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Bayesian analysis of functions and curves is considered, where warping and other geometrical transformations are often required for meaningful comparisons. We focus on two applications involving the classification of mouse vertebrae shape outlines and the alignment of mass spectrometry data in proteomics. The functions and curves of interest are represented using the recently introduced square root velocity function, which enables a warping invariant elastic distance to be calculated in a straightforward manner. We distinguish between various spaces of interest: the original space, the ambient space after standardizing, and the quotient space after removing a group of transformations. Using Gaussian process models in the ambient space and Dirichlet priors for the warping functions, we explore Bayesian inference for curves and functions. Markov chain Monte Carlo algorithms are introduced for simulating from the posterior, including simulated tempering for multimodal posteriors. We also compare ambient and quotient space estimators for mean shape, and explain their frequent similarity in many practical problems using a Laplace approximation. A simulation study is carried out, as well as shape classification of the mouse vertebra outlines and practical alignment of the mass spectrometry functions.MSC 2010 subject classifications: Primary 62F15, 62P10.

This review summarizes the current situation of enhanced coagulation and looks forward to future development.

SummaryWe present methods for diagnosing the effects of model misspecification of the truepredictor distribution in structural measurement error models. We first formulate latent-model robustness theoretically. Then we provide practical technique for examining the adequacy of an assumed latent predictor model. The methods are illustrated via analytical examples, application to simulated data and with data from a study of coronary heart disease.

Generalized linear mixed models (GLMMs) are widely used in the analysis of clustered data. However, the validity of likelihood-based inference in such analyses can be greatly affected by the assumed model for the random effects. We propose a diagnostic method for random-effect model misspecification in GLMMs for clustered binary response. We provide a theoretical justification of the proposed method and investigate its finite sample performance via simulation. The proposed method is applied to data from a longitudinal respiratory infection study.