Hungarian Academy of Sciences under threat

Posted in Statistics with tags , , , , , , , on February 21, 2019 by xi'an

and it only gets worse…

Posted in Kids, pictures, Travel with tags , , , , , , , , , , , , , on February 21, 2019 by xi'an

” A recent survey by Bankrate.com found that just 40% of US households have enough money to cover a $1,000 in emergency expenses.” The Guardian, Feb 2, 2019

““Until we heard those cheers coming from Albany, we thought states were moving beyond such barbaric practices.” Mr. Pence offered his argument as a litmus test of morality; he described the new abortion legislation as a “shameless embrace of a culture of death.” But among conservatives, the White House’s outrage was also greeted as a clear and shrewd political strategy” The New York Times, Feb 1, 2019

“When Senator Elizabeth Warren formally announced her 2020 presidential bid this weekend, President Trump responded with a familiar line of attack. He mocked Ms. Warren for her claims to Native American ancestry, again calling her by the slur “Pocahontas.” Mr. Trump then appeared to refer to the Trail of Tears, the infamously cruel forced relocation of Native Americans in the 19th century that caused thousands of deaths.” The New York Times, Feb 10, 2019

“The United States is suspending one of the last major nuclear arms control treaties with Russia after heated conversations between the two powers recently failed to resolve a long-running accusation that Moscow is violating the Reagan-era treaty. Mr. Pompeo acknowledged a risk of a new arms race if the treaty is ultimately scrapped after the six-month window.” The New York Times, Feb 1, 2019

“In some states, lawmakers have sought to pass laws that would ban or severely restrict abortion in the event that Roe v. Wade is eventually overturned or effectively gutted (…) The court is likely to confront other abortion cases, too, as several state legislatures have recently enacted laws that seem calculated to try to force the Supreme Court to consider overruling Roe v. Wade, the 1973 decision that established a constitutional right to abortion.” The New York Times, Feb 8, 2019

“Mr. Trump’s willingness to invoke emergency powers to circumvent Congress is likely to go down as an extraordinary violation of constitutional norms — setting a precedent that future presidents of both parties may emulate to unilaterally achieve their own policy goals.” The New York Times, Feb 15, 2019

Wolfberger [pinot gris]

Posted in Statistics with tags , , , on February 20, 2019 by xi'an

simulation fodder for future exams

Posted in Books, Kids, R, Statistics with tags , , , , on February 20, 2019 by xi'an

Here are two nice exercises for a future simulation exam, seen and solved on X validated.The first one is about simulating a Gibbs sampler associated with the joint target

exp{-|x|-|y|-a|y-x|}

defined over IR² for a≥0 (or possibly a>-1). The conditionals are identical and non-standard, but a simple bound on the conditional density is the corresponding standard double exponential density, which makes for a straightforward accept-reject implementation. However it is also feasible to break the full conditional into three parts, depending on the respective positions of x, y, and 0, and to obtain easily invertible cdfs on the three intervals.The second exercise is about simulating from the cdf

F(x)=1-\exp\{-ax-bx^{p+1}/(p+1)\}

which can be numerically inverted. It is however more fun to call for an accept-reject algorithm by bounding the density with a ½ ½ mixture of an Exponential Exp(a) and of the 1/(p+1)-th power of an Exponential Exp(b/(p+1)). Since no extra constant appears in the solution,  I suspect the (p+1) in b/(p+1) was introduced on purpose. As seen in the above fit for 10⁶ simulations (and a=1,b=2,p=3), there is no deviation from the target! There is nonetheless an even simpler and rather elegant resolution to the exercise: since the tail function (1-F(x)) appears as the product of two tail functions, exp(-ax) and the other one, the cdf is the distribution of the minimum of two random variates, one with the Exp(a) distribution and the other one being the 1/(p+1)-th power of an Exponential Exp(b/(p+1)) distribution. Which of course returns a very similar histogram fit:

leave Bayes factors where they once belonged

Posted in Statistics with tags , , , , , , , , , , on February 19, 2019 by xi'an

In the past weeks I have received and read several papers (and X validated entries)where the Bayes factor is used to compare priors. Which does not look right to me, not on the basis of my general dislike of Bayes factors!, but simply because this seems to clash with the (my?) concept of Bayesian model choice and also because data should not play a role in that situation, from being used to select a prior, hence at least twice to run the inference, to resort to a single parameter value (namely the one behind the data) to decide between two distributions, to having no asymptotic justification, to eventually favouring the prior concentrated on the maximum likelihood estimator. And more. But I fear that this reticence to test for prior adequacy also extends to the prior predictive, or Box’s p-value, namely the probability under this prior predictive to observe something “more extreme” than the current observation, to quote from David Spiegelhalter.

Bayesian intelligence in Warwick

Posted in pictures, Statistics, Travel, University life, Wines with tags , , , , , , , , , , , , on February 18, 2019 by xi'an

This is an announcement for an exciting CRiSM Day in Warwick on 20 March 2019: with speakers

10:00-11:00 Xiao-Li Meng (Harvard): “Artificial Bayesian Monte Carlo Integration: A Practical Resolution to the Bayesian (Normalizing Constant) Paradox”

11:00-12:00 Julien Stoehr (Dauphine): “Gibbs sampling and ABC”

14:00-15:00 Arthur Ulysse Jacot-Guillarmod (École Polytechnique Fedérale de Lausanne): “Neural Tangent Kernel: Convergence and Generalization of Deep Neural Networks”

15:00-16:00 Antonietta Mira (Università della Svizzera italiana e Università degli studi dell’Insubria): “Bayesian identifications of the data intrinsic dimensions”

[whose abstracts are on the workshop webpage] and free attendance. The title for the workshop mentions Bayesian Intelligence: this obviously includes human intelligence and not just AI!

Le Monde puzzle [#1085]

Posted in Books, Kids, R with tags , , , , , on February 18, 2019 by xi'an

A new Le Monde mathematical puzzle in the digit category:

Given 13 arbitrary relative integers chosen by Bo, Abigail can select any subset of them to be drifted by plus or minus one by Bo, repeatedly until Abigail reaches the largest possible number N of multiples of 5. What is the minimal possible value of N under the assumption that Bo tries to minimise it?

I got stuck on that one, as building a recursive functiion led me nowhere: the potential for infinite loop (add one, subtract one, add one, …) rather than memory issues forced me into a finite horizon for the R function, which then did not return anything substantial in a manageable time. Over the week and the swimming sessions, I thought of simplifying the steps, like (a) work modulo 5, (b) bias moves towards 1 or 4, away from 2 and 3, by keeping only one entry in 2 and 3, and all but one at 1 and 4, but could only produce five 0’s upon a sequence of attempts… With the intuition that only 3 entries should remain in the end, which was comforted by Le Monde solution the week after.