"So far we have that the SMC sampler is just a bunch of parallel Markov chains, not very impressive, right? Well not that fast. SMC proceed by moving _sequentially_ trough a series of stages, starting from a simple to sample distribution until it get to the posterior distribution. All this intermediate distribution (or _tempered posterior distributions_) are controlled by _tempering_ parameter called $\\beta$. SMC takes this idea from other _tempering_ methods originated from a branch of physics known as _statistical mechanics_. The idea is as follow the number of accessible states a _real physical_ system can reach is controlled by the temperature, if the temperature is the lowest possible ($0$ Kelvin) the system is trapped in a single state, on the contrary if the temperature is $\\infty$ all states are equally accessible! In the _statistical mechanics_ literature $\\beta$ is know as the inverse temperature, the higher the more constrained the system is. Going back to the Bayesian statistics context a _natural_ analogy to these physical systems is given by the following formula:\n",
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