arXiv subjects
Publications and source records attributed to Rasmus Waagepetersen.
This tutorial provides an introduction to Palm distributions for spatial point processes. Initially, in the context of finite point processes , we give an explicit definition of Palm distributions in terms of their density functions. Then we review Palm distributions in the general case. Finally we discuss some examples of Palm distributions for specific models and some applications.
This paper establishes a remarkable result regarding Palmdistributions for a log Gaussian Cox process: the reduced Palmdistribution for a log Gaussian Cox process is itself a log Gaussian Coxprocess which only differs from the original log Gaussian Cox processin the intensity function. This new result is used to study functionalsummaries for log Gaussian Cox processes.
Fitting regression models for intensity functions of spatial point processes is of great interest in ecological and epidemiological studies of association between spatially referenced events and geographical or environmental covariates. When Cox or cluster process models are used to accommodate clustering not accounted for by the available covariates, likelihood based inference becomes computationally cumbersome due to the complicated nature of the likelihood function and the associated score function. It is therefore of interest to consider alternative more easily computable estimating functions. We derive the optimal estimating function in a class of first-order estimating functions. The optimal estimating function depends on the solution of a certain Fredholm integral equation which in practice is solved numerically. The approximate solution is equivalent to a quasi-likelihood for binary spatial data and we therefore use the term quasi-likelihood for our optimal estimating function approach. We demonstrate in a simulation study and a data example that our quasi-likelihood method for spatial point processes is both statistically and computationally efficient.
The presence of different transcripts of a gene across samples can be analysed by whole-transcriptome microarrays. Reproducing results from published microarray data represents a challenge due to the vast amounts of data and the large variety of pre-processing and filtering steps employed before the actual analysis is carried out. To guarantee a firm basis for methodological development where results with new methods are compared with previous results it is crucial to ensure that all analyses are completely reproducible for other researchers. We here give a detailed workflow on how to perform reproducible analysis of the GeneChip Human Exon 1.0 ST Array at probe and probeset level solely in R/Bioconductor, choosing packages based on their simplicity of use. To exemplify the use of the proposed workflow we analyse differential splicing and differential gene expression in a publicly available dataset using various statistical methods. We believe this study will provide other researchers with an easy way of accessing gene expression data at different annotation levels and with the sufficient details needed for developing their own tools for reproducible analysis of the GeneChip Human Exon 1.0 ST Array.