It took me a long time to understand Bayesian statistics. So many angles from which to approach it: the Bayes' Theorem, probability as a degree of belief, Bayesian updating, priors, and posteriors, ... But my favorite angle is the following first principle:
May 9, 2023·edited May 9, 2023Liked by Christoph Molnar
Thanks for this article! I'm taking a bayesian statistics course and would to clarify something. Is it true that P(X) is the normalizing constant, and in practice, we can just take the numerator P(X|θ) P(θ) which is proportional to the posterior distribution, and MCMC is used to sample from an unknown form of the posterior distribution. And there is no need to deal with P(X)?
You got that right. There are just a few cases where it's possible to compute P(X). But in most applications you sample with MCMC. And such sampling is based on the numerator.
I don't think I've laughed this much reading an article on Bayesian modeling. This was such a fun read!
Mission accomplished then
Thanks for this article! I'm taking a bayesian statistics course and would to clarify something. Is it true that P(X) is the normalizing constant, and in practice, we can just take the numerator P(X|θ) P(θ) which is proportional to the posterior distribution, and MCMC is used to sample from an unknown form of the posterior distribution. And there is no need to deal with P(X)?
You got that right. There are just a few cases where it's possible to compute P(X). But in most applications you sample with MCMC. And such sampling is based on the numerator.
Hi Christopher,
Good article. But would appreciate if you gave credits for the interstellar meme :)
https://www.linkedin.com/posts/venkat-raman-analytics_datascience-statistics-bayesianstatistics-activity-6966363753294544896-2WDC?utm_source=share&utm_medium=member_desktop