainfall-Runoff Modeling

Animation of rainfall-unit hydrograph-runoff simulation by Bo-Yu Chen.

**1-hr unit hydrograph UH(1,t) of Wu-Duh flow station and hourly rainfalls of two storm events****SSM11 Rainfall frequency analysis using annual maximum series (AMS) and event maximum series (EMS)**### SSM12 IDF Uncertainty - Bootstrap sampling

**Hourly rainfall data of two rainfall stations in northern Taiwan**. (**Hourly_Rainfall_Data.zip**)- Extract annual maximum rainfalls of various durations (1, 2, 3, 6, 12, 24, 48 hours). These are known as the annual maximum series (AMS).
- Conduct goodness-of-fit test to choose the best probability distribution for rainfall frequency analysis.
- Determine distribution parameters by using the method of moments and method of L-moments.
- For a specific duration, calculate the design rainfall depths of 5, 10, 25, 50, 100 and 200-year return periods.
- Plot the Duration-Depth-Frequency (return period) curve and Intensity-Depth-Frequency (IDF) curve.
- Evaluate the results
- Investigate uncertainty of the IDF curve by bootstrapping from the annual maximum series.

**RSLAB - NTU**

**Prof. Ke-Sheng Cheng **

RSLAB_BSE_NTU

No. 1, Section 4, Roosevelt Road

Bioenvironmental Syst. Eng., National Taiwan University