Category Archives: maths

New Meetup: Massachusetts Mosses and Lichens

I have started a new Meetup group: Massachusetts Mosses and Lichens. I am inviting anyone with an interest in mosses and lichens to join in, particularly if you live in the “greater Massachusetts area”. Because of pandemic, there’ll be no … Continue reading

Posted in ABLS, American Bryological and Lichenological Society, American Statistical Association, biology, Botany, Brent Mishler, bryology, bryophytes, citizen data, citizen science, ecology, field biology, field research, field science, Hale Reservation, Janice Glime, Jerry Jenkins, lichenology, lichens, longitudinal survey of mosses, macrophotography, maths, mesh models, mosses, Nancy G Slack, National Phenology Network, population biology, population dynamics, Ralph Pope, science, spatial statistics, statistical ecology, Sue Williams, the right to know, Westwood | Leave a comment

We are all Mathematicians

Bobby Seagull. Great.

Posted in mathematics, mathematics education, maths | Leave a comment

“The truly common core”

Repost of “The truly common core“, from Ben Orlin‘s Math with Bad Drawings blog. https://mathwithbaddrawings.com/2020/02/19/uncommon-core-standards/

Posted in education, mathematics, mathematics education, maths | Leave a comment

Cumulants and the Cornish-Fisher Expansion

“Consider the following.” (Bill Nye the Science Guy) There are random variables drawn from the same kind of probability distribution, but with different parameters for each. In this example, I’ll consider random variables , that is, each drawn from a … Continue reading

Posted in Calculus, closed-form expressions, Cornish-Fisher expansion, cumulants, descriptive statistics, mathematics, maths, multivariate statistics, statistical models, statistics, theoretical statistics | Leave a comment

Repeating Bullshit

Yeah, how much was it? And was it different? I mean, not based on how Curry or Tisdale feel, but by the numbers.

Posted in American Statistical Association, anomaly detection, changepoint detection, climate change, Grant Foster, Mathematics and Climate Research Network, maths, science, statistics, Tamino, time series, unreason | Leave a comment

The Johnson-Lindenstrauss Lemma, and the paradoxical power of random linear operators. Part 1.

Updated, 2018-12-04 I’ll be discussing the ramifications of: William B. Johnson and Joram Lindenstrauss, “Extensions of Lipschitz mappings into a Hilbert space, Contemporary Mathematics, 26:189–206, 1984. for several posts here. Some introduction and links to proofs and explications will be … Continue reading

Posted in clustering, data science, dimension reduction, information theoretic statistics, Johnson-Lindenstrauss Lemma, k-NN, Locality Sensitive Hashing, mathematics, maths, multivariate statistics, non-parametric model, numerical algorithms, numerical linear algebra, point pattern analysis, random projections, recommender systems, science, stochastic algorithms, stochastics, subspace projection methods | 1 Comment

Numbers, feelings, and imagination

“But numbers don’t make noises. They don’t have colours. You can’t taste them or touch them. They don’t smell of anything. They don’t have feelings. They don’t make you feel. And they make for pretty boring stories.” That’s from here, … Continue reading

Posted in mathematics, maths, numbers, numerics, oceanography | Leave a comment

Sampling: Rejection, Reservoir, and Slice

An article by Suilou Huang for catatrophe modeler AIR-WorldWide of Boston about rejection sampling in CAT modeling got me thinking about pulling together some notes about sampling algorithms of various kinds. There are, of course, books written about this subject, … Continue reading

Posted in accept-reject methods, American Statistical Association, Bayesian computational methods, catastrophe modeling, data science, diffusion processes, empirical likelihood, Gibbs Sampling, insurance, Markov Chain Monte Carlo, mathematics, Mathematics and Climate Research Network, maths, Monte Carlo Statistical Methods, multivariate statistics, numerical algorithms, numerical analysis, numerical software, numerics, percolation theory, Python 3 programming language, R statistical programming language, Radford Neal, sampling, slice sampling, spatial statistics, statistics, stochastic algorithms, stochastic search | Leave a comment

When linear systems can’t be solved by linear means

Linear systems of equations and their solution form the cornerstone of much Engineering and Science. Linear algebra is a paragon of Mathematics in the sense that its theory is what mathematicians try to emulate when they develop theory for many … Continue reading

Posted in Calculus, dynamic linear models, mathematics, maths, nloptr, numerical algorithms, numerical analysis, numerical linear algebra, numerics, SVD | Leave a comment

The Rule of 135

From SingingBanana.

Posted in Conway's Game of Life, dynamical systems, finite-state machines, mathematical publishing, mathematics, mathematics education, maths, Patterson's Worm, random walks, state-space models, statistical dependence, statistics | Leave a comment

Is the answer to the democratization of Science doing more Citizen Science?

I have been following, with keen interest, the post and comment thread pertaining to “Democratising science” at the blog I monitor daily, … and Then There’s Physics. I think the core subject being discussed is a little different from my … Continue reading

Posted in American Association for the Advancement of Science, American Meteorological Association, American Statistical Association, AMETSOC, astronomy, astrophysics, biology, citizen data, citizen science, citizenship, data science, ecology, education, environment, evidence, life purpose, local self reliance, marine biology, mathematics, mathematics education, maths, moral leadership, new forms of scientific peer review, open source scientific software, science, science education, statistics, the green century, the right to know | Leave a comment

Chesterton’s fence, ecological sensitivity, and the disruption of ecological services

Hat tip to Matt Levine for introducing me to the term Chesteron’s fence: Chesterton’s fence is the principle that reforms should not be made until the reasoning behind the existing state of affairs is understood. … In the matter of … Continue reading

Posted in dynamic generalized linear models, dynamical systems, ecological services, ecology, Ecology Action, mathematics, mathematics education, maths, XKCD | Leave a comment

Cathy O’Neil’s WEAPONS OF MATH DESTRUCTION: A Review

(Revised and updated Monday, 24th October 2016.) Weapons of Math Destruction, Cathy O’Neil, published by Crown Random House, 2016. This is a thoughtful and very approachable introduction and review to the societal and personal consequences of data mining, data science, … Continue reading

Posted in citizen data, citizen science, citizenship, civilization, compassion, complex systems, criminal justice, Daniel Kahneman, data science, deep recurrent neural networks, destructive economic development, economics, education, engineering, ethics, Google, ignorance, Joseph Schumpeter, life purpose, machine learning, Mathbabe, mathematics, mathematics education, maths, model comparison, model-free forecasting, numerical analysis, numerical software, open data, optimization, organizational failures, planning, politics, prediction, prediction markets, privacy, rationality, reason, reasonableness, risk, silly tech devices, smart data, sociology, Techno Utopias, testing, the value of financial assets, transparency | Leave a comment

Polls, Political Forecasting, and the Plight of Five Thirty Eight

On 17th October 2016 AT 7:30 p.m., Nate Silver of FiveThirtyEight.com wrote about how, as former Secretary of State Hillary Clinton’s polling numbers got better, it was more difficult for FiveThirtyEight‘s models to justify increasing her probability of winning, although … Continue reading

Posted in abstraction, American Statistical Association, anemic data, citizen science, citizenship, civilization, economics, education, forecasting, information theoretic statistics, mathematics, maths, politics, prediction markets, sociology, the right to know, theoretical physics, thermodynamics | Leave a comment

NextGen VOICES: `On data’, `On setbacks’, and `On discovery’

Science Magazine has a periodic column called Science in brief and occasionally that column features a set of what they call “NextGen VOICES”, meaning young scientists. They gather the survey using Twitter (of course) via the hashtag #NextGenSci. For the … Continue reading

Posted in American Association for the Advancement of Science, big data, data science, evidence, Mathbabe, maths, maxims, science, Science magazine, smart data, statistics | Leave a comment

Repaired R code for Markov spatial simulation of hurricane tracks from historical trajectories

(Slight update, 28th June 2020.) I’m currently studying random walk and diffusion processes and their connections with random fields. I’m interested in this because at the core of dynamic linear models, Kalman filters, and state-space methods there is a random … Continue reading

Posted in American Meteorological Association, American Statistical Association, AMETSOC, Arthur Charpentier, atmosphere, diffusion, diffusion processes, dynamic linear models, dynamical systems, environment, geophysics, hurricanes, Kalman filter, Kerry Emanuel, Lévy flights, Lorenz, Markov chain random fields, mathematics, mathematics education, maths, MCMC, mesh models, meteorological models, meteorology, model-free forecasting, Monte Carlo Statistical Methods, numerical analysis, numerical software, oceanography, open data, open source scientific software, physics, random walk processes, random walks, science, spatial statistics, state-space models, statistical dependence, statistics, stochastic algorithms, stochastics, time series | 1 Comment

“Holy crap – an actual book!”

You’ll find links to Cathy O’Neil’s important book in the Blogroll here, as well as a link to reviews of it. I have not read it yet. While I have pre-ordered it, it’s not available. I have read the reviews, … Continue reading

Posted in American Association for the Advancement of Science, Buckminster Fuller, business, citizen science, citizenship, civilization, complex systems, confirmation bias, data science, data streams, deep recurrent neural networks, denial, economics, education, engineering, ethics, evidence, Internet, investing, life purpose, machine learning, mathematical publishing, mathematics, mathematics education, maths, moral leadership, multivariate statistics, numerical software, numerics, obfuscating data, organizational failures, politics, population biology, prediction, prediction markets, privacy, quantitative biology, quantitative ecology, rationality, reason, reasonableness, rhetoric, risk, Schnabel census, smart data, sociology, statistical dependence, statistics, the right to be and act stupid, the right to know, the value of financial assets, transparency, UU Humanists | Leave a comment

David Spiegelhalter on `how to spot a dodgy statistic’

In this political season, it’s useful to brush up on rhetorical skills, particularly ones involving numbers and statistics, or what John Allen Paulos called numeracy. Professor David Spiegelhalter has written a guide to some of these tricks. Read the whole … Continue reading

Posted in abstraction, anemic data, Bayes, Bayesian, chance, citizenship, civilization, corruption, Daniel Kahneman, disingenuity, Donald Trump, education, games of chance, ignorance, maths, moral leadership, obfuscating data, open data, perceptions, politics, rationality, reason, reasonableness, rhetoric, risk, sampling, science, sociology, statistics, the right to know | Leave a comment

France, and Mathematics

Cédric Villani, does Mathematics. “Problems worthy of attack, prove their worth by hitting back.” — Piet Hein

Posted in abstraction, Google, mathematics, mathematics education, maths, networks, Pagerank, percolation theory, point pattern analysis, probability, rationality, reasonableness, stochastic algorithms | Leave a comment

On Smart Data

One of the things I find surprising, if not astonishing, is that in the rush to embrace Big Data, a lot of learning and statistical technique has been left apparently discarded along the way. I’m hardly the first to point … Continue reading

Posted in Akaike Information Criterion, Bayes, Bayesian, Bayesian inversion, big data, bigmemory package for R, changepoint detection, data science, data streams, dlm package, dynamic generalized linear models, dynamic linear models, dynamical systems, Generalize Additive Models, generalized linear models, information theoretic statistics, Kalman filter, linear algebra, logistic regression, machine learning, Markov Chain Monte Carlo, mathematics, mathematics education, maths, maximum likelihood, MCMC, Monte Carlo Statistical Methods, multivariate statistics, numerical analysis, numerical software, numerics, quantitative biology, quantitative ecology, rationality, reasonableness, sampling, smart data, state-space models, statistical dependence, statistics, the right to know, time series | Leave a comment

“Catching long tail distribution” (Ted Dunning)

One of the best presentations on what can happen if someone takes a naive approach to network data. It also highlights what is, to my mind, the greatly underappreciated t-distribution, which is typically only used in connection with frequentist Student … Continue reading

Posted in Cauchy distribution, complex systems, data science, Lévy flights, leptokurtic, mathematics, maths, networks, physics, population biology, population dynamics, regime shifts, sampling, statistics, Student t distribution, time series | Leave a comment

Six cases of models

The previous post included an attempt to explain land surface temperatures as estimated by the BEST project using a dynamic linear model including regressions on both quarterly CO2 concentrations and ocean heat content. The idea was to check the explanatory … Continue reading

Posted in AMETSOC, anemic data, Anthropocene, astrophysics, Bayesian, Berkeley Earth Surface Temperature project, BEST, carbon dioxide, climate, climate change, climate data, climate disruption, climate models, dlm package, dynamic linear models, dynamical systems, environment, fossil fuels, geophysics, Giovanni Petris, global warming, greenhouse gases, Hyper Anthropocene, information theoretic statistics, maths, maximum likelihood, meteorology, model comparison, numerical software, Patrizia Campagnoli, Rauch-Tung-Striebel, Sonia Petrone, state-space models, stochastic algorithms, stochastic search, SVD, time series | 1 Comment

On Munshi mush

(Slightly updated on 2016-06-11.) Professor Emeritus Jamal Munshi of Sonoma State University has papers recently cited in science denier circles as evidence that the conventional associations between mean global surface temperature and cumulative carbon emissions are, well, bunk, due to … Continue reading

Posted in Bayes, Bayesian, Berkeley Earth Surface Temperature project, BEST, carbon dioxide, cat1, climate, climate change, climate data, climate education, climate models, convergent cross-mapping, dynamic linear models, ecology, ENSO, environment, Ethan Deyle, evidence, geophysics, George Sughihara, global warming, greenhouse gases, information theoretic statistics, Kalman filter, mathematics, maths, meteorology, model comparison, NOAA, oceanography, prediction, state-space models, statistics, Takens embedding theorem, Techno Utopias, the right to know, theoretical physics, time series, zero carbon | 1 Comment

Climate Denial Fails Pepsi Challenge

Posted in American Association for the Advancement of Science, American Statistical Association, card draws, card games, chance, climate, climate change, climate data, climate education, confirmation bias, data science, denial, disingenuity, education, false advertising, fear uncertainty and doubt, fossil fuels, games of chance, geophysics, global warming, ignorance, mathematics, mathematics education, maths, obfuscating data, rationality, reasonableness, risk, science, science education, sociology, the right to know | Leave a comment

Cory Lesmeister’s treatment of Simson’s Paradox (at “Fear and Loathing in Data Science”)

(Updated 2016-05-08, to provide reference for plateaus of ML functions in vicinity of MLE.) Simpson’s Paradox is one of those phenomena of data which really give Statistics a substance and a role, beyond the roles it inherits from, say, theoretical … Continue reading

Posted in Akaike Information Criterion, approximate Bayesian computation, Bayes, Bayesian, evidence, Frequentist, games of chance, information theoretic statistics, Kalman filter, likelihood-free, mathematics, maths, maximum likelihood, Monte Carlo Statistical Methods, probabilistic programming, rationality, Rauch-Tung-Striebel, Simpson's Paradox, state-space models, statistical dependence, statistics, stochastics | Leave a comment

“Lucky d20” (by Tamino, with my reblogging comments)

Careful consideration to really basic things like this is, for me, incredibly refreshing, and helps with the self-discipline needed to deal with real-world problems, those often being messy and having distracting entanglements. A couple of thoughts: I think the mechanism … Continue reading

Posted in Bayes, Bayesian, card decks, card draws, card games, chance, D&D, Dungeons and Dragons, games of chance, mathematics, maths, Monte Carlo Statistical Methods, probability, statistical dependence, statistics, stochastic algorithms, stochastics, Wizards of the Coast | Leave a comment

Gavin Simpson updates his temperature analysis

See the very interesting discussion at his blog, From the bottom of the heap. It would be nice to see some information theoretic measures on these results, though.

Posted in AMETSOC, Anthropocene, astrophysics, Berkeley Earth Surface Temperature project, carbon dioxide, changepoint detection, climate, climate change, climate data, climate disruption, climate models, ecology, environment, evidence, Gavin Simpson, Generalize Additive Models, geophysics, global warming, HadCRUT4, hiatus, Hyper Anthropocene, information theoretic statistics, Kalman filter, maths, meteorology, numerical analysis, R, rationality, reasonableness, splines, time series | Leave a comment

Of my favorite things …

(Clarifying language added 4 Apr 2016, 12:26 EDT.) I just watched an episode from the last season of Star Trek: The Next Generation entitled “Force of Nature.” As anyone who pays the least attention to this blog knows, opposing human … Continue reading

Posted in Anthropocene, bridge to somewhere, bucket list, Buckminster Fuller, Carl Sagan, climate, climate change, climate disruption, climate education, compassion, data science, Earle Wilson, ecology, Ecology Action, environment, evolution, geophysics, George Sughihara, global warming, Hyper Anthropocene, life purpose, mathematics, mathematics education, maths, numerical analysis, optimization, philosophy, physical materialism, physics, population biology, population dynamics, proud dad, quantitative biology, quantitative ecology, rationality, reasonableness, science, sociology, statistics, stochastic algorithms | 5 Comments

HadCRUT4 and GISTEMP series filtered and estimated with simple RTS model

Happy Vernal Equinox! This post has been updated today with some of the equations which correspond to the models. An assessment of whether or not there was a meaningful slowdown or “hiatus” in global warming, was recently discussed by Tamino … Continue reading

Posted in AMETSOC, anemic data, Bayesian, boosting, bridge to somewhere, cat1, changepoint detection, climate, climate change, climate data, climate disruption, climate models, complex systems, computation, data science, dynamical systems, geophysics, George Sughihara, global warming, hiatus, information theoretic statistics, machine learning, maths, meteorology, MIchael Mann, multivariate statistics, physics, prediction, Principles of Planetary Climate, rationality, reasonableness, regime shifts, sea level rise, time series | 5 Comments

patents disincentivize progress

Very interesting.

Posted in business, data centers, destructive economic development, economics, high frequency trading, humanism, Hyper Anthropocene, mathematics, maths, rationality, reasonableness, risk, selfishness, stochastics | 1 Comment