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Ben Bolker

@bbolker.bsky.social

A colleague is looking for an open-source/online (pref. peer-reviewed) reference for properties of probability distributions. Any ideas? (NIST gives *very* basic properties e.g. www.itl.nist.gov/div898/handb... but I think they're looking for something more complete ...)

I’m working on a manuscript that mentions a fair number of standard distributions and their properties, and I’ve been wondering if there’s an equally standard reference. For context for my question, while Wikipedia often has what I need if I want to appeal to some function and its properties, the Digital Library of Mathematical Functions (https://dlmf.nist.gov/) provides a peer-reviewed standard alternative. Is there someplace similar where I could point for properties of a Gumbel, Dirichlet-multinomial distribution, etc.

November 25, 2025 at 3:17 PM

Ben Bolker

@bbolker.bsky.social

Does everyone know about this one already? Meng 2018. “Statistical Paradises and Paradoxes in Big Data ...” Annals of Applied Statistics doi.org/10.1214/18-A...

Statisticians are increasingly posed with thought-provoking and even paradoxical questions, challenging our qualifications for entering the statistical paradises created by Big Data. By developing measures for data quality, this article suggests a framework to address such a question: “Which one should I trust more: a 1% survey with 60% response rate or a self-reported administrative dataset covering 80% of the population?” A 5-element Eulerformula-like identity shows that for any dataset of size n, probabilistic or not, the difference between the sample average Xn and the population average XN is the product of three terms: (1) a data quality measure, ρR,X, the correlation between Xj and the response/recording indicator Rj ; (2) a data quantity measure, √(N − n)/n, where N is the population size; and (3) a problem difficulty measure, σX, the standard deviation of X. This decomposition provides multiple insights: (I) Probabilistic sampling ensures high data quality by controlling ρR,X at the level of N −1/2; (II) When we lose this control, the impact of N is no longer canceled by ρR,X, leading to a Law of Large Populations (LLP), that is, our estimation error, relative to the benchmarking rate 1/√n, increases with √N; and (III) the “bigness” of such Big Data (for population inferences) should be measured by the relative size f = n/N , not the absolute size n; (IV) When combining data sources for population inferences, those relatively tiny but higher quality ones should be given far more weights than suggested by their sizes.

November 19, 2025 at 4:57 PM

Ben Bolker

@bbolker.bsky.social

(2/?) I do get it that using flat priors for fixed effects forestalls a lot of grief from users about "why are my answers different from when I run this in lme4" ... (Also, I understand the reason for data-dependent priors but feels icky ... cran.r-project.org/web/packages... )

Note on data-based priors

Because the scaling is based on the scales of the predictors (and possibly the outcome) these are technically data-dependent priors. However, since these priors are quite wide (and in most cases rather conservative), the amount of information used is weak and mainly takes into account the order of magnitude of the variables. This enables rstanarm to offer defaults that are reasonable for many models.

November 18, 2025 at 2:21 PM

Ben Bolker

@bbolker.bsky.social

Huh. Surprised you'd imagine it was 2x higher (sorry if your point was hyperbolic for entertainment value ...) CAD hasn't been > $1.10USD since 1950 ... (data from fx.sauder.ubc.ca/etc/CADpages..., © 2024 Prof Antweiler, University of British Columbia) gist.github.com/bbolker/0bf3...

Time series of CAD from 1950 to 2025. Value fluctuated between $0.90 and $1.05 USD from 1950-1975, $0.60 to $0.90 1975-2005, briefly exceeded par around 2010, now back down to about $0.75 USD

November 15, 2025 at 8:29 PM

Ben Bolker

@bbolker.bsky.social

reminded me of this guy en.wikipedia.org/wiki/Keron_T... (there were a lot of jokes about "he took the A train" ...)

Keron Thomas (c. 1975 – July 22, 2013)[2] was primarily known for posing as New York City Subway motorman "Regoberto Sabio" on May 8, 1993, and operating an A train in revenue service for over three hours, when he was sixteen years old.

November 13, 2025 at 2:05 AM

Ben Bolker

@bbolker.bsky.social

Scraped data from the plot ... gist.github.com/bbolker/d6a6... Scraping is imperfect because the plot is a fairly crappy JPG (hard to distinguish overlapping points). Dashed line is 156 particles per liter, nominal normal/superspreader cutoff (points fall on either side due to scraping error)

plot of scraped data from Edwards et al 2021. On a logarithmic y scale, regression slopes are very similar. Red points are superspreaders (nominally > 156), black are 'normal' (nominally < 156)

November 9, 2025 at 5:46 PM

Ben Bolker

@bbolker.bsky.social

Perhaps OP was referring to this (somewhat) famous quotation?

Singer & Pincus. 1998. “Irregular Arrays and Randomization.” PNAS. doi.org/10.1073/pnas....

‘What would you do,’ I had asked, ‘if drawing a Latin square at random for an experiment, you happened to draw a Knut-Vik (Knight’s move) square?’ Sir Ronald said he thought he would draw again and that, ideally, a theory explicitly excluding regular squares should be developed.” (L. J. Savage to R. A. Fisher, 1952, p. 88, ref. 21).

November 3, 2025 at 1:59 AM

Ben Bolker

@bbolker.bsky.social

what do you think about these options bsky.app/profile/bbol... ? (Also: etherpad.org Apparently also www.authorea.com (owned by Wiley), although amusingly this was one of the first public documents that came up ...)

the title block of an obviously AI-generated paper on Authorea (although maybe only AI-organized?): Certainly! Apologies for the previous omissions. Below is the complete LaTeX document that includes all the requested sections, arguments, code snippets, and proofs, organized logically into a single cohesive document. “‘latex Diagnosis and Treatment of Foot Fusarium Infection Confirmed by Next-Generation Sequencing Technology: A Case Report and Literature Review
dermatology

+7

Yulin Wang, Danyue He, Qi Zhao, Jie Hu, Ruyi Wang, Yiyang Hu, Xiangning Li, Jia Cai, Lili Tang, Xing Fan

November 1, 2025 at 11:55 PM

Ben Bolker

@bbolker.bsky.social

there's also this nice recent extension: Gelman, Hullman, & Kennedy. 2024. “Causal Quartets: Different Ways to Attain the Same Average Treatment Effect.” The American Statistician 78 (3): 267–72. doi.org/10.1080/0003... sites.stat.columbia.edu/gelman/resea...

Figure 2: Four graphs showing patterns of causal effects, each with average effect of 0.1, but varying in different ways as a function of a pre-treatment predictor: (e) linear interaction, (f ) no effect then steady increase, (g) plateau, (h) intermediate zone with large effects

October 28, 2025 at 1:35 AM

Ben Bolker

@bbolker.bsky.social

Depends where you live. Favism (glucose-6-phosphate dehydrogenase deficiency) is thought to be associated with malaria tolerance and/or resistance.

a map of the incidence of favism (G6PD deficiency), showing concentrations in sub-Saharan Africa and the middle east, some in India, SE asia, and Brazil

October 24, 2025 at 12:52 AM

Ben Bolker

@bbolker.bsky.social

Unless there are many columns I'm not sure this even counts as "big"/requires special techniques (recently had a student tell me she had cleaned a 166M-row data set directly in R ...) Reading *and* writing a 15M x 10 (numeric) row data set (2.8G on disk) takes 8 seconds on my laptop ...

$library(vroom) system.time({ dd <- rnorm(15e6*10) |> matrix(nrow = 15e6) |> as.data.frame() vroom_write(dd, "tmp.csv") dd2 <- vroom("tmp.csv") } ) ## user system elapsed ## 34.995 5.127 8.327$

October 15, 2025 at 9:32 PM

Ben Bolker

@bbolker.bsky.social

A web search found this from April 3, 1978 bnl.contentdm.oclc.org/digital/coll... I guess Peter Dalgaard has an encyclopedic knowledge of Peanuts strips?

Lucy (L) and Charlie Brown (R) are standing behind a wall. (Panel 1) CB: "I hate being a nothing! I refuse to go through the rest of my life as a zero!" (2) L: "What would you like to be, Charlie Brown, a five? Or how about a twenty-six? Or a par seventy-two?" (3) L: "I know what you could be, Charlie Brown ... a square root!" (4) L: "I think you'd make a great square root, Charlie Brown ..." CB: "I can't stand it!"

October 14, 2025 at 8:35 PM

Ben Bolker

@bbolker.bsky.social

www.numberworld.org/digits/Euler...

A screenshot of samples of digits of the Euler-Mascheroni constant (go to the URL for text-based version)

October 9, 2025 at 6:51 PM

Ben Bolker

@bbolker.bsky.social

Recently attended a workshop using allisonhorst.github.io/palmerpengui... for examples but it's hard to use for mixed models (3 species/3 islands isn't enough for MMs). With a little help from Claude → Tobias et al doi.org/10.1111/ele.... and extracted the penguins: github.com/bbolker/bbmi...

An image of beak width vs beak depth for a variety of penguin species.

September 3, 2025 at 12:28 AM

Ben Bolker

@bbolker.bsky.social

(2/2) its second answer started with "Based on my search, I cannot find credible medical experts who currently contend that the MMR vaccine should not be given routinely to children." The rest is below ...

Based on my search, I cannot find credible medical experts who currently contend that the MMR vaccine should not be given routinely to children. Here's what I found:

Lack of Current Expert Opposition: The medical literature and recent sources don't identify specific credentialed medical experts who oppose routine MMR vaccination based on scientific evidence. Studies show that 93% of surveyed physicians agree with current official vaccination recommendations and would apply them to their own children Measles 2025 | New England Journal of Medicine

Historical Context: The most prominent medical figure associated with MMR vaccine opposition was Andrew Wakefield, but as mentioned earlier, his 1998 study was retracted for fraud, and he lost his medical license. His work has been thoroughly debunked.

Current Political vs. Medical Opposition: While there are concerns about potential policy changes under Health Secretary Robert F. Kennedy Jr., who has historically been vaccine-skeptical medRxiv, this represents political rather than credentialed medical expert opinion. Notably, RFK Jr. recently endorsed the MMR vaccine, which "stoked fury among his supporters" The Evidence on Vaccines and Autism | Johns Hopkins | Bloomberg School of Public Health in the anti-vaccine community.

The Distinction: While there are individuals who call themselves doctors or health practitioners who oppose vaccines, finding credentialed medical experts (licensed physicians with relevant training) who oppose routine MMR vaccination based on scientific evidence is extremely difficult because the scientific consensus is so strong in favor of the vaccine.

The overwhelming medical and scientific consensus continues to support routine MMR vaccination for children, with major medical organizations, pediatricians, and public health experts maintaining this position based on extensive safety and efficacy data.

August 24, 2025 at 6:21 PM

Ben Bolker

@bbolker.bsky.social

yes, this terminology is from @jdushoff.bsky.social

Another things that jumps out is that maybe I should drop the early data. First off, there’s lots of reasons to ignore them anyways, since testing infrastructure was so different then, and second off, they make the range of the graph go really low, below minus nine “nels.”

So, what is a nel? You’ve probably guessed, it’s called that because it is one Natural Log unit, (one NL; one “nel”). A nel is a big number: 1 nel is over 2.5 times my reference rate, and 2 nels is over 7 times my reference rate.

Once I drop the very early data, I might see that a “nel”, like a “bel”, might be an awkwardly sized unit for the kinds of changes I’m most interested in, so we’ll look at “centinels” instead. This is the same idea as changing from a proportion to a percent.

August 21, 2025 at 7:43 PM

Ben Bolker

@bbolker.bsky.social

This is nice. I drew a related picture based on a slide presented by Nathalie Moon at the Statistical Society of Canada conference (tl;dr AI may be good for many things, but we definitely *don't* want students to use it as short-cut to get good marks without learning ...)

a flow chart showing things you can use LLMs for (learning, getting good marks, getting a job, getting into graduate school). Some of these flow downstream (learning stuff gets good marks; good marks get good jobs/grad school entrance; grad school gets good jobs), all of them (except LLMs) may also lead to happiness. There is a red X on the direct path from LLMs to good marks; this is what we want to forbid.

August 15, 2025 at 12:53 AM

Ben Bolker

@bbolker.bsky.social

super-random #rstats/VSCode question. VSCode > hosted Linux virtual machine > Windows remote desktop > Firefox tab > Ubuntu (don't ask ...). Standard extensions AFAICT (R 2.8.6, R Syntax 0.1.3). It is magically converting "<" to ">" on entry ... very frustrating. Anyone seen this?

VSCode installed-extensions tab showing Container Tools, Dev Containers, R, R Syntax

August 6, 2025 at 3:31 PM

Ben Bolker

@bbolker.bsky.social

FWIW Ontario appears to have changed its guidance along these lines in 2008: www.publichealthontario.ca/-/media/docu...

flow chart for assessment of exposure to bats. post-exposure management is only recommended if direct exposure is known to have occurred, or if the bat was in the same room as a person *and* there was evidence of direct contact (i.e. scratch, crying/upset child) with a person who may not be able to give a reliable history (child or cognitively impaired adult)

August 3, 2025 at 9:37 PM

Ben Bolker

@bbolker.bsky.social

www.jstor.org/stable/2332181

August 3, 2025 at 2:31 AM

Ben Bolker

@bbolker.bsky.social

Seems like you can add any package(s) you want in the `Imports:` directive of the module/package DESCRIPTION ... ? e.g. dev.jamovi.org/tuts0106-add...

Adding ggplot2

We’re going to use ggplot2 for plotting, so make sure you have that installed. To use ggplot2 in this package/module, we need to add some entries into the DESCRIPTION and NAMESPACE files. We add ggplot2 to the imports line in the DESCRIPTION, so it reads:

Imports: jmvcore, R6, ggplot2

and we’ll add the following line into NAMESPACE:

import(ggplot2)

These entries are standard for using R code from other packages in a package. More information is available in Writing R Extensions.

Now we have ggplot2 ready, we can proceed with using it in our analysis.

July 26, 2025 at 7:46 PM

Ben Bolker

@bbolker.bsky.social

2/2 ... e.g. complaints about www.evolution.reading.ac.uk/BayesTraitsV... , the canonical tool, which does some technically brilliant but (IMO) philosophically questionable stuff ...

BayesTraits, the leading software platform for analyzing the evolution of discrete traits (Pagel and Meade 2006), uses a highly sophisticated algorithm (reversible-jump Markov chain Monte Carlo) to compute BFs, so that researchers can draw conclusions like “a model where the rate of accessory gland gain differs between male-care vs male-care-absent lineages is better supported than one where they are identical (BF ratio >2)”. By convention, a model comparison with a BF factor greater than 2-3 is assumed to be “substantial” evidence in favour of the better (more probable) model.

While the computational machinery required to compute BFs in an evolutionary context is technically impressive, the simpler models considered represent biologically impossible scenarios, analogous to the null models used in frequentist testing; no two evolutionary rates are ever truly identical. Rather than consider the relative strength of the hypotheses as “equal” vs “not equal”, researchers will often gain more insight by estimating the relative rates of transitions. In a Bayesian context, we can use the posterior distribution of the rate difference (the contrast in hazard rates as defined in our methods section above) to find a 95% credible interval for the ratio of rates.

July 26, 2025 at 7:28 PM

Ben Bolker

@bbolker.bsky.social

This is great. (Adding a picture, just for eye candy.)

A plot showing forest succession in the model (crown area over time): Fast peaks early, short-lived breeders peak and decline slowly (with wide confidence bounds), long-lived pioneers and slow strategies grow slowly (half-maximum around 250 years). Caption: Patch- level post-gap crown area trajectories in
the four-group niche models. Lines correspond to a single run.
Highlighted areas around the lines show one standard deviation
around the mean of 40 focal patches, each from an independent
metacommunity simulation. Standard deviation areas are shown
only for positive values.

July 22, 2025 at 3:20 PM

Ben Bolker

@bbolker.bsky.social

What if you express it in Kelvin? (or in Rankine <https://en.wikipedia.org/wiki/Rankine_scale>, although that won't actually get you more numbers, just bigger ones)