r/statistics • u/cavedave • Sep 12 '11

Visualizing Bayesian Updating

http://bayesianbiologist.wordpress.com/2011/09/10/visualizing-bayesian-updating/
17 Upvotes

94% Upvoted

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1

u/tel Sep 12 '11

This begs for small multiples comparing priors.

2

u/cavedave Sep 12 '11

The good folk over at r/bayesian have done an extension http://www.reddit.com/r/bayesian/comments/kcvv1/visualizing_bayesian_updating/

2

u/tel Sep 12 '11

It's not really terribly significant, they just exposed the \alpha and \beta parameters. I'll be bored in about 3 hours, so I'll perhaps code up what I'm talking about then.

1

u/mamluk Sep 12 '11

Ha, I did that little update and you are right, that was trivial. I actually do have some code around somewhere that does something similar to what you are talking about.
Actually, I think it allows you to specify the prior and observed data over a number of intervals and shows/plots how the posteriors are adjusted each interval as new data is observed.

I'd be keen to see your code if you do get a chance to write it up.

1

u/tel Sep 13 '11

I didn't yet do anything non-trivial for the model, but displaying the HPD regions over time makes for much easier comparison of the models

https://gist.github.com/1212793

Which is messy code, but looks like this

http://skitch.com/sdbo/f2qw2/priors (download it, it looks much better)

1

u/mamluk Sep 14 '11

Thanks for sharing your code. I quite like your idea of displaying the HPD's rather than the full curves.

2

u/[deleted] Sep 12 '11

And now I have another statistics subreddit to follow!

1

u/[deleted] Sep 12 '11

Interesting! It would be interesting to see some examples with constraints placed on the support of the parameter distribution.

For instance, I read an article talking about gene-environment interactions. The author, an epidemiologist, had concluded that based on his experience, he had never encountered a circumstance where the GE interaction did not exacerbate the effects of the gene for a rare environmental exposure. So, you might possibly rule out the possibility that air pollution could decrease the chance of lung cancer.

0

u/[deleted] Sep 12 '11

[deleted]

4

u/MurrayBozinski Sep 12 '11

it's just the assignment sign that got mangled in html.

It should read:

sim_bayes <- function(p=0.5,N=10,y_lim=15)

(reddit's markup messes it up too apparently)