My data is a group of 10 thousand points (each having an node location (x,y)) that are spread across a plane. They are also chromatically-colored based on their weight. I need to finalize a bayesian nonparametric clustering method that groups points on mainly weight, but also on distance: that is, clusters are by defintion have some relevance to distance, but there are clear topological distinguishing factors between the first quarter and the last quarter of data (I say quarter as …

Could someone explain in simple words what are gaussian processes how does bayesian optimization work and their combination?

I am looking for a recommendation for basic introductory material on Bayesian Non-parametric methods, specifically Dirichlet Process / Chinese Restaurant Process. I am looking for material which covers the modeling part as well as the inference part from ground-up. Most of the material I found on the internet has slightly advanced material and they skip the inference part, which is usually harder to grasp.

Since we can compute the mean and the standard deviation of a set of random variables, why do we use Maximum Likelihood Estimation to estimate these parameters?