Timeline for How do we define the kernel to calculate the acceptance ratio for Metropolis-Hastings Markov Chain Monte Carlo?
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| Jan 25, 2021 at 18:04 | comment | added | fool | You use MCMC to draw samples from a desired target distribution f(x)=g(x)C. For the simple case, you should know g(x) as part of your problem. For the kernel/proposal distribution, this is a choice you make (there are adapative schemes), but you can start with N(x, 1) for example. A quick googled example: stephens999.github.io/fiveMinuteStats/MH_intro.html | |
| Jan 25, 2021 at 8:10 | comment | added | Radu | @user228809 Oh, evaluating g(y)/g(x) is the same as f(y)/f(x), I see! Now I’m still asking my initial question, how can we find a g function proportional to f? Considering my example above. | |
| Jan 25, 2021 at 7:25 | comment | added | fool | To understand what "up to a constant" means, consider a target f(x)=g(x)C, and you can only evaluate g(x) but not f(x) because you don't know C. Think of C as the constant that normalizes g(x) to f(x). You only need to evaluate g(x) because in the acceptance ratio of MH, you actually evaluate f(x), but it simplifies g(y)c/[g(x)c=]g(y)/g(x). | |
| Jan 25, 2021 at 6:15 | answer | added | Xi'an | timeline score: 1 | |
| Jan 24, 2021 at 23:34 | comment | added | Radu | @Xi'an What do you mean by “up to a constant”? Also, isn’t the kernel a distribution that is proportional to the target distribution, and not the proposal distribution? | |
| Jan 24, 2021 at 21:23 | comment | added | Xi'an | you need to know the target density up to a constant, but the kernel is usually understood as the density of the proposal distribution which is completely arbitrary. | |
| Jan 24, 2021 at 20:56 | review | First posts | |||
| Jan 25, 2021 at 2:19 | |||||
| Jan 24, 2021 at 20:51 | history | asked | Radu | CC BY-SA 4.0 |