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Thursday, 8 April 2021

BAYESIAN HISTORY: 8.OVERVIEW

 






 


                                          


                                               Alan Turing O.B.E, F.R.S (1912-1954)

                                         Founder of Modern Practical Bayesian Statistics




    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.

   

    George Tiao, Carlos Pereira, Pilar Iglesias, and Jose Bernardo popularised Bayesian concepts in the Far East, Chile, Brazil, and Spain. Meanwhile, P. Jeffrey Harrison and Michael West purveyed the wonderful advantages of Kalman-style forecasting around the world, 

    In America, the key Purveyors of the Word included Jimmie Savage, Arnold Zellner, Jay Kadane and Rob Kass, and the quintessence of Yankee and immigrant academia. In Britain they included Jack Good, Dennis Lindley, and Sir Adrian Smith, .

 

    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.  And Jay Kadane still overemphasises the importance of the Expected Utility Hypothesis, as ever faithful to the memory of Jimmie Savage 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 seemed to converge..

    In response to MCMC and the early 21 st. century development by Spiegelhalter et al 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, lest the conclusions be spuriously evidence-based. 

    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 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 and they currently lead the rest of Europe

    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 towards its Seventh Heaven at the Harvard and Chicago Business Schools, and notably at Carnegie-Mellon, aided and abetted by the adventurous ‘people’ in Wisconsin and the small all-Bayesian team at Duke. Nowadays, Bayes is alive and kicking in every 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

NOTE ADDED APRIL 2021' I HAVE RECENTLY EXPRESSED ON-LINE CONCERN ABOUT SOME OF THE HIGHLY COMPLEX DEVELOPMENTS IN BAYESIAN NON-PARAMETRICS e.g. by DUNSON ET AL (2021), WHICH APPEAR TO SEEK EVER MORE COMPLEX WHEN CONVERGENT SIMULATION PROCEDURES BECOME LESS AND LESS FEASIBLE. IN MORE GENERAL TERMS, I OFTEN WONDER WHAT THESE GUYS ARE ABOUT e.g. IN THE AREA OF NEUROLOGICAL IMAGING WHERE THE RELEVANT MODELS CAN BE MUCH TOO COMPLEX TO EVER HOPE TO ANALYSE PROPERLY.. THEY SEEM TO BE EXAGGERATING THE SCOPE OF THE BAYESIAN PARADIGM TO THE SCIENTIFIC COMMUNITY IN A MANNER WHICH COULD BE TAKEN TO BE BOTH ARROGANT AND ACADEMICALLY ELITE. 

    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 ridiculously named "Bayes Theorem" following the 17th. development of conditional probability, by the pioneering Frenchman Blaise Pascal and Pierre Fermat,.

    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 clarifiedthe 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. Both Alan Turing and Allan Birnbaum would have been proud.

I believe that most statistical investigations are inherently subjective in nature, and that statisticians should no longer attempt to achieve ‘false objectivity’. Rather than attempting to educate the public in a possibly misleading manner, I think that our leading statistical societies should focus on encouraging their members to invariably insist on fairness, professionalism, and impartial honesty, while acknowledging the subjective nature of their conclusions. It is only then that we can hope to properly educate the public regarding the real benefits that can be gained from statistical investigations.

Note added 8th April 2021. THE MISTREATMENT AND EXPLOITATION OF BAYESIAN WOMEN: I have recently become quite disillusioned by the ISBA sex scandal, and a scandal at Berkeley starting in 2002 and involving the alleged attempted exploitation of a young woman trying to make a start in academia,.As a gay person on the receiving end of endless homophobia and ableism in academia, I am appalled by this mistreatment and abuse of many Bayesian women.. I now realise that the apparent cosiness and bonhomie at many early Bayesian conferences, including Valencia 1 and Valencia 6 which I attended, may have concealed dark undertones, with which several of my male contemporaries may have been associated. I however feel reassured by the ongoing renewal of ISBA. More women and people from all countries are involved. I think that I can perceive precisely where the sexist attitudes originated in European Bayesian academia. I am completely dismayed about those situations in which power seems to have prevailed, particularly when some Bayesian women may have started their careers by being inappropriately treated at Mediterranean conferences or by their male mentors..

                                                             

                                                Tom Leonard in his flat in central Edinburgh
 

                                                                          

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