Create PhyloGradients.md

Author: maxbiostat

ProgrammingProjects/PhyloGradients.md

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+## Efficient implementation of the phylogenetic likelihood and its gradients
+
+Phylogenetics is awesome. But it is also a rather difficult problem, both statistically and computationally.
+Somewhat recent advances have made efficient algorithms such as [Hamiltonian Monte Carlo (HMC)](https://mc-stan.org/docs/reference-manual/hamiltonian-monte-carlo.html) go mainstream.
+While we can't do proper HMC for trees just yet, we can fix the tree and do HMC on branch lengths and other parameters.
+But for that to work, we need the phylogenetic likelihood to be programmed efficiently. 
+
+Your job is to take the implementation of the phylogenetic likelihood in [**phylostan**](https://github.com/4ment/phylostan) and code it directly in the templated C++ required by the [Stan math library](https://github.com/stan-dev/math).
+You'll also need to code up the gradients of the likelihood.
+For this project you might want to check out [my notes](https://github.com/maxbiostat/Statistical_Phylogenetics_resources) on learning phylogenetics. 
+
+This is not a project for the faint of heart: there will be A LOT of work to get this working. Hopefully the speedups will be worth it. Nae guarantees.