Independent Metropolis Hastings, not jumping

#1
I'm trying to sample from a posterior (with 50 dimensions) and I've got a proposal distribution which gives a overall acceptance rate of 0.3. However when I take 20000 draws, there are a couple occasions where the proposal is rejected 500-1000 times consecutively.

I haven't much experience in this area and I was wondering how big an issue is this?

Would it perhaps be better to run shorter chains and take the last value from each?

Thanks for any advice it is greatly appreciated.
 
#2
This all is not really a problem, it just means that you need very large number of samples to get a reasonable estimate of the posterior distribution.

It could be that your jump variance is too low? So occasionally a value gets accepted with a low probability that is "far out", if you have a low jump-width it will take a great deal of samples to get back into the "good zone". If this is so your samples will show high auto-correlation. Check this. If so it can be reduced by changing the average size of a jump, which you can do by tinkering with the variance of your jump distribution. However, watch out, too large a jump variances will increase the likelihood of rejection of the proposed jump. Also, you can program a jump variance that increases or decreases automatically pased on the acceptance rate - which should solves this too.