This article introduces a Laplace approximation to Bayesian inference in Dirichlet regression models, which can be used analyze set of variables on simplex exhibiting skewness and heteroscedasticity, without having transform the data. These data, mainly consist proportions or percentages disjoint categories, are widely known as compositional data common areas such ecology, geology, psychology. ...

In classification problem, we assume that the samples around the class boundary are more likely to be incorrectly annotated than others, and propose boundaryconditional class noise (BCN). Based on the BCN assumption, we use unnormalized Gaussian and Laplace distributions to directly model how class noise is generated, in symmetric and asymmetric cases. In addition, we demonstrate that Logistic ...

Quantile regression provides a convenient framework for analyzing the impact of covariates on the complete conditional distribution of a response variable instead of only the mean. While frequentist treatments of quantile regression are typically completely nonparametric, a Bayesian formulation relies on assuming the asymmetric Laplace distribution as auxiliary error distribution that yields po...

this article is devoted to study of the autoconvolution equations and generalized mittag-leffler functions. these types of equations are given in terms of the laplace transform convolution of a function with itself. we state new classes of the autoconvolution equations of the first kind and show that the generalized mittag-leffler functions are solutions of these types of equations. in view of ...

In this paper, we derive a nonlinear Picone identity to the pseudo p-Laplace operator, which contains some known Picone identities and removes a condition used in many previous papers. Some applications are given including a Liouville type theorem to the singular pseudo p-Laplace system, a Sturmian comparison principle to the pseudo p-Laplace equation, a new Hardy type inequality with weight an...

The text of Laplace, Sur l’application du calcul des probabilités à la philosophie naturelle, (Théorie Analytique des Probabilités. Troisième Édition. Premier Supplément), 1820, is quoted in the context of the Gram-Schmidt algorithm. We provide an English translation of Laplace’s manuscript (originally in French) and interpret the algorithms of Laplace in a contemporary context. The two algorit...