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jakevdp / jakevdp.github.io

Pythonic Perambulations website. Source at http://github.com/jakevdp/jakevdp.github.io-source
http://jakevdp.github.io/
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Question about your series on Bayesian vs Frequentist statistics. #7

Closed codesuki closed 7 years ago

codesuki commented 7 years ago

Sorry to hijack your GitHub issues for that. In https://jakevdp.github.io/blog/2014/06/06/frequentism-and-bayesianism-2-when-results-differ/ you are saying that Markov chains allow you to marginalize parameters. Then you go on to extract some parameters from the chain. Does that mean: 'not looking at some parameter is marginalization'?

I am not sure what exactly to google for here >_< It would be great if you could point me in the right direction to learn more about the details.

Thank you for this great series of articles! They are very informative!

jakevdp commented 7 years ago

Yes, when looking at samples from a multi-dimensional distribution, ignoring a dimension is mathematically equivalent to marginalizing over it. It's one thing that makes MCMC quite convenient.

codesuki commented 7 years ago

Thanks for the fast answer! I see, I will read up on markov chains again. I thought to marginalize we need to do integration / summation. MCMC really seems super convenient.

jakevdp commented 7 years ago

You do need to do integration, but MCMC is effectively a numerical integration via the sampling method. That's why ignoring a dimension is equivalent to integrating over it.

codesuki commented 7 years ago

Thanks again! That actually confirms some of my assumptions!