Composite quantile regression is based on the convex combination of single loss functions and enjoys many advantages over regression. The Bayesian extension finite mixture asymmetric Laplace densities. This article mainly aims to contribute theoretical justification composite from perspective density estimation. As such, we further show that distribution can be used for estimation in general. We obtain upper bounds rates convergence mixtures For mixtures, parametric rate up a logarithmic...

Integrating spatial transcriptomics with antibody-based proteomics enables the investigation of biological regulation within intact tissue architecture. However, current approaches for multi-omics integration often depend on dimensionality reduction or autoencoders, which disregard context, limit interpretability, and face challenges scalability. To address these limitations, we developed INLAomics, a multivariate hierarchical Bayesian framework that models protein abundance in sections by...

Abstract $$L^p$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>L</mml:mi><mml:mi>p</mml:mi></mml:msup></mml:math> -quantiles are a class of generalized quantiles defined as minimizers an asymmetric power function. They include both quantiles, $$p=1$$ xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> , and expectiles, $$p=2$$...

Bayesian quantile regression generally relies on the asymmetric Laplace distribution (ALD) as error distribution. We consider methods for Lp-quantile based skewed exponential power (SEPD). Both and frequentist estimation procedures are outlined compared with previous work SEPD. find that our proposed greatly outperform a method in terms of estimation. Further, standard regression, we perform better root mean square (RMSE). Empirical evidence statistical properties models is provided through...

Clinical trials involving multiple time-to-event outcomes are increasingly common. In this paper, permutation tests for testing group differences in multivariate data proposed. Unlike other two-sample survival data, the proposed attain nominal type I error rate. A simulation study shows that outperform their competitors when degree of censored observations is sufficiently high. When censoring low, it seen naive such as Hotelling's T2 tailored to data. Computational and practical aspects...

[[EQUATION]] -quantiles are a class of generalized quantiles defined as minimizers an asymmetric power function. This paper is the first to study composite -quantile regression, where Bayesian approach considered. The proposed method shown outperform quantile regression in most aspects.

Linear mixed models are standard to analyze repeated measures or longitudinal data under the assumption of normality for random components in model. Although often used both frequentist and Bayesian inference, their evaluation from robustness perspective has not received as much attention inference frequentist. The aim this study is evaluate tests normality. We use a general class exponential power distributions, EPD, particularly focus on testing fixed effects models. EPD contains light...

Tests based on Neyman's C(α) approach are proposed for the shape parameter of exponential power distribution (EPD). Earlier work maximum likelihood estimators EPD shows that asymptotic normality is hard to establish under classic regularity conditions due a discontinuity in its density functions and non-dominated third derivatives. Nevertheless, local optimality test can be established via Le Cam's differentiability quadratic mean, with alternatives order n−1/2. We mainly focus setting null...