Introducing elliptic, an R Package for Elliptic and Modular Functions

This paper introduces the elliptic package of R routines, for numerical calculation of elliptic and related functions. Elliptic functions furnish interesting and instructive examples of many ideas of complex analysis, and the package illustrates these numerically and visually. A statistical application in fluid mechanics is presented.

Introducing untb, an R Package For Simulating Ecological Drift Under the Unified Neutral Theory of Biodiversity

The distribution of abundance amongst species with similar ways of life is a classical problem in ecology. The unified neutral theory of biodiversity, due to Hubbell, states that observed population dynamics may be explained on the assumption of per capita equivalence amongst individuals. One can thus dispense with differences between species, and differences between abundant and rare species: all individuals behave alike in respect of their probabilities of reproducing and death. It is a striking fact that such a parsimonious theory results in a non-trivial dominancediversity curve (that is, the simultaneous existence of both abundant and rare species) and even more striking that the theory predicts abundance curves that match observations across a wide range of ecologies. This paper introduces the untb package of R routines, for numerical simulation of ecological drift under the unified neutral theory. A range of visualization, analytical, and simulation tools are provided in the package and these are presented with examples in the paper.

Introducing BACCO, an R Bundle for Bayesian Analysis of Computer Code Output

This paper introduces the BACCO bundle of R routines for carrying out Bayesian analysis of computer code output. The bundle comprises packages emulator and calibrator, computerized implementations of the ideas of Oakley and O'Hagan (2002) and Kennedy and O'Hagan (2001a) respectively. The bundle is self-contained and fully documented R code, and includes a toy dataset that furnishes a working example of the functions. Package emulator carries out Bayesian emulation of computer code output; package calibrator allows the incorporation of observational data into model calibration using Bayesian techniques. The package is then applied to a dataset taken from climate science.

Exact Tests for Two-Way Contingency Tables with Structural Zeros

Fisher's exact test, named for Sir Ronald Aylmer Fisher, tests contingency tables for homogeneity of proportion. This paper discusses a generalization of Fisher's exact test for the case where some of the table entries are constrained to be zero. The resulting test is useful for assessing cases where the null hypothesis of conditional multinomial distribution is suspected to be false. The test is implemented in the form of a new R package, aylmer.

A Generalization of the Dirichlet Distribution

This paper discusses a generalization of the Dirichlet distribution, the 'hyperdirichlet', in which various types of incomplete observations may be incorporated. It is conjugate to the multinomial distribution when some observations are censored or grouped. The hyperdirichlet R package is introduced and examples given. A number of statistical tests are performed on the example datasets, which are drawn from diverse disciplines including sports statistics, the sociology of climate change, and psephology