Vignette on parallel tempering currently jumps in at the deep end. Change text to ramp up, starting by talking about issues with correlation and how these can often be fixed with other methods (e.g. reparameterisation). When it comes to temperature rungs, make sure it's clear to the user exactly what order to do things in - i.e. better to get the model mixing nicely over a single output chain before adding more chains.
Vignette on parallel tempering currently jumps in at the deep end. Change text to ramp up, starting by talking about issues with correlation and how these can often be fixed with other methods (e.g. reparameterisation). When it comes to temperature rungs, make sure it's clear to the user exactly what order to do things in - i.e. better to get the model mixing nicely over a single output chain before adding more chains.