Agricultural Risk Management - Experiences from an Action Research Approach

A new model for risk management in agriculture is described in the paper. The risk model is constructed as a context dependent process, which includes four main phases. The model is aimed at agricultural advisors, who wish to facilitate and disseminate risk management to farmers. It is developed and tested by an action research approach in an attempt to make risk management more applicable on family farms. Our obtained experiences indicate that farmers don't apply probabilistic thinking and other concepts according to formal decision theory.Risk management, consulting, action research, farm families, Risk and Uncertainty,

Multivariate phase-type theory for the site frequency spectrum

Linear functions of the site frequency spectrum (SFS) play a major role for understanding and investigating genetic diversity. Estimators of the mutation rate (e.g. based on the total number of segregating sites or average of the pairwise differences) and tests for neutrality (e.g. Tajima's D) are perhaps the most well-known examples. The distribution of linear functions of the SFS is important for constructing confidence intervals for the estimators, and to determine significance thresholds for neutrality tests. These distributions are often approximated using simulation procedures. In this paper we use multivariate phase-type theory to specify, characterize and calculate the distribution of linear functions of the site frequency spectrum. In particular, we show that many of the classical estimators of the mutation rate are distributed according to a discrete phase-type distribution. Neutrality tests, however, are generally not discrete phase-type distributed. For neutrality tests we derive the probability generating function using continuous multivariate phase-type theory, and numerically invert the function to obtain the distribution. A main result is an analytically tractable formula for the probability generating function of the SFS. Software implementation of the phase-type methodology is available in the R package phasty, and R code for the reproduction of our results is available as an accompanying vignette

Kirkegårdens placering i landskabet

Intet resumé

Kirkegården under forandring

Intet resumé

Cuspidal discrete series for semisimple symmetric spaces

We propose a notion of cusp forms on semisimple symmetric spaces. We then study the real hyperbolic spaces in detail, and show that there exists both cuspidal and non-cuspidal discrete series. In particular, we show that all the spherical discrete series are non-cuspidal.Comment: Minor corrections, to appear in J. Funct. Ana