## and it only gets worse

Posted in Books, Kids, Travel with tags , , , , , , , , , , , on September 15, 2021 by xi'an

“The law, known as Senate Bill 8, amounts to a nearly complete ban on abortion in Texas, one that will further fuel legal and political battles over the future of Roe v. Wade, the 1973 decision that established a constitutional right to abortion. The law makes no exceptions for pregnancies resulting from incest or rape.” NYT, Sept. 1

“The [Supreme] Court’s order is stunning,” Justice Sonia Sotomayor wrote in her dissent. “Presented with an application to enjoin a flagrantly unconstitutional law engineered to prohibit women from exercising their constitutional rights and evade judicial scrutiny, a majority of justices have opted to bury their heads in the sand.” NYT, Sept. 2

“A judge in Ohio ordered a hospital to treat a Covid-19 patient with ivermectin, despite warnings from experts that the anti-parasitic drug has not proved effective against the virus and can be dangerous in large doses.” The Guardian, Aug. 31

“More than half of the world’s people have no social protections, the United Nations has warned, even after the pandemic pushed many governments to offer services to their populations.” The Guardian, Sept. 1

## integral theorems for Monte Carlo

Posted in Books, pictures, Statistics with tags , , , , , , , on August 12, 2021 by xi'an

Nhat Ho and Stephen G. Walker have just arXived a paper on the use of (Fourier) integral theorems for Monte Carlo estimators, following the earlier entry of Parzen: namely that for any integrable function,

$m(y)=\frac{1}{(2\pi)^d}\int_{\mathbb R^d}\int_{\mathbb R^d}\cos(s^\text{T}(y-x))m(x)\text dx\text ds$

which can be turned into an estimator of a density m based on a sample from m. This identity can be rewritten as

$m(y)=\lim_{R\to\infty}\frac{1}{\pi^d}\int_{\mathbb R^d}\prod_{i=1}^d\dfrac{\sin(R(y_i-x_i))}{y_i-x_i}\;m(x)\,\text dx$

and the paper generalises this identity to all cyclic functions. Even though it establishes that sin is the optimal choice. After reading this neat result, I however remain uncertain on how this could help with Monte Carlo integration.

## the rise of the vigilantes

Posted in Kids, Travel with tags , , , , , , , on July 19, 2021 by xi'an

I was reading the New York Times about the explosion of anti-abortion legislations in the US, with more restrictions voted in the first six months than in any previous year since 1973. Besides laws that create always more burdens and constraints for women seeking an abortion, Mississippi set a 15 week ban and Texas just moved even further with a 6 week ban, which is essentially banning abortion in the State.  Which is unconstitutional (at the moment), except that Texas went a vicious step further, in making people rather than the State in charge of enforcing the law, ie of potentially suing anyone involved in an abortion performed after six weeks! Which makes the defence by abortion providers and pro-choice organisations almost impossible. And sounds like a perversion of justice, since anyone without any connection whatsoever with an abortion case and obviously irresponsible of the destiny of children born under such legislations, can sue. Just because irrational beliefs and self-righteousness make them entitled to irremediably impact others’ choices and live. Just like taliban.

## Arianna Rosenbluth’s hit

Posted in Statistics with tags , , , , , , , , , , on February 8, 2021 by xi'an

## approximation of Bayes Factors via mixing

Posted in Books, Statistics, University life with tags , , , , , , , , , , , on December 21, 2020 by xi'an

A [new version of a] paper by Chenguang Dai and Jun S. Liu got my attention when it appeared on arXiv yesterday. Due to its title which reminded me of a solution to the normalising constant approximation that we proposed in the 2010 nested sampling evaluation paper we wrote with Nicolas. Recovering bridge sampling—mentioned by Dai and Liu as an alternative to their approach rather than an early version—by a type of Charlie Geyer (1990-1994) trick. (The attached slides are taken from my MCMC graduate course, with a section on the approximation of Bayesian normalising constants I first wrote for a short course at Jim Berger’s 70th anniversary conference, in San Antonio.)

A difference with the current paper is that the authors “form a mixture distribution with an adjustable mixing parameter tuned through the Wang-Landau algorithm.” While we chose it by hand to achieve sampling from both components. The weight is updated by a simple (binary) Wang-Landau version, where the partition is determined by which component is simulated, ie by the mixture indicator auxiliary variable. Towards using both components on an even basis (à la Wang-Landau) and stabilising the resulting evaluation of the normalising constant. More generally, the strategy applies to a sequence of surrogate densities, which are chosen by variational approximations in the paper.