Unit IV: Laws Of Large Numbers And Inference

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In this section, we start with a discussion of limit theorems: the weak law of large numbers and the central limit theorem. We then introduce the subject of inference (estimation and hypothesis testing), from two alternative viewpoints: first, Bayesian inference, which relies on a prior distribution for unknown quantities and on the Bayes rule to incorporate new evidence; and, second, classical inference, in which no probabilistic assumptions are made on the unknown quantities and instead relies heavily on the laws of large numbers to provide statistical guarantees, e.g., in the form of confidence intervals.

Lecture_19.jpg Lecture 19: Weak Law of Large Numbers

Lecture_20.jpg Lecture 20: Central Limit Theorem

Lecture_21.jpg Lecture 21: Bayesian Statistical Inference - I

Lecture_22.jpg Lecture 22: Bayesian Statistical Inference - II

Lecture_23.jpg Lecture 23 Classical Statistical Inference - I

Lecture_24.jpg Lecture 24: Classical Inference - II

Lecture_25.jpg Lecture 25: Classical Inference - III

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