 By James V Stone

ISBN-10: 0956372848

ISBN-13: 9780956372840

Discovered through an 18th century mathematician and preacher, Bayes' rule is a cornerstone of recent chance conception. during this richly illustrated publication, a number obtainable examples is used to teach how Bayes' rule is basically a normal outcome of logic reasoning. Bayes' rule is then derived utilizing intuitive graphical representations of chance, and Bayesian research is utilized to parameter estimation. As an relief to knowing, on-line machine code (in MatLab, Python and R) reproduces key numerical effects and diagrams. the academic variety of writing, mixed with a finished word list, makes this an awesome primer for newcomers who desire to get to grips with the elemental ideas of Bayesian analysis.

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Additional info for Bayes’ Rule: A Tutorial Introduction to Bayesian Analysis

Example text

3. 1. Next, we are going to choose one coin bias, and then (separately) we will choose one coin flip outcome (by choosing a coin and then flipping it). 9* After replacing this coin in the container, we again pick a coin, but this time we flip it, and we observe a head. 9 )This procedure would normally ensure that the bias of the first coin chosen has no effect on the flip outcome of the next coin chosen ; so that bias and head/tail outcome within each pair would be independent. However, to make matters more interesting (albeit a little contrived), 33 2 Bayes’ Rule in Pictures we will assume that there is a slight tendency for the same coin to be chosen on consecutive draws.

Example 3: Flipping Coins to represent the parameter whose value we wish to estimate, and x to represent the data used to estimate the true value of 9. 6, for example). Suppose we flip this coin twice, and obtain a head Xh followed by a tail xt, which define the ordered list or permutation X = (xh,xt). 2 or Appendix C). 40) More generally, for a coin with a bias 9, the probability of a head Xh is p{xh\9) = 9, and the probability of a tail Xt is therefore p(xt\9) = (1—9). 41) which will prove useful below.

Once all those bias markings have been removed from the coins, we choose one coin, flip it, and observe that it lands heads up. 9 given that a head Xh was observed? 75. 9 ) that the coin chosen has a bias of 69,9 and that coins chosen from our container landed heads up is the area a, whereas the average probability p(xh) that a coin lands heads up is the area (a + b) (see the sum rule above). 19) which is a posterior or inverse probability (see Chapter 1). 37 2 Bayes9 Rule in Pictures T h e P r o d u c t R u le U sing G e om etric Area: In order to find the posterior probability using Bayes’rule (instead of the joint probability, as above), we will need the product rule.