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!]

patterned random matrices [not a book review]

Mahalanobis at the bus-stop [jatp]

Two bus-stops around the Indian Statistical Institute, featuring its founder, Prasanta Chandra Mahalanobis.

 

back to Kolkata [শুভ নব বর্ষ]

With high probability (!), I am off to Kolkata tonight, almost an exact year after I visited the city and the Department of Statistics of the University of Kolkata. On this occasion, I will attend a conference celebrating the 125th birthday of Mahalanobis and be staying at the Indian Statistical Institute, in another part of the city. Although I will only stay there for three days, I am looking forward meeting old friends and new faces, enjoying Bengali food and replenishing my reserves of Darjeeling tea. Shubho Nabobarsho (Happy New Year in Bengali)! As in the previous trip, I was also invited at a second conference at the Indian Association For Productivity, Quality & Reliability, on New Paradigms in Statistics for Scientific and Industrial Research, but decided against talking there for fear of being stuck for hours in the infamous Kolkata traffic.