the first Bayesian

In the first issue of Statistical Science for this year (2018), Stephen Stiegler pursues the origins of Bayesianism as attributable to Richard Price, main author of Bayes’ Essay. (This incidentally relates to an earlier ‘Og piece on that notion!) Steve points out the considerable inputs of Price on this Essay, even though the mathematical advance is very likely to be entirely Bayes’. It may however well be Price who initiated Bayes’ reflections on the matter, towards producing a counter-argument to Hume’s “On Miracles”.

“Price’s caution in addressing the probabilities of hypotheses suggested by data is rare in early literature.”

A section of the paper is about Price’s approach data-determined hypotheses and to the fact that considering such hypotheses cannot easily fit within a Bayesian framework. As stated by Price, “it would be improbable as infinite to one”. Which is a nice way to address the infinite mass prior.

 

Mathematical underpinnings of Analytics (theory and applications)

“Today, a week or two spent reading Jaynes’ book can be a life-changing experience.” (p.8)

I received this book by Peter Grindrod, Mathematical underpinnings of Analytics (theory and applications), from Oxford University Press, quite a while ago. (Not that long ago since the book got published in 2015.) As a book for review for CHANCE. And let it sit on my desk and in my travel bag for the same while as it was unclear to me that it was connected with Statistics and CHANCE. What is [are?!] analytics?! I did not find much of a definition of analytics when I at last opened the book, and even less mentions of statistics or machine-learning, but Wikipedia told me the following:

“Analytics is a multidimensional discipline. There is extensive use of mathematics and statistics, the use of descriptive techniques and predictive models to gain valuable knowledge from data—data analysis. The insights from data are used to recommend action or to guide decision making rooted in business context. Thus, analytics is not so much concerned with individual analyses or analysis steps, but with the entire methodology.”

Barring the absurdity of speaking of a “multidimensional discipline” [and even worse of linking with the mathematical notion of dimension!], this tells me analytics is a mix of data analysis and decision making. Hence relying on (some) statistics. Fine.

“Perhaps in ten years, time, the mathematics of behavioural analytics will be common place: every mathematics department will be doing some of it.”(p.10)

First, and to start with some positive words (!), a book that quotes both Friedrich Nietzsche and Patti Smith cannot get everything wrong! (Of course, including a most likely apocryphal quote from the now late Yogi Berra does not partake from this category!) Second, from a general perspective, I feel the book meanders its way through chapters towards a higher level of statistical consciousness, from graphs to clustering, to hidden Markov models, without precisely mentioning statistics or statistical model, while insisting very much upon Bayesian procedures and Bayesian thinking. Overall, I can relate to most items mentioned in Peter Grindrod’s book, but mostly by first reconstructing the notions behind. While I personally appreciate the distanced and often ironic tone of the book, reflecting upon the author’s experience in retail modelling, I am thus wondering at which audience Mathematical underpinnings of Analytics aims, for a practitioner would have a hard time jumping the gap between the concepts exposed therein and one’s practice, while a theoretician would require more formal and deeper entries on the topics broached by the book. I just doubt this entry will be enough to lead maths departments to adopt behavioural analytics as part of their curriculum…

Bayes.2.5.0 reminder

Just a reminder that Bayes 250 at the RSS is taking place in less than three weeks and that it would be a good idea to register now (using a form and not an on-line page, unfortunately)! Here is the official program.

Current Schedule
11:00 Registration and tea
11:30 Welcome
11:35 Anthony O’Hagan (Warwickshire) and Dennis Lindley (Somerset) – video recorded interview
12:15 Gareth Roberts (University of Warwick) “Bayes for differential equation models”

12:45 14:00 Lunch and posters

14:00 Sylvia Richardson (MRC Biostatistics Unit) “Biostatistics and Bayes”
14:30 Dennis Prangle (Lancaster University) “Approximate Bayesian Computation”
14:50 Phil Dawid (University of Cambridge), “Putting Bayes to the Test”

15:20 tea

16:00 Mike Jordan (UC Berkeley) “Feature Allocations, Probability Functions, and Paintboxes”
16:30 Iain Murray (University of Edinburgh) “Flexible models for density estimation”
16:50 YeeWhye Teh (University of Oxford) “MCMC for Markov and semi-Markov jump processes”

17:20 posters and drinks

Day 2:

09:30 Michael Goldstein (Durham University) “Geometric Bayes”
10:00 Andrew Golightly (Newcastle University), “Auxiliary particle MCMC schemes for partially observed diffusion processes”
10:20 Nicky Best (Imperial College London) “Bayesian space-time models for environmental epidemiology”

10:50 tea

11:15 Christophe Andrieu (University of Bristol) “Inference with noisy likelihoods”
11:45 Chris Yau (Imperial College London) “Understanding cancer through Bayesian approaches”
12:05 Stephen Walker (University of Kent) “The Misspecified Bayesian”

12:35 Lunch

13:30 Simon Wilson (Trinity College Dublin), “Linnaeus, Bayes and the number of species problem”
14:00 Ben Calderhead (UCL) “Probabilistic Integration for Differential Equation Models”
14:20 Peter Green (University of Bristol and UT Sydney) “Bayesian graphical model determination”
14:50 Closing Remarks Adrian Smith (University of London)

Bayes 250 in Durham

Reproducing an email from ISBA (sorry about the confusion purposely created by the title, this is Durham, North Carolina, not Durham, England, just as the London in Bayes 250 in London was London, England, not London, Ontario!):

ISBA announces a special celebration of the 250th anniversary of the presentation (December 23, 1763) of Thomas Bayes’ seminal paper “An Essay towards solving a Problem in the Doctrine of Chances” that will be held at Duke University in conjunction with the O-Bayes 13 Workshop (December 15-19) and EFab@ Bayes250 Workshop (December 15-17). (I am part of the scientific committee for O-Bayes 13!)

Speakers for the anniversary celebration are legendary contributors to the Bayesian literature, spanning a range of fields:

• Stephen Fienberg, Carnegie-Mellon University
• Michael Jordan, University of California, Berkeley
• Christopher Sims, Princeton University
• Adrian Smith, University of London
• Stephen Stigler, University of Chicago

There will be a banquet in the evening, with a speech by Sharon Bertsch McGrayne, noted author of the popular book “The Theory That Would Not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines and Emerged Triumphant From Two Centuries of Controversy.”

Price’s theorem?

A very interesting article by Martyn Hooper in Significance Feb. 2013 issue I just received. (It is available on-line for free.) It raises the question as to how much exactly Price contributed to the famous Essay… Given the percentage of the Essay that can be attributed to Price with certainty (Bayes’ part stops at page 14 out of 32 pages), given the lack of the original manuscript by Bayes, given the delay between the composition of this original manuscript (1755?), its delivery to Price (1761?) and its publication in 1763, given the absence of any other document published by Bayes on the topic, I tend to concur with Martyn Hooper (and Sharon McGrayne) that Price contributed quite significantly to the 1763 paper. Of course, it would sound quite bizarre to start calling our approach to Statistics Pricean or Pricey (or even Priceless!) Statistics, but this may constitute one of the most striking examples of Stigler’s Law of Eponymy!