In this lecture, Prof. Rigollet talked about Hessian, Fisher information, weighted least squares, and iteratively reweighed least squares.

24. Generalized Linear Models (cont.)

In this lecture, Prof. Rigollet talked about strict concavity, optimization methods, quadratic approximation, Newton-Raphson method, and Fisher-scoring method.

23. Generalized Linear Models (cont.)

In this lecture, Prof. Rigollet talked about log-likelihood function, link function, and canonical link, etc.

22. Generalized Linear Models (cont.)

In this lecture, Prof. Rigollet talked about linear model, generalization, and examples of disease occurring rate, prey capture rate, Kyphosis data, etc.

21. Generalized Linear Models

In this lecture, Prof. Rigollet talked about principal component analysis: main principle, algorithm, example, and beyond practice.

20. Principal Component Analysis (cont.)

In this lecture, Prof. Rigollet reviewed linear algebra and talked about multivariate statistics.

19. Principal Component Analysis

In this lecture, Prof. Rigollet talked about Bayesian confidence regions and Bayesian estimation.

18. Bayesian Statistics (cont.)

In this lecture, Prof. Rigollet talked about Bayesian approach, Bayes rule, posterior distribution, and non-informative priors.

17. Bayesian Statistics

In this lecture, Prof. Rigollet talked about significance test and other tests.

15. Regression (cont.)

In this lecture, Prof. Rigollet talked about linear regression with deterministic design and Gaussian noise.

14. Regression (cont.)

In this lecture, Prof. Rigollet talked about linear regression and multivariate case.

13. Regression

In this lecture, Prof. Rigollet talked about Kolmogorov-Lilliefors test, Quantile-Quantile plots, and Kai-squared goodness-of-fit test.

12. Testing Goodness of Fit (cont.)

In this lecture, Prof. Rigollet talked about Glivenko-Cantelli Theorem (fundamental theorem of statistics), Donsker’s Theorem, and Kolmogorov-Smirnov test.

11. Parametric Hypothesis Testing (cont.) and Testing Goodness of Fit

In this lecture, Prof. Rigollet talked about Wald's test, likelihood ratio test, and testing implicit hypotheses.

9. Parametric Hypothesis Testing (cont.)

In this lecture, Prof. Rigollet talked about statistical formulation, Neyman-Pearson’s paradigm, and Kai-squared distribution.

8. Parametric Hypothesis Testing (cont.)

In this lecture, Prof. Rigollet talked about parametric hypothesis testing and discussed Cherry Blossom run and clinical trials as examples.

7. Parametric Hypothesis Testing

In this lecture, Prof. Rigollet continued on maximum likelihood estimators and talked about Weierstrass Approximation Theorem (WAT), and statistical application of the WAT, etc.

6. Maximum Likelihood Estimation (cont.) and the Method of Moments

In this lecture, Prof. Rigollet talked about maximizing/minimizing functions, likelihood, discrete cases, continuous cases, and maximum likelihood estimators.

5. Maximum Likelihood Estimation (cont.)

In this lecture, Prof. Rigollet talked about confidence intervals, total variation distance, and Kullback-Leibler divergence.

4. Parametric Inference (cont.) and Maximum Likelihood Estimation

In this lecture, Prof. Rigollet talked about statistical modeling and the rationale behind statistical modeling.

3. Parametric Inference

Statistics for Applications

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