A PERSONAL HISTORY OF BAYESIAN STATISTICS

 

Thomas Hoskyns Leonard
 
Retired Professor of Statistics, Universities of Wisconsin-Madison and Edinburgh
 

8: OVERVIEW

 

Tell the audience what you’re going to say, say it,
Then tell them what you’ve said.
(Dale Carnegie)

 

Begin at the beginning and go on till you come to the end;
Then stop.
(The King of Hearts)

 

Gabriel, the Dark Knight of Heaven, by Hugh D’Arcy
 

If I could afford a diamond-encrusted platinum bowl to award to the best Bayesian researcher of all time, then my candidates would include Rudolf Kálmán, Michael Newton, Peter Wakker, Subhashis Ghoshal, David Dunson and Timothy Wallstrom. So I’d probably fill it with the Elixir of Life, and invite them to all take a sip.

    I’d give Susie Bayarri, Grace Wahba, Sylvia Richardson, Nicky Best, and Sara Martino my silver Scottish quaich, and fill it with Jura.

    Every discipline needs its Purveyors of the Word, prominent, extrovert figures who are prepared to stand on a pedestal and project its concepts and ideas across other disciplines, throughout Society, and around the world, at the risk of appearing to be peering down their noses at the children on the pavement.

    St. Paul of Tarsus, the thirteenth Apostle, though maybe a phoney one since he only ever met the Son of God in a vision on the road to Damascus, purveyed his assimilations of the Word of Christ outside Palestine and throughout the Roman Empire.

    George Tiao, Carlos Pereira, Pilar Iglesias, and Jose Bernardo popularised Bayesian concepts in the Far East, Brazil, Chile and Spain in somewhat sounder and more convincing ways. P. Jeffrey Harrison and his merry band purveyed the wonderful advantages of Kalman-style forecasting around the world, albeit in at times quasi-intellectual and ‘Back to the Future’ fashion.

    In America, the key Purveyors of the Word included Jimmie Savage, Arnold Zellner, Jay Kadane and Rob Kass, and the quintessence of Yankee and alien immigrant academia. In Britain they included Richard Price, Jack Good, Dennis Lindley, and Sir Adrian Smith, and represented all the extremities and idiosyncrasies of this class-conscious Sceptred Isle.

    Unfortunately, St. Paul sometimes got it wrong. He, for example, distorted the representation in Matthew 25 of the Second Coming, and emphasised faith in Christ, rather than good deeds, much more than James the Less, or our good Lord, who was recognised in the Qur’an as the earthly Prophet Isa, would have ever dreamt of.

    The purveyors of the Bayesian cause have sometimes got it wrong too. When a ‘child on the sidewalk’ once inquired about the frequency coverage of his 95% Bayesian interval, Arnold replied to the effect that he didn’t given a toss. As a Nobel Prize nominee, he doubtlessly felt entitled. And Jay Kadane still overemphasises the importance of the Expected Utility Hypothesis, as ever faithful to the memory of Jimmie Savage despite his Lord and Master’s long-time battering over his stern adherence to the glaringly fallacious Sure Thing Principle and his over-formalisation of the key conceptual ideas of utility of the eighteenth century Swiss mathematician Daniel Bernoulli, which were published in St. Petersburg in 1738.

    Sir Adrian Smith got it triumphantly right, with Alan Gelfand, when he popularised MCMC during the 1990s, and he blinked in joy when the simulations eventually converged.

    In response to MCMC and the early 21 st. century development by two proud men and two bright women of the model comparison criterion DIC, a pragmatic rather than a quasi-religious view of Bayesianism has emerged. Bayes theorem and DIC are nowadays regarded as useful parts of many statisticians’ toolkits. But they’re not the be all and end all, in particular in situations where the choice of sampling model is unclear.

    Sir Adrian has more recently taken the concepts of evidence-based medicine and evidence-based performance indicators into the widely-influential area of evidence-based public policy making. But beware poorly collected or skilfully reshuffled data, out of your Department of Health or youth crime statistics or wherever, lest the conclusions be spuriously evidence-based. Maybe the Prophet Isa is watching us, as the ultimate ripple from above. According to my Moslem friends, he will return in mortal form before the Final Day to judge us.

    In Britain, the Rising of the Bayesian Paradigm, like a phoenix from the ashes, began at Bletchley Park and the Universities of Manchester and Cambridge during the 1940s and 50s, continued in Aberystwyth during the 1960s, and led to a brilliant resurgence at University College London which almost flew out of control. In the 1970s, the now multi-lingual Bayesians at the University of Warwick took up the cudgel while reportedly experiencing a group psychosis and they currently lead the rest of Europe in preserving the Word and the Force.

    The development of Bayesianism in the United States was subjected to some not inconsiderable post-birth traumas during the McCarthy era.

    But the paradigm soared majestically , on the wings of seagulls and eagles, towards its Seventh Heaven at the Harvard and Chicago Business Schools, and notably at Carnegie-Mellon, aided and abetted by the adventurous ‘Jonathan Livingston Seagulls’ in Wisconsin and the small all-Bayesian team at Duke. Nowadays, Bayes is alive and kicking in every God-damned state in the USA, and in almost every country around the globe.

    Meanwhile, the International Society for Bayesian Analysis has enhanced the links to other disciplines with a plethora of electronic communications. And new, at times highly eminent, scientific and socio-economic Bayesians are springing out of the woodwork from all directions.

    Moreover, many generalisations of the conditional Laplacian approximations of the 1980s have now been well computer-packaged in INLA by Håvard Rue and his colleagues, and they provide extremely valid alternatives, in a great many situations, to the wild and woolly ramifications of MCMC, MMCMC, Particle MCMC, reversible jump MCMC, arty smarty crafty MCMC and so on and so forth.

    The pendulum has already swung, as various high quality applications of INLA begin to trickle in, and some of the old theoretical arts of Bayesianism from the Halcyon days are being restored.

    Perhaps the pendulum will swing even more, and maybe Le Marquis Pierre-Simon de Laplace will have the last laugh. He was of course the guy way across the Channel who had the cheek to develop the general forms of our much-fêted Bayes-Price Theorem.

    A potentially debilitating mote has nevertheless been cast into our eyes by the gross misrepresentations and misuses of Bayes theorem in Courts of Law, for example when evaluating DNA evidence, and these have stained our profession for many years to come. If our cynical Establishments do not put a quick end to them, the ancient Greek Goddess Themis may perchance find it necessary to fry a token forensic scientist or Bayes factorist or two on her scales of justice.

    As evidenced by the material critiqued in my Ch. 7, the kaleidoscope of Bayesian discovery has now fully blossomed into an enrichment of many areas of science, medicine, and socio-economics. While the practical advantages of the Bayesian contributions to Genomics and Economics have yet to be completely clarified, the beneficial influences in Medicine, the Environment, Social Progress, Artificial Intelligence, and Machine Learning have been ginormous, to the point where the creative research within some of these areas has itself been rejuvenated.

 
 
Alan Turing (1912-1959)   Alan Birnbaum (1923-1976)
 

    Our much revered modern founding father Alan Turing, a victim of the proverbial Poisoned Apple, would have been proud. So would Allan Birnbaum, and so, for the record, am I, as one of the more ordinary survivors of the anti-authoritarian bunch as I feel like a cat looking at two kings.

    Let’s face it. Bayes theorem isn’t just a quirky paradigm. All free spirits have a bit of ‘God’ within their inner ids, and Bayesian inference is the thus inspired Word of the living God.

 
 
 
  © Thomas Hoskyns Leonard, 2014