The Embedding Problem for Markov Models of Nucleotide Substitution

10.1371/journal.pone.0069187PLoS ONE87-POLN

Bayesian Analysis of Curves Shape Variation Through Registration and Regression

This manuscript reviews the use of Bayesian hierarchical curve registration in Biostatistics and Bioinformatics.Several models allowing for unit-specific random time scales are discussed and applied to longitudinal dataarising in biomedicine, pharmacokinetics and time-course genomics. We consider representations of random functionals based on P-spline priors. Under this framework, straightforward posterior simulation strategies are outlined for inference.Beyond curve registration, we discuss jointregression modeling of both random effects and population level functional quantities. Finally, the use of mixture priors is discussed in the setting of differential expression analysis

Anisotropic Matern correlation and spatial prediction using REML

The Matérn correlation function provides great flexibility for modeling spatially correlated random processes in two dimensions, in particular via a smoothness parameter, whose estimation allows data to determine the degree of smoothness of a spatial process. The extension to include anisotropy provides a very general and flexible class of spatial covariance functions that can be used in a model-based approach to geostatistics, in which parameter estimation is achieved via REML and prediction is within the E-BLUP framework. In this article we develop a general class of linear mixed models using an anisotropic Matérn class with an extended metric. The approach is illustrated by application to soil salinity data in a rice-growing field in Australia, and to fine-scale soil pH data. It is found that anisotropy is an important aspect of both datasets, emphasizing the value of a straightforward and accessible approach to modeling anisotropy. © 2007 American Statistical Association and the International Biometric Society