# Code

To get the ball rolling I figure it would be worthwhile to write a simple R script to implement nested sampling with MCMC moves for exploring the likelihood-constrained prior as benchmark for this comparison exercise.  Ideally the prior and likelihood should be plug-in functions with minimal requirements such that those not familiar with nested sampling can easily get it up & running on their favourite toy problem.  Eventually I suppose the same will have to be done for SMC; or alternatively, an SMC advocate may decide to contribute his/her go-to SMC script for this purpose.

I have created a github repository to store the code produced here, though at present it contains only a readme file! which now contains a barely debugged R script I hacked together, along with a more refined Python script contributed by Brendon Brewer.

https://github.com/drewancameron/NSwMCMC

Comment: In hacking together this nested sampling script (a script I’ve probably written from scratch on about five different occasions) I am reminded just how similar nested sampling is to SMC: that is, the live particle population is evolved through the sequence of target densities $\pi(\cdot)I[L(\cdot)>L^\ast_{i}]$ for $L^\ast_i$ a non-decreasing sequence, the only complexity being that the successive $L^\ast_i$ is chosen as the minimum of the likelihoods amongst particles in the $i-1$th population.  The need for an (e.g.) MCMC algorithm to find a replacement live particle is then no different to the need for the same to avoid particle degeneracy in an SMC / particle filtering code.