This function allows us to generate a sample output of fitting the univariate gaussian model. No arguments are needed to be passed.
The purpose of this function is to serve as a demo for users to understand the model's output, without diving too deep into details. By default,
this demo generates a sample dataset of dimension 500x1, where the MCMC sampler is specified to run for 2000 iterations, with a burn-in of 1000, and a thinning interval of 10. All possible outputs
that can be produced by
AM_mcmc_fit are returned (see return value below).
A list containing the following items:
the vector (or matrix) containing the synthetic data used to fit the model.
the vector containing the final cluster assignment of each observation.
AM_mcmc_output object, which is the typical output of
mvn_output <- AM_demo_uvn_poi()
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