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This work relates the framework of model-based clustering for spatial functional data where the data are surfaces. We first introduce a Bayesian spatial spline regression model with mixed-effects (BSSR) for modeling spatial function data. The BSSR model is based on Nodal basis functions for spatial regression and accommodates both common mean behavior for the data through a fixed-effects part, and variability inter-individuals thanks to a random-effects part. Then, in order to model populations of spatial functional data issued from heterogeneous groups, we integrate the BSSR model into a mixture framework. The resulting model is a Bayesian mixture of spatial spline regressions with mixed-effects (BMSSR) used for density estimation and model-based surface clustering. The models, through their Bayesian formulation, allow to integrate possible prior knowledge on the data structure and constitute a good alternative to recent mixture of spatial spline regressions model estimated in a maximum likelihood framework via the expectation-maximization (EM) algorithm. The Bayesian model inference is performed by Markov Chain Monte Carlo (MCMC) sampling. We derive two Gibbs sampler to infer the BSSR and the BMSSR models and apply them on simulated surfaces and a real problem of handwritten digit recognition using the MNIST data set. The obtained results highlight the potential benefit of the proposed Bayesian approaches for modeling surfaces possibly dispersed in particular in clusters.
To fast approximate maximum likelihood estimators with massive data, this paper studies the Optimal Subsampling Method under the A-optimality Criterion (OSMAC) for generalized linear models. The consistency and asymptotic normality of the estimator f
In spatial statistics, it is often assumed that the spatial field of interest is stationary and its covariance has a simple parametric form, but these assumptions are not appropriate in many applications. Given replicate observations of a Gaussian sp
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A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using Gaussian pro
Regression models with crossed random effect errors can be very expensive to compute. The cost of both generalized least squares and Gibbs sampling can easily grow as $N^{3/2}$ (or worse) for $N$ observations. Papaspiliopoulos et al. (2020) present a