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Our problem is to find a good approximation to the P-value of the maximum of a random field of test statistics for a cone alternative at each point in a sample of Gaussian random fields. These test statistics have been proposed in the neuroscience literature for the analysis of fMRI data allowing for unknown delay in the hemodynamic response. However the null distribution of the maximum of this 3D random field of test statistics, and hence the threshold used to detect brain activation, was unsolved. To find a solution, we approximate the P-value by the expected Euler characteristic (EC) of the excursion set of the test statistic random field. Our main result is the required EC density, derived using the Gaussian Kinematic Formula.
The infinite-dimensional Hilbert sphere $S^infty$ has been widely employed to model density functions and shapes, extending the finite-dimensional counterpart. We consider the Frechet mean as an intrinsic summary of the central tendency of data lying
We consider Bayesian inference of sparse covariance matrices and propose a post-processed posterior. This method consists of two steps. In the first step, posterior samples are obtained from the conjugate inverse-Wishart posterior without considering
We apply Gaussian process (GP) regression, which provides a powerful non-parametric probabilistic method of relating inputs to outputs, to survival data consisting of time-to-event and covariate measurements. In this context, the covariates are regar
Gaussian processes (GP) are widely used as a metamodel for emulating time-consuming computer codes. We focus on problems involving categorical inputs, with a potentially large number L of levels (typically several tens), partitioned in G << L groups
The cross-classified sampling design consists in drawing samples from a two-dimension population, independently in each dimension. Such design is commonly used in consumer price index surveys and has been recently applied to draw a sample of babies i