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resampling-stats / resampling-with

Source repository for third edition of "Resampling: The New Statistics"
https://resampling-stats.github.io
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Ben/bayesian analysis #135

Closed ben-herbst closed 1 year ago

ben-herbst commented 1 year ago
ben-herbst commented 1 year ago

Messed around with monte_carlo.Rmd. Will resolve the conflicts

ben-herbst commented 1 year ago

Hi Pete

A gentle introduction is necessary, please go ahead!

I'll finish the rest of the chapter. Plan to replace his example using the normal distribution with a discrete example, e.g. coin tosses.

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On Mon, Aug 28, 2023 at 5:30 PM pxr687 @.***> wrote:

@.**** commented on this pull request.

In source/bayes_simulation.Rmd https://github.com/resampling-stats/resampling-with/pull/135#discussion_r1307579747 :

+\sum_X P(X, Y) = \sum_X P(X | Y) P(Y), +$$ +or +$$ +\sum_X P(X, Y) = P(Y) \sum_X P(X | Y). +$$ +Since $P(X | Y)$ is a probability distribution over $X$, we have $ \sum_X P(X | Y) = 1$. We therefore have +$$ +P(Y) = \sum_X P(X, Y). +$$ +Similarly, +$$ +P(X) = \sum_Y P(X, Y). +$$ + +These are called the marginal distributions of $X$ and $Y$.

I wonder if that could do with a gentle intro page by itself? Maybe we could use that Pew democrat/republican abortion data? Happy to work on that if you both think it could be useful?

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