Articles by xi'an

likelihood inference with no MLE

July 28, 2021 | xi'an

“In a regular full discrete exponential family, the MLE for the canonical parameter does not exist when the observed value of the canonical statistic lies on the boundary of its convex support.” Daniel Eck and Charlie Geyer just published an interesting and intriguing paper on running efficient inference for discrete ...

$\lim_{n\to\infty} \ell(\theta_n|x) = \sup_\theta \ell(\theta|x) := h(x)$

multinomial but unique

July 15, 2021 | xi'an

A quick riddle from the Riddler, where the multinomial M(n¹,n²,100-n¹-n²) probability of getting three different labels out of three possible ones out of three draws is 20%, inducing a single possible value for (n¹,n²) up to a permutation. Since this probability is n¹n²(100-n¹-n²)/161,700, ...

almost reversed 2-lag Markov chain

July 6, 2021 | xi'an

Another simple riddle from the Riddler: take a binary sequence and associate to this sequence a score vector made of the numbers of consecutive ones from each position. If the sequence is ten step long and there are 3 ones located at random, what is the expected total score? (The original ... [Read more...]

breaking sticks of various length

July 5, 2021 | xi'an

A riddle from the Riddler with a variation on the theme of breaking sticks: Given a stick of length L, what is the optimal manner to break said stick to achieve a maximal product of the individual lengths? While the pen & paper resolution is a one-line back-of-the-envelope calculation, with an ...

inf R ! [book review]

June 9, 2021 | xi'an

Thanks to my answering a (basic) question on X validated involving an R code, R mistakes and some misunderstanding about Bayesian hierarchical modelling, I got pointed out to Patrick Burns’ The R inferno. This is not a recent book as the second edition is of 2012, with a 2011 version still available ...

on approximations of Φ and Φ⁻¹

June 2, 2021 | xi'an

As I was working on a research project with graduate students, I became interested in fast and not necessarily very accurate approximations to the normal cdf Φ and its inverse. Reading through this 2010 paper of Richards et al., using for instance (with another version replacing 2/π with the squared root of π/8) and $...

$F_0(x) =\frac{1}{2}(1+\sqrt{1-\exp(-2x^2/\pi)})$

scale matters [maths as well]

June 1, 2021 | xi'an

A question from X validated on why an independent Metropolis sampler of a three component Normal mixture based on a single Normal proposal was failing to recover the said mixture… When looking at the OP’s R code, I did not notice anything amiss at first glance (I was about ...

more air for MCMC

May 29, 2021 | xi'an

Aki Vehtari, Andrew Gelman, Dan Simpson, Bob Carpenter, and Paul-Christian Bürkner have just published a Bayesian Analysis paper about using an improved R factor for MCMC convergence assessment. From the early days of MCMC, convergence assessment has been a recurring (and recurrent!) question in the community. First leading to ...

bean bag win

May 18, 2021 | xi'an

A quick riddle from The Riddler, where a multiple step game sees a probability of a 3 point increase of .4 and a probability of a 1 point increase of .3 with a first strategy (A), versus a probability of a 3 point increase of .4 and a probability of a 1 point increase of […]

R rexp()

May 17, 2021 | xi'an

Following a question on X validated about the reasons for coding rexp() following Ahrens & Dieter (1972) version, I re-read Luc Devroye’s explanations. Which boils down to an optimised implementation of von Neumann’s Exponential generator. The central result is that, for any μ__0, M a Geometric variate with failure probability exp(... [Read more...]

unbalanced sampling

May 16, 2021 | xi'an

A question from X validated on sampling from an unknown density f when given both a sample from the density f restricted to a (known) interval A , f¹ say, and a sample from f restricted to the complement of A, f² say. Or at least on producing an estimate of ...

warped Cauchys

May 3, 2021 | xi'an

A somewhat surprising request on X validated about the inverse cdf representation of a warped Cauchy distribution. I had not come across this distribution, but its density being means that it is the superposition of shifted Cauchys on the unit circle (with nice complex representations). As such, it is easily ...

one-way random walks

May 1, 2021 | xi'an

A rather puzzling riddle from The Riddler on an 3×3 directed grid and the probability to get from the North-West to the South-East nodes following the arrows. Puzzling because while the solution could be reasonably computed with an R code like suc...

a common confusion between sample and population moments

April 28, 2021 | xi'an

ten computer codes that transformed science

April 22, 2021 | xi'an

In a “Feature” article of 21 January 2021, Nature goes over a poll on “software tools that have had a big impact on the world of science”. Among those, the Fortran compiler (1957), which is one of the first symbolic languages, developed by IBM. This is the first computer language I learned (in 1982) ...

simulating Maxwell distribution

April 21, 2021 | xi'an

A question that came out on X validated a few days ago is how to efficiently simulate from a distribution with density x²φ(x). (Obviously properly normalised since the second moment of the standard Normal distribution is one.) The first solution that came out (by Jarle Tufto) exploits the fact ...

ABC in Svalbard [the day after]

April 18, 2021 | xi'an

The following and very kind email was sent to me the day after the workshop thanks once again to make the conference possible. It was full of interesting studies within a friendly environment, I really enjoyed it. I think it is not easy to make a comfortable and inspiring conference ...

the new DIYABC-RF

April 14, 2021 | xi'an

My friends and co-authors from Montpellier have released last month the third version of the DIYABC software, DIYABC-RF, which includes and promotes the use of random forests for parameter inference and model selection, in connection with Louis Raynal’s thesis. Intended as the earlier versions of DIYABC for population genetic ...

ABC in Svalbard [#2]

April 13, 2021 | xi'an

The second day of the ABC wwworkshop got a better start than yesterday [for me] as I managed to bike to Dauphine early enough to watch the end of Gael’s talk and Matias Quiroz’ in full on the Australian side (of zoom). With an interesting take on using frequency-domain (...

ABC in Svalbard [#1]

April 12, 2021 | xi'an

It started a bit awkwardly for me as I ran late, having accidentally switched to UK time the previous evening (despite a record-breaking biking-time to the University!), then the welcome desk could not find the key to the webinar room and I ended up following the first session from my ...

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