Related papers: Weyl Prior and Bayesian Statistics
In this paper we show that the classical problem of frequency estimation can be formulated and solved efficiently in an empirical Bayesian framework by assigning a uniform a priori probability distribution to the unknown frequency. We…
We discuss Bayesian inference for a known-mean Gaussian model with a compound symmetric variance-covariance matrix. Since the space of such matrices is a linear subspace of that of positive definite matrices, we utilize the methods of…
We establish a general semiparametric Bernstein-von Mises theorem for Bayesian nonparametric priors based on continuous observations in a periodic reversible multidimensional diffusion model. We consider a wide range of functionals…
This article considers the parametric estimation of $Pr(X<Y<Z)$ and its generalizations based on several well-known one-parameter and two-parameter continuous distributions. It is shown that for some one-parameter distributions and when…
Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…
The present paper introduces a fully objective Bayesian analysis to obtain the posterior distribution of an entropy measure. Notably, we consider the gamma distribution, which describes many natural phenomena in physics, engineering, and…
According to both domain expert knowledge and empirical evidence, wavelet coefficients of real signals tend to exhibit clustering patterns, in that they contain connected regions of coefficients of similar magnitude (large or small). A…
The Weyl principle is extended from the Riemannian to the pseudo-Riemannian setting, and subsequently to manifolds equipped with generic symmetric $(0,2)$-tensors. More precisely, we construct a family of generalized curvature measures…
Based on the relationship of symmetric operators with Hermitian symmetric spaces, we introduce the notion of \emph{Weyl curve} for a symmetric operator $T$, which is the geometric abstraction and generalization of the well-known Weyl…
We introduce a Bayesian prior distribution, the Logit-Normal continuous analogue of the spike-and-slab (LN-CASS), which enables flexible parameter estimation and variable/model selection in a variety of settings. We demonstrate its use and…
We address the reconstruction of a potential coefficient in an elliptic partial differential equation from distributed observations within the Bayesian framework. The choice of prior distribution is crucial in such inverse problems,…
In this paper, we consider Bayesian inference on a class of multivariate median and the multivariate quantile functionals of a joint distribution using a Dirichlet process prior. Since, unlike univariate quantiles, the exact posterior…
While Jeffreys priors usually are well-defined for the parameters of mixtures of distributions, they are not available in closed form. Furthermore, they often are improper priors. Hence, they have never been used to draw inference on the…
When the sample size is not too small, M-estimators of regression coefficients are approximately normal and unbiased. This leads to the familiar frequentist inference in terms of normality-based confidence intervals and p-values. From a…
One of the main research areas in Bayesian Nonparametrics is the proposal and study of priors which generalize the Dirichlet process. Here we exploit theoretical properties of Poisson random measures in order to provide a comprehensive…
Completely automatic and adaptive non-parametric inference is a pie in the sky. The frequentist approach, best exemplified by the kernel estimators, has excellent asymptotic characteristics but it is very sensitive to the choice of…
A Bayesian approach to the classification problem is proposed in which random partitions play a central role. It is argued that the partitioning approach has the capacity to take advantage of a variety of large-scale spatial structures, if…
In nonlinear regression models the Fisher information depends on the parameters of the model. Consequently, optimal designs maximizing some functional of the information matrix cannot be implemented directly but require some preliminary…
The use of {\it Mathematica} in deriving mean likelihood estimators is discussed. Comparisons between the maximum likelihood estimator, the mean likelihood estimator and the Bayes estimate based on a Jeffrey's noninformative prior using the…
The prior distribution for the unknown model parameters plays a crucial role in the process of statistical inference based on Bayesian methods. However, specifying suitable priors is often difficult even when detailed prior knowledge is…