Title: Lotka-Volterra Models for Gause's 'Struggle for Existence'
person("Lina", "Mühlbauer", role = c("aut")),
person("Maximilienne", "Schulze", role = c("aut")))
Description: A collection of tools and data for analyzing the Gause microcosm experiments, and for fitting Lotka-Volterra models to time series data. Includes methods for fitting single-species logistic growth, and multi-species interaction models, e.g. of competition, predator/prey relationships, or mutualism. See documentation for individual functions for examples. In general, see the lv_optim() function for examples of how to fit parameter values in multi-species systems. Note that the general methods applied here, as well as the form of the differential equations that we use, are described in detail in the Quantitative Ecology textbook by Lehman et al., available at <http://hdl.handle.net/11299/204551>, and in Lina K. Mühlbauer, Maximilienne Schulze, W. Stanley Harpole, and Adam T. Clark. 'gauseR': Simple methods for fitting Lotka-Volterra models describing Gause's 'Struggle for Existence' in the journal Ecology and Evolution.
Author: Adam Clark [aut, cre] (<https://orcid.org/0000-0002-8843-3278>),

Title: Difference measures for multivariate Gaussian probability
Description: A collection difference measures for multivariate Gaussian
probability density functions, such as the Euclidian mean, the
Mahalanobis distance, the Kullback-Leibler divergence, the
J-Coefficient, the Minkowski L2-distance, the Chi-square
divergence and the Hellinger Coefficient.

probability density functions, such as the Euclidea mean, the

Title: The Gaussian Covariate Method for Variable Selection
Authors@R: person("Laurie", "Davies", role = c("aut","cre"),email ="laurie.davies@uni-due.de")
Description: Given the standard linear model the traditional way of deciding whether to include the jth covariate is to apply the F-test to decide whether the corresponding beta coefficient is  zero. The Gaussian covariate method is completely different. The question as to whether the beta coefficient is or is not zero is replaced by the question as to whether the covariate is better or worse than i.i.d. Gaussian noise. The P-value for the covariate is the probability that Gaussian noise is better. Surprisingly this can be given exactly and it is the same a the P-value for the classical model based on the F-distribution. The Gaussian covariate P-value is model free, it is the same for any data set. Using the idea it is possible to do covariate selection for a small number of covariates 25 by considering all subsets.  Post selection inference causes no problems as the P-values hold whatever the data. The idea extends to stepwise regression again with exact probabilities. In the simplest version the only parameter is a specified cut-off P-value which can be interpreted as the probability of a false positive being included in the final selection. For more information see the website below and the accompanying papers: L. Davies and L. Duembgen, "A Model-free Approach to Linear Least Squares Regression with Exact  Probabilities and Applications to Covariate Selection", 2019, <arXiv:1906.01990>. L. Davies, "Lasso, Knockoff and Gaussian covariates: A comparison", 2018, <arXiv:1807.09633v4>.