Maximum-likelihood estimation of the random-clumped multinomial model as a prototype problem for large-scale statistical computing

Numerical methods are needed to obtain maximum-likelihood estimates (MLEs) in many problems. Computation time can be an issue for some likelihoods even with modern computing power. We consider one such problem where the assumed model is a random-clumped multinomial distribution. We compute MLEs for this model in parallel using the Toolkit for Advanced Optimization software library. The computations are performed on a distributed-memory cluster with low latency interconnect. We demonstrate that for larger problems, scaling the number of processes improves wall clock time significantly. An illustrative example shows how parallel MLE computation can be useful in a large data analysis. Our experience with a direct numerical approach indicates that more substantial gains may be obtained by making use of the specific structure of the random-clumped model.