AR and MA representation of partial autocorrelation functions, with applications

We prove a representation of the partial autocorrelation function (PACF), or the Verblunsky coefficients, of a stationary process in terms of the AR and MA coefficients. We apply it to show the asymptotic behaviour of the PACF. We also propose a new definition of short and long memory in terms of the PACF.Comment: Published in Probability Theory and Related Field

A closer look at detectability

The theory underlying line transect and variable circular plot surveys-distance sampling-begins with an assumed detectability function, giving the probabilities of detecting animals at different distances from the observer's path. The nature of these probabilities is unspecified in the general development, leaving users to question whether the actual probability structure matters. In particular, may one use the methodology in surveys where animals at the same distance have different probabilities of detection? This paper presents three examples where probabilities come from different assumptions: from the random placement of transects; from the uniform distribution of animals over the study region; and from cues randomly detected by the observer. These exemplify situations where detectability may not be a function of distance alone. Horvitz-Thompson estimators are displayed which can be used in each example, but some estimators require measuring features other than distance. A result concerning optimally weighted Horvitz-Thompson estimators shows that all three can be brought under the same umbrella if detection areas are measured instead of detection distances and if animals are uniformly distributed

Two-Stage Bayesian approach for GWAS with known genealogy

Genome-wide association studies (GWAS) aim to assess relationships between single nucleotide polymorphisms (SNPs) and diseases. They are one of the most popular problems in genetics, and have some peculiarities given the large number of SNPs compared to the number of subjects in the study. Individuals might not be independent, especially in animal breeding studies or genetic diseases in isolated populations with highly inbred individuals. We propose a family-based GWAS model in a two-stage approach comprising a dimension reduction and a subsequent model selection. The first stage, in which the genetic relatedness between the subjects is taken into account, selects the promising SNPs. The second stage uses Bayes factors for comparison among all candidate models and a random search strategy for exploring the space of all the regression models in a fully Bayesian approach. A simulation study shows that our approach is superior to Bayesian lasso for model selection in this setting. We also illustrate its performance in a study on Beta-thalassemia disorder in an isolated population from Sardinia. Supplementary Material describing the implementation of the method proposed in this article is available online

Statistical consulting interactions: a personal view

Statistical consulting, Interactive graphics,