so I know that Metropolis Hastings is an MCMC (Markov Chain Monte Carlo) method that is very useful in higher dimensions. The advantages it has over something like simple rejection sampling is that there are less points that are rejected, especially in higher dimension systems, and thus it is more efficient (sometimes even to the scale of actually being able to solve a problem in our lifetime vs. not) than rejection sampling.
My question is, in the lower dimensions -- say 1 or 2 dimensions, is it ever worth using Metropolis Hastings or any other MCMC method over just rejection sampling? I feel like rejection sampling at these lower dimensions would almost always be more efficient than MCMC methods especially because (1) in order to sample N number of points Metropolis Hastings also has to go through a burn - in period where many points will be thrown out, and (2) it sucks at multimodal systems. In addition, at these lower dimensions, Metropolis Hastings would never reach situations where rejection sampling is SO bad that it is less efficient than Metropolis Hastings.
Anyone with good knowledge on this subject, if you can provide some insight I would very much appreciate it. Thanks!