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### What is the intuition behind the Metropolis-Hastings Algorithm? [duplicate]

I've been studying Bayesian Statistics lately, and just came across the Metropolis-Hastings Algorithm. I understand that the goal is to sample from an intractable posterior - but I'm not really able ...
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### What is Bayesian and Monte Carlo Simulation? [duplicate]

Can someone explain in plain language for a layperson what are Bayesian and Monte Carlo simulations and the relationship between the two? I thought Bayesian was the same as Monte Carlo Simulation...
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### OpenBUGS intuition with data [duplicate]

I've recently discovered Bayesian statistics, currently I am experimenting with Openbugs, yet I cant grasp the concept of what happens with the inputted data. I understand mcmc, yet all of examples I'...
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### Metropolis Hastings algorithm and Markov chains [duplicate]

Why does Metropolis Hastings algorithm need/make a sequence of interdependent samples, i.e., a Markov chain in order to generate a posterior distribution?
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### Posterior distribution and MCMC [duplicate]

I have read something like 6 articles on Markov Chain Monte carlo methods, there are a couple of basic points I can't seem to wrap my head around. How can you "draw samples from the posterior ...
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### Bayesian logit model - intuitive explanation?

I must confess that I previously haven't heard of that term in any of my classes, undergrad or grad. What does it mean for a logistic regression to be Bayesian? I'm looking for an explanation with a ...
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### A practical example for MCMC

I was going through some lectures related to MCMC. However, I don't find a good example of how it is used. Can anyone give me a concrete example. All I can see that is they run a Markov chain and say ...
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### MCMC/EM limitations? MCMC over EM?

I am currently learning hierarchical Bayesian models using JAGS from R, and also pymc using Python ("Bayesian Methods for Hackers"). I can get some intuition from this post: "you will end up with a ...
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### What are Monte Carlo simulations?

Is Monte Carlo Simulation the same as just conducting experiment several times and then averaging results? Why is it then called like that?
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### MCMC; Can we be sure that we have a ''pure'' and ''large enough'' sample from the posterior? How can it work if we are not?

Referring to this thread: How would you explain Markov Chain Monte Carlo (MCMC) to a layperson?. I can see that it is a combination of Markov Chains and Monte Carlo: a Markov chain is created with ...
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### Using Markov Chain Monte Carlo to compute the chances that a particular solitaire laid out with 52 cards would come out successfully

Based on some references I got from another question I learned that: While convalescing from an illness in 1946, Stan Ulam was playing solitaire. It, then, occurred to him to try to compute the ...