Rejecting/thinning modes based on average density

Questions
4

So you are trying to scale the marginal posterior (e.g., smoothed histogram) by the exp(logp())? Besides some simple cases, I dont think this approach is sounded.
Just take a simple example:

with pm.Model():
    pm.NormalMixture('m', 
        mu=np.array([0., 5.]), 
        w=np.array([.5, .5]), 
        sd=np.array([1., 1.]))
    trace = pm.sample(1000)
pm.traceplot(trace);

image
image.jpg850×136 47.6 KB

As an example, take the yellow chain and the green chain, the logp(x) at each point would be the same even though the shape marginal density is different. And the situation would just get worse in higher dimension.