Can someone help me understand the difference between simulation and estimation of different Bayesian statistical methods like MCMC or metropolis-hasting etc.
Simulation is a methodology we use to generate data that mimics the behavior of some system of interest. Statistics is the set of mathematical techniques and tools we use to quantify data which has randomness. Stochastic simulations require statistics, but the converse is not a given.
In sum, simulation is a tool for generating data while statistics is a tool for turning data into information.