Non-parametric Bayesian Models

In machine learning the most probable hypothesis given the data is the hypothesis that makes the data most probable (follows from Bayes rule if we assume identical prior probabilities for hypotheses).
Most models used in ML are parametric, they usually incorporate some assumptions about the data, its amount and complexity.
Non-parametric models can adapt to changing structure of the data and increasing complexity and amount.
- Essentially this is achieved through infinite number of parameters but at any one time only a finite number of them is non-zero.

Chinese restaurant process

https://en.wikipedia.org/wiki/Chinese_restaurant_process
Infinite number of tables (clusters), each of infinite capacity,
A sequence of customers entering and sitting down,
The first customer enters and sits at the first table,
Each subsequent one can join an existing table or take a new one.
Eventually we infer the number of clusters and where they are from the data.
- This last point is a bit handwavy and I don't quite understand how random seating method is combined with similarity to produce the clustering.