Math

A parent category for all things related to mathematics and any of its myriad subcategories (probability, statistics, real analysis, combinatorics, actuarial science, etc.).

A Practical Example of Calculating Padé Approximant Coefficients Using R

Published by on June 4, 2015 | 1 Response
A Practical Example of Calculating Padé Approximant Coefficients Using R

Introduction I recently had the opportunity to use Padé approximants. There is a lot of good information available on line on the theory and applications of using Padé approximants, but I had trouble finding a good example explaining just how to calculate the co-efficients. Basic Background Hearken back to undergraduate calculus for a moment. For Read the full article…

New package on CRAN: lamW

Published by on May 26, 2015

Recently, in various research projects, the Lambert-W function arose a number of times. Somewhat frustratingly, there is no built-in function in R to calculate it. The only options were those in the gsl and LambertW packages, the latter merely importing the former. Importing the entire GNU Scientific Library (GSL) can be a bit of a Read the full article…

Gelman on Meehl

Published by on March 23, 2015

Today, Andrew Gelman posted about a paper written over thirty years ago by Paul Meehl. Even though I believe actuaries are less exposed than social science statisticians to some of the pitfalls of what Gelman calls the “garden of forking paths,” we are still exposed, and I’d recommend reading Gelman’s posts on the issue. I Read the full article…

I’ve updated the directions as to how to build 64-bit R for Windows linking to OpenBLAS, as the entire R build process for Windows will change for R version 3.2 and subsequent. I’ve turned it into a static page, instead of a post, in case the build process changes again. While the title has 3.2 in it, the URL doesn’t, so it should be future-proof. Then again, that’s number 47 on the list of 996 famous last words! As always, I’m interested in hearing if anyone successfully builds it and how much of a difference it makes.

Flavors of risk: process, parameter, model, and unknown

Published by on September 15, 2014 | 1 Response

I’ve recently been asked a number of times as to the differences between various sources of risks one is exposed to when creating a model, in specific, for the difference between parameter and model risk. I’ve used the following allegory a number of times to explain how I see the differences between process, parameter, model, Read the full article…

Big Data, Correlations, and the Hales-Jewett Theorem

Published by on May 21, 2014 | 3 Responses

“Big Data” has become one of the most heralded tools, or at least buzzwords, of this decade. The use of “big data” is trumpeted by many studies in almost all disciplines, and, too an extent, understandably so. Hand-in-hand with the geometric progression of computing power has been the development of algorithms that can parse huge Read the full article…

An OpenBLAS-based Rblas for Windows 64

Published by on October 22, 2013 | 6 Responses

One of the more important pieces of software that powers R is its BLAS, which stands for Basic Linear Algebra Subprograms. This is the suite of programs which, as its name implies, performs basic linear algebra routines such as vector copying, scaling and dot products; linear combinations; and matrix multiplication. It is the engine on Read the full article…

Correcting a pseudo-correlation matrix to be positive semidefinite

Published by on August 19, 2013 | 2 Responses

In a recent LinkedIn conversation, the topic of correlation between multiple financial indices was raised. While the actual details are not relevant, the discussion reminded me of one of the concerns I have whenever multivariate correlation is used—how to populate the correlation matrix. First, some background. Unfortunately, most financial random variables are not normally distributed—they Read the full article…