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Bayesian Methods for Hackers: Probabilistic Programming and Bayesian Inference
book

Bayesian Methods for Hackers: Probabilistic Programming and Bayesian Inference

by Cameron Davidson-Pilon
October 2015
Beginner to intermediate content levelBeginner to intermediate
300 pages
7h 19m
English
Addison-Wesley Professional
Content preview from Bayesian Methods for Hackers: Probabilistic Programming and Bayesian Inference

4. The Greatest Theorem Never Told

4.1 Introduction

This chapter focuses on an idea that is always bouncing around our minds, but is rarely made explicit outside books devoted to statistics. In fact, we’ve been using this simple idea in every example thus far.

4.2 The Law of Large Numbers

Let Zi be N independent samples from some probability distribution. According to the Law of Large Numbers, so long as the expected value E[Z] is not infinity, the following holds:

Image

In words:

The average of a set of random variables from the same distribution converges to the expected value of that distribution.

This may seem like a boring result, but it will ...

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Publisher Resources

ISBN: 9780133902914Purchase book