a mixture of normals as the proposal distribution. The idea is to not only find the global mode, but any local ones as well, and center each mixture component at each of those local modes. The algorithm itself would remain unchanged, as long as the global posterior mode matches the global proposal mode. We recognize that finding all of the local modes could be a hard problem, and there is no guarantee that any optimization algorithm will find all local extrema in a reasonable amount of time. In practical terms, MCMC, offers no such guarantees either. Even if the log posterior density is unimodal, one should take care that the mode-finding optimizer does not stop until reaching the optimum. For R , trustOptim (Braun 2014) is one such package, in that its stopping rule depends on the norm of the gradient being sufficiently close to zero. There are a number of packages for the R statistical programming language that can help with implementation of our method. The bayesGDS package (Braun 2013a) includes functions to run the rejection sampling phase (lines 20-36 in Algorithm 1). This package also includes a function that estimates the log marginal likelihood from the output of the algorithm. If the proposal dis- tribution is MVN, and either the covariance or precision matrix is sparse, then one can use the sparseMVN (Braun 2013c) package to sample from the MVN by taking advantage of that sparsity. The sparseHessianFD (Braun 2013b) package estimates a sparse Hessian by taking finite differences of gradients of the function, as long as the user can supply the sparsity pattern (which should be the case under conditional independence). Finally, the trustOptim package (Braun 2014) is a non- linear optimization package that uses a sparse Hessian to include curvature information in the algorithm. The authors acknowledge research assistance from Jonathan Smith, and are grateful for helpful suggestions and comments from Eric Bradlow, Peter Fader, Fred Feinberg, John Liechty, Blake McShane, Steven Novick, John Peterson, Marc Suchard, Stephen Walker and Daniel Zantedeschi. Acknowledgment References Allenby, Greg M, Eric T Bradlow, Edward I George, John Liechty, and Robert E McCulloch (2014). Perspec- tives on Bayesian Methods and Big Data. Customer Needs and Solutions 1 , 169–175. Bates, Douglas and Dirk Eddelbuettel (2013). Fast and Elegant Numerical Linear Algebra Using the RcppEigen Package. Journal of Statistical Software 52 (5), 1–24. 32