BINGO---A Much Neglected Bayesian Computer Package

                                                                          

                                                                           



During the 1980s. Professor Ewart Shaw, while still at Nottingham University, developed Bayes Four and BINGO, two seminal computer packages for highly accurate approximate Bayesian Inference, which extended the 1982 approach by Naylor and Smith, His approach effectively solved Bayesian inference for a very wide range of sampling models.

        However, during the 1990s, Bayesians went MCMC crazy  and Ewart's highly effective packages seem to have been large neglected in favour of paradigms which were often inferior, because of the very problematic convergence difficulties with MCMC

       In my opinion BINGO is still largely the state of the art and Ewart has not received enough credit for his pioneering packages




Here is what Ewart, and Brad Carlin and Tom Louis, have to say about his methodology:




Bayesian inference I subscribe to the Bayesian view of statistics, in which all uncertainty is treated using probability. This is the natural approach to making predictions and informed decisions in the real world. I have for many years been developing practical and very general methods for realistic Bayesian statistical modelling, initially while working as part of the Nottingham University Statistics group led by Adrian F. M. Smith. I devised and implemented the multivariable function reconstruction & display,12,63,66 and the novel numerical integration methodology for > 10 dimensions in Bayes Four.64,65,77 More recently I have designed and developed a computer system called BINGO,79 an earlier version of which is well described in a standard textbook (Carlin & Louis 2000, page 361)156 as follows: 



                                                                                

BINGO An acronym for Bayesian Inference—Numerical, Graphical and Other stuff, this program is an extended version of Bayes Four, developed by Prof. Ewart Shaw at Warwick University. Built for portable APL workspaces, an initial version is available at http://www.warwick.ac.uk/statsdept/Staff/JEHS/index.html BINGO features a “multi-kernel” version of the Naylor and Smith (1982) algorithm, highly efficient (“designed”) numerical integration rules, device-independent graphics, and facilities for other approaches. The user must apply APL code for the likelihood and so on, similar to Bayes Four. Other facilities include built-in reparametrizations, Monte Carlo importance sampling and the Metropolis-Hastings algorithm, quasirandom sequences, Laplace approximations, function maximization, APLTEX, and the compact device-independent graphics language WGL (Warwick Graphics Language, pronounced “wiggle”). (3) Computation & numerical methods 


The practical importance of realistic statistical modelling has prompted my research into high-dimensional numerical integration and into approximating & summarising high-dimensional functions,2,12,16,19,26,38–42,60, 63–69,71,75 and hence into quasirandom sequences,2,18,19,70,72 computer algebra,39,84,86,101 and the interlinked areas of coding theory, combinatorial designs, lattices, sphere-packing, symmetry & distance-regular graphs.26,39,83,96,97,99,100 


Here is an excerpt from my (Tom's) Personal History of Bayesian Statistics:

    Sir Adrian’s influence across the discipline was by the mid-1990s becoming enormous. After assuming a number of important leadership roles, he is currently Vice-Chancellor of London University, and also deputy head of the U.K. Statistics Authority. Adrian has supervised 41 successful Bayesian Ph.D. students altogether, most of whom have gone on to achieve greater heights. They include Michael Goldstein, Uri Makov, Allan Skene, Lawrence Pettit, John Naylor, Ewart Shaw, Susan Hills, Nick Polson, David Spiegelhalter and Mike West, a phenomenal achievement. Both John Naylor and Ewart Shaw provided Adrian with remarkably sound computing expertise during the 1980s and before Bayesian MCMC came into vogue. They, for example, developed a computer package known as Bayes 4 which employed some reassuringly convincing, algebraically expressed, approximate Bayesian techniques. Bayes 4 has recently been incorporated into Ewart Shaw’s larger package BINGO. Maybe Sir Adrian should be regarded as the Sir Isaac Newton of modern Bayesian Statistics.