Your use of the terms parametric vs. nonparametric doesn’t seem to be that used by people working in nonparametric Bayesian statistics, where the distinction is more like whether your statistical model has a fixed finite number of parameters or has no such bound. Methods such as Dirichlet processes, and its many variants (Hierarchical DP, HDP-HMM, etc), go beyond simple modeling of surface similarities using similarity of neighbours.
See, for example, this list of publications coauthored by Michael Jordan:
Your use of the terms parametric vs. nonparametric doesn’t seem to be that used by people working in nonparametric Bayesian statistics, where the distinction is more like whether your statistical model has a fixed finite number of parameters or has no such bound. Methods such as Dirichlet processes, and its many variants (Hierarchical DP, HDP-HMM, etc), go beyond simple modeling of surface similarities using similarity of neighbours.
See, for example, this list of publications coauthored by Michael Jordan:
Bayesian Nonparametrics http://www.cs.berkeley.edu/~jordan/bnp.html