dynamic traceplot for jupyter notebooks

Summary:

It would be super cool to provide a dynamic traceplot of the value of lp__ (total joint log probability for the model) across all chains during warmup and sampling - is this possible?

Description:

showed Andrew Gelman Colab jupyter notebooks (R version) and he asked for this dynamic visualization. we could pull this off the output files similar to the way that the tqdm progress bar monitors standard out. given the current Stan csv format, the first column is the lp__ - the total joint log probability. generally, when lp__ converges, all params have converged, conversely, if any params have not converged, lp__ will not converge either, so this would be good enough

we want to discourage folks from trying to monitor a particular param - there are other more appropriate tools that should be used - so simple feature - just monitor lp__ across chains!

Additional Information:

Current Version:

Start by reviewing how the tqdm progress bar monitors standard output and how Stan CSV output files expose lp__ across chains. Define the notebook-facing behavior for a dynamic lp__ trace during warmup and sampling; done means the visualization updates across chains without monitoring individual parameters.