Print out & go through these files before class and bring them to class.

 

List of Topics:

 

1  Introduction (Probability Theory and Random Variables)  

1.1 Basic Probability, Operation of Sets, Kolmogorov’s Axioms  
1.2 Counting Methods  

1.3 Conditional Probabilities, Independence of Events
1.4 Bayes’ Rule, Bernoulli Experiments
1.5 Discrete Random Variables, Special Probability Mass Functions (p.m.f’s)  
1.6 Continuous Random Variables, special probability density functions  

Last part: multiple continuous random variables etc.

A gallery of common distributions

2 Data, Sampling and Basic Statistical Inference  

2.1 Data Summary, Graphical and Tabular Representations: part 1, part 2

(a list of common graphical techniques)

2.2 Sampling from a population-Parameter and Statistics, sampling results (supplementary handout – T, F, chi-square distributions)- see also sampling applet here

2.3 Central Limit Theorem (CLT)   

Sampling Handout (CORRECTED)

2.4 Parameter Estimation                                                       (Method of Moments-example)

2.5 Confidence intervals                                                      (Another example – Non-normal-small sample, smallest width C.I)          

2.6 Hypothesis Testing                                                      (Tests for Variance)           
2.7 Goodness of Fit Tests, Independence Test
                        Handout for Chi-quare tests (for goodness of fit), ANOTHER EXAMPLE  Example of Independence test

  

2.8 Tesing for Normality, Non-Parametric Alternatives: Wilcoxon Rank Sum test, Wilcoxon Signed rank test

Learning R, classnotes from 3rd march …………. More examples of paired t-test

 

3. Regression 

3.1 Simple linear Regression and Inference. (R)

3.2 Multiple Linear Regression (handout) … (R)

3.3 Regression Diagnostics (see class notes, some R-commands)

3.4. Confounding and interaction (another webpage)

3.5 GLM, Logistic and Poisson regression(R) 

 

4. Basic concepts in experimental design and ANOVA 

4.1 Completely Randomized design,  Randomized Block Designs , another handout – oneway-anova and contrasts  

4.2 Factorial Designs: intro,         details for 2^k factorial expt,              another reference

5. Stochastic Processes  

5.1 Introduction, Bernoulli Process, Splitting & Merging Bernoulli Processes,

5.2 Poisson Process, Birth & Death process, Balance equations, Steady State Probabilities, Random Telegraph Signal,

5.3 Brownian Motion, Gaussian White Noise

5.4 Intro to DTMC (discrete time markov chains), Transition probabilities, Absorption probabilities, fundamental matrix

 

6. Elementary Simulation  

5.1 Random Number Generators

5.2 Different methods for generating from distributions

5.3 Simulating from Special Distributions                    Another ref.

5.4 Monte Carlo Integration MCMC (example in Lecture V)… Prof. John Liu’s talk

 

7. Advanced Inference Techniques

6.1 Randomization tests

6.2 Jack-knife

6.3 Bootstrap