Introduction to Statistics and Computation with Data

Instructor : Siva Athreya
Email : athreya@isibang.ac.in
Classes : Friday: 10:00-10:50, 11:10-12:00, 12:10-13:00, 14:00-15:00
Scoring : Final Exam: 40%, Midterm Exam: 20%, Quizzes: 25%, In-class Worksheets: 10%, and Homework: 5%.

Mathematical Statistics and Data Analysis by John A. Rice
Statistics: The Art and Science of Learning from Data by by Alan Agresti, Christine A. Franklin, Bernhard Klingenberg
Using R for Introductory Statistics by John Verzani
simpleR – Using R for Introductory Statistics by John Verzani
Probability and Statistics with Examples Using R by Siva Athreya, Deepayan Sarkar, and Steve Tanner.
R for Data Science by Hadley Wickham and Garlett Grolemund.

R- Basics: Installing R, Variables, Functions, Workspace, External packages and Data Sets.
Introduction to exploratory Data analysis using R: Descriptive statistics; Graphical representation of data: Histogram, Stem-leaf diagram, Box-plot; Visualizing categorical data.
Review of Basic Probability: Basic distributions, properties; simulating samples from standard distributions using R commands.
Sampling distributions based on normal populations: $t$, $\chi^2$ and $F$ distributions.
Model fitting and model checking: Basics of estimation, method of moments, Basics of testing including goodness of fit tests, interval estimation; Distribution theory for transformations of random vectors;
Nonparametric tests: Sign test, Signed rank test,Wilcoxon-Mann-Whitney test.
Bivariate data: covariance, correlation and least squares.
Resampling methods: Jackknife and Bootstrap.

- Box Plot
- Simulation of Discrete Uniform, Bernoulli and Binomial Random Variables.

- Plotting histograms
- Simulating Uniform $(0,1)$ random variables
- Simulation of Discrete Random Variables.
- Factors and Levels

- Method of moments estimate
- Maximum likelihood estimate
- Simulating ER Graphs
- Working with Factors and Levels

- Sampling Distributions
- Sample Proportion and Relative Frequency
- Sample Mean and Sample Variance

- $t$ and $\chi^2$ distribution
- Markov and Tschebychev's Inequality
- Law of Large Numbers
- Central Limit Theorem
  - Stirling's Formula and DeMoivre-Laplace Central Limit Theorem by Marton Balazs and Balint Toth

- SLLN implies WLLN
- Confidence intervals
- Pivotal Quantity
- Empirical coverage of confidence intervals

- Revisit Tschebychev and Markov Inequalities
- Testing of Hypothesis
  - Introduction
  - Parametric example
  - Non-Parametric example

- Testing of Hypothesis
  - Parametric example
  - Test for Sample Mean under Normality Asuumption
  - $\chi^2$-goodness of fit test
  - $\chi^2$-test for independence

Last Modified: April 12th, 2024.