Non-parametric statistics

Non-parametric statistics is often described as the set of statistical tools/models that do not rely on parameterized families of probability distributions. From this definition, it may sound as if Bayesian non-parametric is not possible since we have learned that the first step in doing Bayesian statistics is precisely combining probability distributions in a full probabilistic model. We said in Chapter 1, Thinking Probabilistically - A Bayesian Inference Primer, that probability distributions are the building blocks of probabilistic models. Under the Bayesian paradigm, non-parametric models refer to models with an infinite number of parameters. So, we will define parametric models as those models for which the number of parameters is allowed to grow with the size of the data. For these models, the theoretical numbers of parameters is infinite and we use the data to collapse it to a finite number, thus we allow the data to effectively determine the number of parameters...