A Comparison of Programming Languages for Markov chain Monte Carlo Applications

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Markov chain Monte Carlo (MCMC) methods are utilized to generate samples from intractable distributions. For example, one MCMC method commonly used is the Gibbs sampler, which draws approximate samples from conditional distributions. The prevalence of the Gibbs sampler and other MCMC methods in various disciplines has created a need for efficient programs to run MCMC algorithms. For our research, we used the following five programming languages to compare computation times for Gibbs samplers in several statistical models: R, C++ (using the Rcpp package in R), Just Another Gibbs Sampler (JAGS), Julia, and MATLAB. From our results, we see that each language had its benefits and limitations. However, with its simple syntax and fast computation time, we contend that Julia is the most optimal programming language for MCMC algorithms.