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I need to give a lecture about Bayesian statistics, introducing it to people who have already basic knowledge of classic statistics (but not too much of it in general).

I want to start with some example, showing the main differences between Bayesian statistics and classic statistics. Is anyone familiar with a very basic intro that I can derive slides from, or actual slides I can use?

I think the best would be to start with an example... I would rather not have a coin toss example, but I can be persuaded to do that :-)

I would also be happy to talk about some of the history.

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    $\begingroup$ why not follow an introductory textbook? Jim Albert's Bayesian Computation with R (Use R!) is one I can recommend (it is certainly full of simple examples). $\endgroup$ – user603 Jan 3 '13 at 20:35
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A good book to read/reference for the history is "The Theory That Would Not Die".

For the example I would start with something that can be done either way, a common dataset that a frequentist would do a simple t-test and confidence interval on, then show how you could analyze the same data/question using a Bayesian approach. Show that for diffuse priors the 2 methods give pretty much the same results. Then talk about when you might use each one, for the simple case the frequentist approach is quick and easy, but the Bayesian case would allow the use of prior information. Then maybe show some other examples that could be done either way, but the Bayesian approach has advantages, maybe think about linear regression and show (or briefly point out) that the slopes can be estimated either way and you can constuct intervals either way, but what about if you know the slopes are all non-negative (or want to constrain that anyways). That can be done using frequentist methods, but it takes more work and it is less clear how to construct the confidence intervals. A Bayes approach is to just use priors on the slopes that are 0 for negative values. Then maybe end with a more complicated example where a Bayesian approach really shines.

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