Distributed Solar: The Democratizaton of Energy
Category Archives: numerical algorithms
Calculating Derivatives from Random Forests
(Edits to repair smudges, 2020-06-28, about 0945 EDT. Closing comment, 2020-06-30, 1450 EDT.) There are lots of ways of learning about mathematical constructs, even about actual machines. One way is to push them into a place of improbable application, asking … Continue reading
Posted in bridge to somewhere, Calculus, dependent data, dynamic generalized linear models, dynamical systems, ensemble methods, ensemble models, filtering, forecasting, hierarchical clustering, linear regression, model-free forecasting, Monte Carlo Statistical Methods, non-mechanistic modeling, non-parametric model, non-parametric statistics, numerical algorithms, prediction, R statistical programming language, random forests, regression, sampling, splines, statistical learning, statistical series, statistics, time derivatives, time series
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JIGSAW-GEO v1.0
See: D. Engwirda, 2017: JIGSAW-GEO (1.0): Locally orthogonal staggered unstructured grid generation for general circulation modelling on the sphere, Geosci. Model Dev., 10, 2117-2140, doi:10.5194/gmd-10-2117-2017 and a general description at NASA. The figure below is copied from there.
Stream flow and P-splines: Using built-in estimates for smoothing
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
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Series, symmetrized Normalized Compressed Divergences and their logit transforms
(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
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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
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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
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Fast means, fast moments (originally devised 1984)
(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
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
forecast for 27th March 2018
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
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on nonlinear dynamics of hordes of people
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''
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What are the odds of net zero?
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
A new feature: Technical publications of the week
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
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