  The marginal Bayesian predictive classifiers (mBpc) as opposed to the
simultaneous Bayesian predictive classifiers (sBpc), handle each data
separately and hence tacitly assumes the independence of the observations.
However, due to saturation in learning of generative model parameters, the
adverse effect of this false assumption on the accuracy of mBpc tends to wear
out in face of increasing amount of training data; guaranteeing the convergence
of these two classifiers under de Finetti type of exchangeability. This result
however, is far from trivial for the sequences generated under Partition
exchangeability (PE), where even umpteen amount of training data is not ruling
out the possibility of an unobserved outcome (Wonderland!). We provide a
computational scheme that allows the generation of the sequences under PE.
Based on that, with controlled increase of the training data, we show the
convergence of the sBpc and mBpc. This underlies the use of simpler yet
computationally more efficient marginal classifiers instead of simultaneous. We
also provide a parameter estimation of the generative model giving rise to the
partition exchangeable sequence as well as a testing paradigm for the equality
of this parameter across different samples. The package for Bayesian predictive
supervised classifications, parameter estimation and hypothesis testing of the
Ewens Sampling formula generative model is deposited on CRAN as PEkit package
and free available from https://github.com/AmiryousefiLab/PEkit.
