The Analytic Garden

Every glass thermometer has subtle variations in the size and shape of the bulb at the bottom and the capillary tube inside, as well as variations in the width of gradations on the side. The compounded effect of these uncertainties is that each thermometer reads temperature slightly differently.  - Sam Kean I loved dinosaurs, I loved space, and I thought maybe I'd be the first paleo-astronaut.  -Bill Maris A while ago, I wrote about using Gibbs sampling for spline regression.  The motivation for that post was this paper  BAYSPLINE: A New Calibration for the Alkenone Paleothermometer by Jessica E. Tierney and Martin P. Tingley. (It's behind a paywall. I'll spare you my rant about taxpayer supported research being a profit center for private companies.) There is accompanying software to the paper in Python and MATLAB . In this post, I'll use the the R software presented previously to reproduce the results from the Tierney and Tingley paper. A few marine s...

In a previous post , I looked at Gaussian process regression. Gaussian processes are powerful.They give you useful error bounds. However, often the results look like curve fitting similar to fitting with splines and I suspect that people have a difficult time interpreting the covariance kernel. Often what people want is a simple interpretation of the data. This is relatively easy if it looks like there is a linear relationship among the  data or the data can be transformed to be somewhat approximately linear. Just crank up your favorite linear or  generalized linear modeling  (GLM) software. The software will fit the model to the data and give you the appropriate coefficients. Since the models are simple, interpretation is easy (well, maybe relatively easy). If the relationships among the data are non-linear, there's software to fit non-linear models, assuming you can come up with an appropriate set of functions to fit the data. Suppose you don't have strong feeling ...