## the quincunx [book review]

Posted in Books, Kids, Statistics with tags , , , , , on July 1, 2013 by xi'an

“How then may we become free? Only by harmonising ourselves with the randomness of life through the untrammelled operation of the market.”

This is a 1989 book that I read about that time and had not re-read till last month…. The Quincunx is a parody of several of Charles Dickens’ novels, written by another Charles, Charles Palliser, far into the 20th Century. The name is obviously what attracted me first to this book, since it reminded me of Francis Galton’s amazing mechanical simulation device. Of course, there is nothing in the book that relates to Galton and its quincunx!

“Your employer has been speculating in bills with the company’s capital and, as you’ll conclude in the present panic, he has lost heavily. There’s no choice now but to declare the company bankrupt. And when that happens, the creditors will put you in Marshalsea.”

As I am a big fan of Dickens, I went through The Quincunx as an exercise in Dickensania, trying to spot characters and settings from the many books written by Dickens. I found connections with Great Expectations (for the John-Henrietta couple and the fantastic features in the thieves’ den, but also encounters with poverty and crime), Bleak House (for the judicial intricacies), Little Dorrit (for the jail system and the expectation of inheritance), Our Mutual Friend (for the roles of the Thames, of money, forced weddings),  Martin Chuzzlewit (again for complex inheritance stories), Oliver Twist (for the gangs of thieves, usury, the private “schools” and London underworld), David Copperfield (for the somehow idiotic mother and the fall into poverty), The Mystery of Edwin Drood (for the murder, of course!) And I certainly missed others. (Some literary critics wrote that Palliser managed to write all Dickens at once.)

“I added to the mixture a badly bent George II guinea which was the finest of all the charms.”

However, despite the perfect imitation in style, with its array of grotesque characters and unbelievable accidents, using Dickens’ irony and tongue-in-cheek circumlocutions, with maybe an excess of deliberate misspellings, Palliser delivers a much bleaker picture of Dickens’ era than Dickens himself. This was the worst of times, if any, where some multifaceted unbridled capitalism makes use of the working class through cheap salaries, savage usury, and overpriced (!) slums, forcing women into prostitution, men into cemetery desecration and sewage exploration. There is no redemption at any point in Palliser’s world and the reader is left with the impression that the central character John Huffam (it would be hard to call him the hero of The Quincunx) is about to fall into the same spiral of debt and legal swindles as his complete family tree.  A masterpiece. (Even though I do not buy the postmodern thread.)

## Galton & simulation

Posted in Books, R, Statistics with tags , , , , , , , , on September 28, 2010 by xi'an

Stephen Stigler has written a paper in the Journal of the Royal Statistical Society Series A on Francis Galton’s analysis of (his cousin) Charles Darwin’ Origin of Species, leading to nothing less than Bayesian analysis and accept-reject algorithms!

“On September 10th, 1885, Francis Galton ushered in a new era of Statistical Enlightenment with an address to the British Association for the Advancement of Science in Aberdeen. In the process of solving a puzzle that had lain dormant in Darwin’s Origin of Species, Galton introduced multivariate analysis and paved the way towards modern Bayesian statistics. The background to this work is recounted, including the recognition of a failed attempt by Galton in 1877 as providing the first use of a rejection sampling algorithm for the simulation of a posterior distribution, and the first appearance of a proper Bayesian analysis for the normal distribution.”

The point of interest is that Galton proposes through his (multi-stage) quincunx apparatus a way to simulate from the posterior of a normal mean (here is an R link to the original quincunx). This quincunx has a vertical screen at the second level that acts as a way to physically incorporate the likelihood (it also translates the fact that the likelihood is in another “orthogonal” space, compared  with the prior!):

“Take another look at Galton’s discarded 1877 model for natural selection (Fig. 6). It is nothing less that a workable simulation algorithm for taking a normal prior (the top level) and a normal likelihood (the natural selection vertical screen) and finding a normal posterior (the lower level, including the rescaling as a probability density with the thin front compartment of uniform thickness).”

Besides a simulation machinery (steampunk Monte Carlo?!), it also offers the enormous appeal of proposing the derivation of the normal-normal posterior for the very first time:

“Galton was not thinking in explicit Bayesian terms, of course, but mathematically he has posterior $\mathcal{N}(0,C_2)\propto\mathcal{N}(0,A_2)\times f(x=0|y)$. This may be the earliest appearance of this calculation; the now standard derivation of a posterior distribution in a normal setting with a proper normal prior. Galton gave the general version of this result as part of his 1885 development, but the 1877 version can be seen as an algorithm employing rejection sampling that could be used for the generation of values from a posterior distribution. If we replace $f(x)$ above by the density $\mathcal{N}(a,B_2)$, his algorithm would generate the posterior distribution of Y given X=a, namely $\mathcal{N}(aC_2/B_2, C_2)$. The assumption of normality is of course needed for the particular formulae here, but as an algorithm the normality is not essential; posterior values for any prior and any location parameter likelihood could in principle be generated by extending this algorithm.” Continue reading