simulating hazard

A rather straightforward X validated question that however leads to an interesting simulation question: when given the hazard function h(·), rather than the probability density f(·), how does one simulate this distribution? Mathematically h(·) identifies the probability distribution as much as f(·),

which means cdf inversion could be implemented in principle. But in practice, assuming the integral is intractable, what would an exact solution look like? Including MCMC versions exploiting one fixed point representation or the other.. Since

using an unbiased estimator of the exponential term in a pseudo-marginal algorithm would work. And getting an unbiased estimator of the exponential term can be done by Glynn & Rhee debiasing. But this is rather costly… Having Devroye’s book under my nose [at my home desk] should however have driven me earlier to the obvious solution to… simply open it!!! A whole section (VI.2) is indeed dedicated to simulations when the distribution is given by the hazard rate. (Which made me realise this problem is related with PDMPs in that thinning and composition tricks are common to both.) Besides the inversion method, ie X=H⁻¹(U), Devroye suggests thinning a Poisson process when h(·) is bounded by a manageable g(·). Or a generic dynamic thinning approach that converges when h(·) is non-increasing.

a journal of the plague year [confined reviews]

Watched TV series His Dark Materials produced for the BBC, which is much much better than the earlier film, as the actors are all fabulous—first and foremost Lyra, but also Ma Costa, the Gyptian Muter Courage—, the gypsy community is given a much stronger role, the characters are deep and complex, as eg Mrs and Mr Coulter, both ready to sacrifice kids for the greater “good” without appearing as absolute monsters! The special effects are a wee bit deficient as often with BBC productions but not enough to make a case. Although I sort of cringed each time a bear moved!

Read The Voyage of the Jerle Shannara trilogy by Terry Brooks, which I noticed standing on my son’s bookshelves. The original Shannara Trilogy was one of the very first fantasy books I read in English in my undergrad years (after Lord of the Rings of course and possibly The Chronicles of Thomas Covenant), which did not leave me with an everlasting feeling of superlative literature, to say the least. This avatar of the original Sword of Shannara trilogy did nothing to improve my feelings as the plot is lazy at best, with super-powered villains suddenly acting, last second deus ex machina rescues, endless internal debates, heavy hints at treacheries and double-treacheries, and, worst of all!, intrusion of 20th century technology, e.g., computers, AIs and robots, that the far future characters make sense of. Only suitable for a time of lockdown and even then… I should have left it on the bookshelf! Incidentally, one fight scene against a cyborg was highly reminiscent of the black knight scene in Holy Grail!

Watched by chance Tarantino’s Reservoir Dogs. For the first time. And was totally un-impressed. Highly pretentious construction falling flat from being a modern reconstruction of antique dramas, endless dialogues (which could have been cut by half if removing all the occurrences of fucking from them), boring and threadbare story, and artificial characters that essentially make no sense. I cannot fathom why this film is so highly ranked..! (And even less to witness it being compared with Rashomon!)

Read [part] of Jin Yong’s Legends of the Condor Heroes (射鵰英雄傳) but, lockdown or not, I simply could not finish it. Despite its fantasy approach to Chinese martial arts, which I usually enjoy (at least in planes!), and some proximity with the Judge Dee stories by van Gulik, the story felt very contrived and somewhat out of reach, plus [not yet] Genghis Khan being depicted in a fairly positive way [at least in the part I read]. Too irrealist for my reading buds, I presume…

Cooked plenty of new dishes, thanks to the delivery of weekly farmer boxes, from radish stems & buckwheat pancakes to celery roots purées, to fregola sarda (leftovers from ISBA 2016!) con acciughe, to chard gratins, to pea pod and cauliflower core soups, to flaxseed bread and buckwheat naans (as we ran out of wheat flour). We also managed to use and survive most of the out-of-date cans and bags that had stood forgotten in the back of our cupboard… Not visiting a supermarket for two months was actually most pleasant, living very nicely from the above mentioned farmer boxes and the occasional delivery from a cheesemonger, and supplementing weekly visits to the baker with attempts at home made bread.

Read Matha Well’s Murderbot diaries, my first read on a Kindle!, for free courtesy of Tor. Starting with All Systems Red, which won the 2017 Nebula Award for Best Novella, the 2018 Hugo Award for Best Novella, the 2018 Locus Award, and the American Library Association‘s Alex Award. Very good if somewhat classical (Blade Runner anyone?!) trope of the rogue robot turned autonomous and human, so human! This is a sequence of novellas which means a fast-paced story and an efficient style. (Including a less exciting third novella, due to a lazy scenario.) More mind-candy à la John Scalzi than profound literature but quite enjoyable for a quick read during lunch or tea break! But which induced me to buy the first and incoming novel in the series,  Network Effect. (To be commented in a subsequent entry…)

Leading to (re)read the Interdependency trilogy by John Scalzi, the last volume in the series being just out. Very lazy buildup, in the traditional spirit of a few people driving the future of the entire Universe, with unlimited resources and unrestricted hacking abilities, but with funny dialogues, as usual with Scalzi. In this binge (re)read, I actually realised the frustrating intricacies of Kindle ordering as (i) I could not use my amazon.com account and hence none of my associate gains (ii) I could not merge several amazon.fr accounts and (iii) prices varied a lot between using directly the Kindle and ordering from amazon.fr…

And even growing some salads and radishes over the two months and eating them before the end of the lockdown, as the weather in Paris was quite mild most of the time. Although it meant a daily-basis fight with slugs. The arugula did not resist that well, though…

Reading Tade Thompson’s Rosewater for more than a month, having trouble keeping my concentration as the story goes in loops and not a particularly well settled plot. With a central idea of an alien race taking over humanity a few cells at a time. Which reminded me of Greg Bear’s Blood Music I read during the first year of my PhD. The book has some appeal, from being located in Nigeria 30 years from now to America having completely vanished from the map after Trump pulled the ultimate drawbridge. It won the 2019 Arthur Clarke Award after all! But I found it too hard to complete to even consider embarking upon the next two volumes on the trilogy…

a new Monty Hall riddle

The Riddler was sort of feeling the rising boredom of being under lockdown when proposing the following variant to the Monty Hall puzzle:

There are zero to three goats, with a probability ¼ each, and they are allocated to different doors uniformly among the three doors of the show. After the player chooses a door, Monty opens another door hidding a goat or signals this is impossible. Given that he did open a door, what is the probability that the player’s door does not hide a goat?

Indeed, a straightforward conditional probability computation considering all eight possible cases with the four cases corresponding to Monty opening a door leads to a probability of ³/₈ for the player’s door. As confirmed by the following R code:

s=sample
m=c(0,0)
for(t in 1:1e6)m=m+(range(s(1:3,s(1:3,1)))>1)

enjoy a cuppa for International Tea Day

It's an art.
It's culture.
It's heritage.
And it's a source of livelihood for millions.

🍵Tea isn't just a drink, it's so much more.

On this first #InternationalTeaDay, we celebrate the history of tea and the farmers that produce it!

👉https://t.co/Zb6CrSURPq pic.twitter.com/kckGVhQXzg

— FAO (@FAO) May 21, 2020

 

and it only gets worse [verbatim]

“They always said nobody got treated worse than Lincoln. I believe I am treated worse.” DT, 03 May

“We’re on the other side of the medical aspect of this [pandemic.]” J. Kushner, 29 April

““We will not see diseases like the coronavirus come here, we will not see terrorism come here, and isn’t that refreshing when contrasting it with the awful Presidency of President Obama?” K. McEnany, 25 February

“You all know what happened in 1917.” DT, 27 April

“Leadership may be hard to define, but in times of crisis it is easy to identify. As the pandemic has spread fear, disease and death, national leaders across the globe have been severely tested. Some have fallen short, sometimes dismally, but there are also those leaders who have risen to the moment, demonstrating resolve, courage, empathy, respect for science and elemental decency, and thereby dulling the impact of the disease on their people.” NYT editorial, 30 April

“In the past month alone, the [US Environmental Protection Agency (EPA)] has dialled down regulations on automobile emissions and fuel efficiency put in place under former president Barack Obama; it has weakened rules on mercury and other pollutants emitted by power plants; and it has shied away from strengthening standards to reduce fine-particle air pollution.“ Nature, 28 April“

“It would have been bad even with the best of government. It has been an absolute chaotic disaster when that mindset — of ‘what’s in it for me’ and ‘to heck with everybody else’ — when that mindset is operationalized in our government.” Barack Obama, 09 May

“““Trump’s constant antics are a danger to the American people. The current approach to science and expertise within the Trump administration is a shame on many levels. Trump’s talking nonsense risks misleading the public, and it distracts top scientists who spend emotional energy neutralizing the damage he causes when they should be tackling the virus (…) Many scientists were dreading that the president would be faced by a test just like coronavirus. “ John Holdren, 03 May

“Probably it was incompetence. Somebody was stupid.” DT [an expert in the field], 10 May

“All I can tell you is so far I seem to be OK (…) I take [hydroxychloroquine] because I think I hear very good things.” DT, 18 May

unorthodox

Another series I watched during quarantine is the short and powerful Unorthodox, by Anna Winger, featuring the fantastic actress Shira Haas as Etsy, fleeing her unhappy marriage and the stifling rules set by her Hasidic community in Williamsburg, New York, to seek refuge in Berlin, although ambivalent to get help from her distanced mother once there. I found the story quite moving and intense in the slow unfolding of Etsy’s progressive unraveling of her un-orthodoxy and of her desperate escape into a world she knows nothing about. While her difficulties in apprehending this new universe are well rendered, I however find the part of the story when she joins a friendly group of music students somewhat too lazy a plot, although her fight there for achieving autonomy by herself only is remarkably transcribed. I am equally quite impressed by the show immersion into the Hasidic community, which is putting a considerable effort in replacing their tradition into an historical perspective and exposing the outworldly separation between men and women, who are essentially reduced to becoming mothers. The main strength of Unorthodox is that it keeps away from manichaeism, with people stuck into a frozen tradition and not seeing the oppression it induces. As most often with fundamentalism.

Keith Jarrett à Juan-les-Pins, 1979