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I am trying to understand the Chinese Restaurant process (CRP) and Weighted Chinese Restaurant process (WCRP). In CRP all the implementations (cf., Infinite mixture models with nonparametric Bayes and the Dirichlet process) have a comparison made with the random number to decide if the customer chooses to sit on a new or existing table. Why this check is made and also how will this check condition differ in WCRP?

I am trying to understand the Chinese Restaurant process (CRP) and Weighted Chinese Restaurant process (WCRP) described in a research paper "Automatic Discovery of Cognitive Skills"- Robert V. Lindsey, Mohammad Khajah, Michael C. Mozer to Improve the Prediction of Student Learning. In CRP all the implementations (cf., Infinite mixture models with nonparametric Bayes and the Dirichlet process) have a comparison made with the random number to decide if the customer chooses to sit on a new or existing table. Why this check is made and also how will this check condition differ in WCRP?

I am trying to understand the Chinese Restaurant process (CRP) and Weighted Chinese Restaurant process (WCRP). In CRP all the implementations (For example: http://blog.echen.me/2012/03/20/infinite-mixture-models-with-nonparametric-bayes-and-the-dirichlet-process/  ) have a comparison made with the random number to decide if the customer chooses to sit on a new or existing table. Why this check is made and also how will this check condition differ in WCRP? Any help would be appreciated.

I am trying to understand the Chinese Restaurant process (CRP) and Weighted Chinese Restaurant process (WCRP). In CRP all the implementations (cf., Infinite mixture models with nonparametric Bayes and the Dirichlet process) have a comparison made with the random number to decide if the customer chooses to sit on a new or existing table. Why this check is made and also how will this check condition differ in WCRP?