Category Archives: Calculus

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 | 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

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

Merry Newtonmas tomorrow! On finding the area of the Batman Shape using Monte Carlo integration

It’s Newtonmas 2017 tomorrow! What better way to celebrate than talk about integration! The Batman Shape (sometimes called the Batman Curve, somewhat erroneously, I think) looks like this: You can find details about it at Wolfram MathWorld, including its area … Continue reading

Posted in Bayes, Calculus, Markov Chain Monte Carlo | Tagged , , , , | 1 Comment