Metropolis–Hastings :"We assume that the posterior density is locally flat over the region we sample from"

I’m working through Ben Lambert’s Students-Guide. (Chapter 13: Random Walk)
I understood why Metropolis hasting on the surface, but didn’t really get it.
Here, “We assume that the posterior density is locally flat over the region we sample from.” (13.8)
What does this assumption mean? Could someone explain what do we actually do to generate the posterior via MH from a dataset? or point me to an intuitive representation?
Thank you!

unfortunately, I don’t think this is a good forum for these types of questions, we usually deal primarily with things regarding practical applications of Bayesian stats with Stan and sometimes the broader class of HMC, NUTS and similar algorithms. We rarely (if ever) have people ask questions about introductory courses on theory as such. (And I am personally ill-equipped to advice on this subject). This forum may sometime in the future spawn a category for similar discussions, but we aren’t currently there.

Sorry and hope you are able to find help somewhere.

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Hey sorry I don’t have the book but a friend and I have some kind of discussion of MCMC methods in general. So if you wanna share something or further discussion of MCMC samplers send me a mail:

Its always fun to make your own sampler :)


@asael_am mailing you now…thank you :)

@martinmodrak Hi, do you know any place or resources where I can maybe discuss doubts from books/worksheets?

I unfortunately don’t know of a better place than Cross Validated, although getting a question answered on Cross Validated is somewhat hard (many questions get 0 replies).

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@martinmodrak My response variable includes values <0.Most of my data resembles inverse gaussian , but this doesn’t take negative value.Which family should I specify under brms for this case?

Please start this as a new topic and include a bit more detail: the question can’t be answered without knowing what the data represent and how were they measured, ideally also some plots of he data.