Category Archives: numerical algorithms

Stream flow and P-splines: Using built-in estimates for smoothing

Posted on 28 January 2019 by

Mother Brook in Dedham Massachusetts was the first man-made canal in the United States. Dug in 1639, it connects the Charles River at Dedham, to the Neponset River in the Hyde Park section of Boston. It was originally an important … Continue reading →

Posted in American Statistical Association, citizen data, citizen science, Clausius-Clapeyron equation, Commonwealth of Massachusetts, cross-validation, data science, dependent data, descriptive statistics, dynamic linear models, empirical likelihood, environment, flooding, floods, Grant Foster, hydrology, likelihood-free, meteorological models, model-free forecasting, non-mechanistic modeling, non-parametric, non-parametric model, non-parametric statistics, numerical algorithms, precipitation, quantitative ecology, statistical dependence, statistical series, stream flow, Tamino, the bootstrap, time series, water vapor | 2 Comments

Series, symmetrized Normalized Compressed Divergences and their logit transforms

Posted on 3 January 2019 by

(Major update on 11th January 2019. Minor update on 16th January 2019.) On comparing things The idea of a calculating a distance between series for various purposes has received scholarly attention for quite some time. The most common application is … Continue reading →

Posted in Akaike Information Criterion, bridge to somewhere, computation, content-free inference, data science, descriptive statistics, divergence measures, engineering, George Sughihara, information theoretic statistics, likelihood-free, machine learning, mathematics, model comparison, model-free forecasting, multivariate statistics, non-mechanistic modeling, non-parametric statistics, numerical algorithms, statistics, theoretical physics, thermodynamics, time series | 4 Comments

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

Posted on 20 November 2018 by

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

Sampling: Rejection, Reservoir, and Slice

Posted on 29 September 2018 by

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

Fast means, fast moments (originally devised 1984)

Posted on 6 September 2018 by

(Updated 4th December 2018.) There are many devices available for making numerical calculations fast. Modern datasets and computational problems apply stylized architectures, and use approaches to problems including special algorithms for just calculating dominant eigenvectors or using non-classical statistical mechanisms … Continue reading →

Posted in image processing, mathematics, numerical algorithms, numerical software, numerics | 3 Comments

When linear systems can’t be solved by linear means

Posted on 13 June 2018 by

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

forecast for 27th March 2018

Posted on 21 March 2018 by

Today is the 21st of March, 2018. We are supposed to get our fourth nor’easter tomorrow this late Winter, and the third nor’easter in nearly as many weeks. ECMWF hosted, in this incarnation, at the Meteocentre UQAM in Montreal created … Continue reading →

Posted in American Association for the Advancement of Science, American Meteorological Association, American Statistical Association, AMETSOC, atmosphere, climate, climate change, climate disruption, climate education, climate models, coastal communities, ensemble methods, ensemble models, fluid dynamics, forecasting, global warming, Hyper Anthropocene, Mathematics and Climate Research Network, meteorological models, meteorology, numerical algorithms, physics, science, science education, spaghetti plots, tragedy of the horizon, water vapor | Leave a comment

on nonlinear dynamics of hordes of people

Posted on 6 February 2018 by

I spent a bit of last week at a symposium honoring the work of Charney and Lorenz in fluid dynamics. I am no serious student of fluid dynamics. I have a friend, Klaus, an engineer, who is, and makes a … Continue reading →

Posted in Anthropocene, bifurcations, biology, Carl Safina, causation, complex systems, dynamic generalized linear models, dynamic linear models, dynamical systems, ecological services, ecology, Emily Shuckburgh, finance, Floris Takens, fluid dynamics, fluid eddies, games of chance, Hyper Anthropocene, investments, Lenny Smith, Lorenz, nonlinear, numerical algorithms, numerical analysis, politics, population biology, population dynamics, prediction markets, Principles of Planetary Climate, public transport, Ray Pierrehumbert, risk, sampling networks, sustainability, Timothy Lenton, Yale University Statistics Department, zero carbon, ``The tide is risin'/And so are we'' | 1 Comment

What are the odds of net zero?

Posted on 1 January 2018 by

What’s the Question? A question was posed by a colleague a couple of months ago: What are the odds of a stock closing at the same price it opened? I found the question interesting, because, at first, it appeared to … Continue reading →

Posted in dependent data, evidence, financial series, investing, investments, model-free forecasting, numerical algorithms, state-space models, statistics, time series, trading | Leave a comment

A new feature: Technical publications of the week

Posted on 18 February 2017 by

I’m beginning a new style of column, called technical publications of the week. While I can’t promise these will be weekly, I will, from time to time, highlight technical publications I’ve recently read which I consider to be noteworthy. I … Continue reading →

Posted in Anthropocene, big data, climate change, climate disruption, data science, data streams, earthquakes, geophysics, global warming, Hyper Anthropocene, Locality Sensitive Hashing, LSH, MinHash, numerical algorithms, numerical analysis, random projections, seismology, subspace projection methods, SVD, the right to be and act stupid, the tragedy of our present civilization, the value of financial assets | 1 Comment