The same but different – how to introduce variation within computing assessment tasks

In this article, suggestions are made for introducing an individual element into formative assessment of the ability to use computer software for statistics.

Bivariate distribution modeling with tree diameter and height data

The Logit-Logistic (LL), Johnson's SB, and the Beta (GBD) are flexible four-parameter probability distribution models in terms of the (skewness-kurtosis) region covered, and each has been used for modeling tree diameter distributions in forest stands. This article compares bivariate forms of these models in terms of their adequacy in representing empirical diameter-height distributions from 102 sample plots. Four bivariate models are compared: SBB, the natural, well-known, and much-used bivariate generalization of SB; the bivariate distributions with LL, SB, and Beta as marginals, constructed using Plackett's method (LL-2P, etc.). All models are fitted using maximum likelihood, and their goodness-of-fits are compared using minus log-likelihood (equivalent to Akaike's Information Criterion, the AIC). The performance ranking in this case study was SBB, LL-2P, GBD-2P, and SB-2P

An algorithm for total variation inpainting based on nonlinear multi-grid methods

Image inpainting refers to restoring a damaged image with missing information. The total variation (TV) inpainting model is one such method that simultaneously fills in the regions with available information from their surroundings and eliminates noises. The method works well with small narrow inpainting domains. However there remains an urgent need to develop fast iterative solvers, as the underlying problem sizes are large. In addition one needs to tackle the imbalance of results between inpainting and denoising. When the inpainting regions are thick and large, the procedure of inpainting works quite slowly and usually requires a significant number of iterations and leads inevitably to oversmoothing in the outside of the inpainting domain. To overcome these difficulties, we propose a solution for TV inpainting method based on the nonlinear multi-grid algorithm.