Statistics for Applications

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

This lecture is the second part of the introduction to the mathematical theory behind statistical methods.

In this lecture, Prof. Rigollet talked about the importance of the mathematical theory behind statistical methods and built a mathematical model to understand the accuracy of the statistical procedure.