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).