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I am seeking advice on how to incorporate C or C++ code into my R code to speed up a MCMC program, using a Metropolis-Hastings algorithm. I am using an MCMC approach to model the likelihood, given various covariates, that an individual will be assigned a particular rank in a social status hierarchy by a 3rd party (the judge): each judge (approx 80, across 4 villages) was asked to rank a group of individuals (approx 80, across 4 villages) based on their assessment of each individual's social status. Therefore, for each judge I have a vector of ranks corresponding to their judgement of each individual's position in the hierarchy. To model this I assume that, when assigning ranks, judges are basing their decisions on the relative value of some latent measure of an individual's utility, u . Given this, it can then be assumed that a vector of ranks, r , produced by a given judge is a function of an unobserved vector, u , describing the utility of the individuals being ranked, where the individual with the kth highest value of u will be assigned the kth rank. I model u , using the covariates of interest, as a multivariate normally distributed variable and then determine the likelihood of the observed ranks, given the distribution of u generated by the model. In addition to estimating the effect of, at most, 5 covariates, I also estimate hyperparameters describing variance between judges and items. Therefore, for every iteration of the chain I estimate a multivariate normal density approximately 8-10 times. As a result, 5000 iterations can take up to 14 hours. Obviously, I need to run it for much more than 5000 runs and so I need a means for dramatically speeding up the process. Given this, my questions are as follows: (i) Am I right to assume that the best speed gains will be had by running some, if not all of my chain in C or C++? (ii) assuming the ans

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