On the Edge: Statistics & Computing
A number of issues common to both statistical research and collaboration that impact the verification, under standing, and subsequent application of novel statistical pro cedures are discussed.
Abstract
i\ lany recent results in statistical research are based on sim ulation or experiment-based procedures which have been facilitated by technological advances in computing (Beran 200 I), While mathematical theory is still very important, these computational techniques, including Monte-Carlo, i\ larkov Chain Monte-Carlo, and rcsumpling methods, arc increasingly used to obtain results which sometimes are more relevant than those based upon low-order approximations to asymptotic theory, These simulation-based techniques can help to lill gaps in understanding theoretical and mathemat ical procedures as well as provide numerical approximations to computationally infeasible exact solutions, This article will discuss a number of issues common to both statistical research and collaboration that impact the verification, under standing, and subsequent application of novel statistical pro cedures, Complicated numerical algorithms must often he used even when we have sound theoretical results, Implementa tion of these procedures can be just as difficult as the con struction of proofs, However, while publication of research papers is based on the verification or proper referencing of proofs for every theorem, there isa tendency to accept seem ingly realistic computational results, as presented by figures and tables, without any proofof correctness. Yl't, these results an,'critical forjustifying the proposed methods and represent