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In this paper, a novel Bayesian nonparametric test for assessing multivariate normal models is presented. While there are extensive frequentist and graphical methods for testing multivariate normality, it is challenging to find Bayesian counterparts. The proposed approach is based on the use of the Dirichlet process and Mahalanobis distance. More precisely, the Mahalanobis distance is employed as a good technique to transform the $m$-variate problem into a univariate problem. Then the Dirichlet process is used as a prior on the distribution of the Mahalanobis distance. The concentration of the distribution of the distance between the posterior process and the chi-square distribution with $m$ degrees of freedom is compared to the concentration of the distribution of the distance between the prior process and the chi-square distribution with $m$ degrees of freedom via a relative belief ratio. The distance between the Dirichlet process and the chi-square distribution is established based on the Anderson-Darling distance. Key theoretical results of the approach are derived. The procedure is illustrated through several examples, in which the proposed approach shows excellent performance.
This paper studies nonparametric estimation of parameters of multivariate Hawkes processes. We consider the Bayesian setting and derive posterior concentration rates. First rates are derived for L1-metrics for stochastic intensities of the Hawkes pro
We propose a new one-sample test for normality in a Reproducing Kernel Hilbert Space (RKHS). Namely, we test the null-hypothesis of belonging to a given family of Gaussian distributions. Hence our procedure may be applied either to test data for norm
A Bayesian nonparametric estimator to entropy is proposed. The derivation of the new estimator relies on using the Dirichlet process and adapting the well-known frequentist estimators of Vasicek (1976) and Ebrahimi, Pflughoeft and Soofi (1994). Sever
Bayesian methods are developed for the multivariate nonparametric regression problem where the domain is taken to be a compact Riemannian manifold. In terms of the latter, the underlying geometry of the manifold induces certain symmetries on the mult
Bayesian nonparametric statistics is an area of considerable research interest. While recently there has been an extensive concentration in developing Bayesian nonparametric procedures for model checking, the use of the Dirichlet process, in its simp