transformation MCMC

For reasons too long to describe here, I recently came across a 2013 paper by Dutta and Bhattacharya (from ISI Kolkata) entitled MCMC based on deterministic transforms, which sounded a bit dubious until I realised the deterministic label apply to the choice of the transformation and not to the Metropolis-Hastings proposal… The core of the proposed method is to make a proposal that simultaneously considers a move and its inverse, namely from x to either x’=T(x,ε) or x”=T⁻¹(x,ε) , where ε is an independent random noise, possibly degenerated to a manifold of lesser dimension. Due to the symmetry the acceptance probability is then a ratio of the target, multiplied by the x-Jacobian of T (as in reversible jump). I tried the method on a mixture of Gamma distributions target (in red) with an Exponential scale change and the resulting sample indeed fitted said target.

The authors even make an argument in favour of a unidimensional noise, although this amounts to running an implicit Gibbs sampler. Argument based on a reduced simulation cost for ε, albeit the full dimensional transform x’=T(x,ε) still requires to be computed. And as noted in the paper this also requires checking for irreducibility. The claim for higher efficiency found therein is thus mostly unsubstantiated…

“The detailed balance requirement also demands that, given x, the regions covered by the forward and the backward transformations are disjoint.”

The above statement is also surprising in that the generic detailed balance condition does not impose such a restriction.

 

another book on J.B.S. Haldane [review of a book review]

As I noticed a NYT book review of a most recent book on J.B.S. Haldane, I realised several other books had already been written about him. From an early 1985 biography, “Haldane: the life and work of J.B.S. Haldane with special references to India” followed by a “2016 biography “Popularizing Science” along an  2009 edited book on some Haldane’s essays, “What I require from life“, all by Krishna R. Dronamraju to a 1969 biography with the cryptic title “J.B.S.“, by Richard Clarke, along with a sensational 2018 “Comrade Haldane Is Too Busy to Go on Holiday: The Genius Who Spied for Stalin” by Gavan Tredoux, depicting him as a spy for the Soviet Union during WW II. (The last author is working on a biography of Francis Galton, hopefully exonerating him of spying for the French! But a short text of him comparing Haldane and Darlington appears to support the later’s belief in racial differences in intelligence…) I also discovered that J.B.S. had written a children book, “Mr Friend Mr. Leaky“, illustrated by Quentin Blake, Roald Dahl’s illustrator. (Charlotte Franken Haldane, J.B.S.’s first wife, also wrote a considerable number of books.)

The NYT review is more a summary of Haldane’s life than an analysis of the book itself, hard as it is not to get mesmerised by the larger-than-life stature of J.B.S. It does not dwell very long on the time it took Haldane to break from the Communist Party for its adherence to the pseudo-science Lysenko (while his wife Charlotte had realised the repressive nature of the Soviet regime much earlier, which may have led to their divorce). While the review makes no mention at all of Haldane’s ideological move to the ISI in Kolkata, it concludes with “for all his failings, he was “deeply attractive during a time of shifting, murky moralities.”” [The double quotes being the review quoting the book!]

A la Bienale di Venezia

Taking advantage of staying in Venezia over the weekend, we went to the huge international contemporary art exhibit located all over the city but mostly in the Arsenale and in the gardens. This was quite impressive in terms of diversity and style, of course, although the general feeling was rather bleak, centering on pollution and apocalyptic themes. The particularly ugly French exhibit was for instance a highly polluted sea surface, made of glass and only accessible by going around piles of gravel in the basement of the pavilion. Most exhibits also involved videos, often not making much sense, and comparatively few paintings or photographs. Within this depressing catalogue, a few beautiful highlights from my own perspective. One was a construct of several thousands shell-like objects, sculpted from sheep leather by Zahrah Al Ghamdi, a female Saudi Arabia artist Another one, representing Ghana, by the artists El Anatsui and Ibrahim Mahama, recycled aluminum stickers into huge maps, reminding me of the recycled maps in Munbai airport.Yet another one, difficult to catch, was a huge construct from the Philippines by Mark Justiniani, made of glass that gave an impression of infinite depth and again recycled different objects into wells, reminding me of the automated art pieces appearing in Gibson’s Count Zero. Called “Island Weather” to reflect upon the elusive nature of truth and the notion that everyone is an island, with bottomless layers of accumulated memories.

A series [called Angst] of remarkable night photographs by Soham Gupta of some inhabitants of the slums in Kolkata where the persons chose to act in relation with the hardship or trauma that led them to survive in the street. And still exhibiting joy and engaging into farciful behaviours. A video was however striking [from my perspective], describing the fight of a Nunavuk father to prevent his children being sent far away for schooling by the Canadian government, as it reminded me of a so different time when, as a child then, a catholic missionary from the Far North had come to our primary school and told us fascinating stories of the cruelly beautiful (or beautifully cruel?) like in the Arctic, in what did not appear yet as a strongly biased manner… The title of the Bienale this year was May you live in interesting times, which prompted many attendees to scrawl Theresa May you leave in interesting times over the exhibit panels! Interesting if bleak times indeed.

patterned random matrices [not a book review]

in the bus [jatp]