caracas: Computer Algebra in R via SymPy

It is with great pleasure that we can announce the release of caracas version 1.0.1 to CRAN (https://cran.r-project.org/package=caracas). The package enables user to make computer algebra from R using the Python library SymPy. You can now install the caracas package as follows: install.packages("caracas") And then load it by: library(caracas) The source code and the development version is available at https://github.com/r-cas/caracas/. Online documentation (of the development version) can be found at https://r-cas.

Shiny apps with math exercises

It is often very useful to practise mathematics by automatically generated exercises. One approach is multiple choice quizzes (MCQ), but it turns out to be fairly difficult to generate authentic wrong answers. Instead, we want the user to input the answer and be able to parse the answer and check whether this is the correct answer. There are many fun challenges in this, e.g. to verify that 2 is equal to 1 + 1 (as text strings the two are different, but mathematically they are equal, at least to a convenient approximation in this case).

Ryacas version 1.0.0 released!

It is with great pleasure that I can announce that Ryacas version 1.0.0 is now released to CRAN (https://cran.r-project.org/package=Ryacas). I wish to thank all co-authors: Rob Goedman, Gabor Grothendieck, Søren Højsgaard, Grzegorz Mazur, Ayal Pinkus. It means that you can install the package by (possible after binaries have been built): install.packages("Ryacas") Followed by: library(Ryacas) (The source code is available at https://github.com/mikldk/ryacas/.) Now you have the yacas computer algebra system fully available!

Approximating small probabilities using importance sampling

Update Oct 14, 2019: Michael Höhle caught a mistake and notified me on Twitter. Thanks! The problem is that I used \(\text{Unif}(-10, 10)\) as importance distribution; this does not have infinite support as the target has. This is required, see e.g. Art B. Owen (2013), “Monte Carlo theory, methods and examples”. I have now updated the post to use a normal distribution instead. Box plots are often used. They are not always the best visualisation (e.

How much pizza and how much frozen yogurt? ...with Gröbner bases

In a recent blog post I tried to get yacas to solve a system of polynomial equations. Unfortunately it could not do that, so I solved it numerically instead. Now it is possible – together with many other systems of polynomial equations thanks to fixing a small error in yacas. It has now been fixed, also in Ryacas (development version), so hurry up and update Ryacas to the latest version 0.

Prediction intervals for Generalized Additive Models (GAMs)

Update on Aug 9, 2022: In the code chunk below, sd = summary(fit_gam)$scale) was changed to sd = sqrt(summary(fit_gam)$scale)): y_sim <- matrix(rnorm(n = prod(dim(exp_val_sim)), mean = exp_val_sim, sd = summary(fit_gam)$scale), nrow = nrow(exp_val_sim), ncol = ncol(exp_val_sim)) Thanks to David Kaplan (IRD, France) Finding prediction intervals (for future observations) is something different than finding confidence intervals (for unknown population parameters). Here, I demonstrate one approach to doing so.

Correlation is not transitive, in general at least: A simulation approach

Let \(\rho_{XY}\) be the correlation between the stochastic variables \(X\) and \(Y\) and similarly for \(\rho_{XZ}\) and \(\rho_{YZ}\). If we know two of these, can we say anything about the third? In a recent blog post I dealt with the problem mathematically and I used the concept of a partial correlation coefficient. Here I will take a simulation approach. First z is simulated. Then x and y is simulated based on z in a regression context with a slope between \(-1\) and \(1\).

Automatic 'testthat' test skeletons with new R package 'roxytest' extending 'roxygen2'

It is important to test software. One approach is unit-testing, and for R packages this can e.g. be done using testthat. It is also important to document software. For R packages roxygen2 is really helpful: It enables you to write documentation in the code file in the R/ folder where the function is implemented. And then roxygen2 takes care of handling the Rd files in the man/ folder. I have made a new R package that combines these approaches: roxytest.

Correlation is not transitive, in general at least

Update Aug 10, 2019: I wrote a new blog post about the same as below but using a simulation approach. Update Aug 27, 2019: Minor change in how equations are solved (from version Let \(\rho_{XY}\) be the correlation between the stochastic variables \(X\) and \(Y\) and similarly for \(\rho_{XZ}\) and \(\rho_{YZ}\). If we know two of these, can we say anything about the third? Yes, sometimes, but not always.

How much pizza and how much frozen yogurt?

Update Aug 27, 2019: I wrote a new blog post showing that Ryacas can now solve the system of equations directly without using optim(). As you may know, I am maintaining the Ryacas package (with online documentation) for doing symbolic mathematics (and other stuff) in R using the yacas software (with online documentation). Søren Højsgaard and I have been preparing a new major release of Ryacas (see blog post on it).