# Statistics And Data Analysis

In this course, we study some basic probility and sampling theories which are commonly used in machine learning.

This GitBook notes are maintained by zealscott.

# Syllabus

Lecture | Key | Notes | Reading Material |
---|---|---|---|

1. Statistics review |
- Random Variable - pdf/cdf/pmf - Joint distribution - Expectation/covariance - Conditional expectation |
Probability theory Review | - Chernoff bound |

2. common distributions |
- Discrete - Continuous |
Useful distribution Conjugate Prior Normal - Gamma Conjugate |
- expoential family |

3. sample and limit theory |
- sampling mean and variance - order statistics distribution - weak and strong law of large numbers - central limit theorem |
sample and limit theory | |

4. T and F distribution |
- $\chi^2$ distribution - $t$ distribution - $F$ distribution |
T and F distribution | |

5. Sampling |
- Sample Random sampling - Confident interval - MCMC - Gibbs Sampling |
Survey Sampling | - 拒绝采样 - 别名采样 - MCMC |

6. Estimation of Parameters&Fitting of Probability Distribution |
- MLE（parameter） - MLE for exponential family - Conjugate family （Bayes） - EM algorithm |
LDA思考与总结 | - 文本主题模型之LDA(一) LDA基础 |

7. Testing Hypotheses and assessing Goodness of fit |
- Neyman-Perason lemma - Likelihood Ratio Tests |
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8. Testing and Summarizing |
Testing and Summarizing) | ||

9. The analysis of Variance |
The Analysis Of Variance | ||

10. notes for exam |
Notes For Exam |