Related papers: Multi-level Bayes and MAP monotonicity testing
Estimation and hypothesis tests for the covariance matrix in high dimensions is a challenging problem as the traditional multivariate asymptotic theory is no longer valid. When the dimension is larger than or increasing with the sample…
Multivariate locally stationary functional time series provide a flexible framework for modeling complex data structures exhibiting both temporal and spatial dependencies while allowing for time-varying data generating mechanism. In this…
In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention. This paper examines the robustness of the Bayesian approach by analyzing the stability…
The multinomial probit model is often used to analyze choice behaviour. However, estimation with existing Markov chain Monte Carlo (MCMC) methods is computationally costly, which limits its applicability to large choice data sets. This…
In this paper we propose methods for inference of the geometric features of a multivariate density. Our approach uses multiscale tests for the monotonicity of the density at arbitrary points in arbitrary directions. In particular, a…
In this paper, we consider the problem of simultaneous testing of multivariate normal means under arbitrary covariance dependence. Specifically, let $\boldsymbol{X}\sim N_n(\boldsymbol{\theta},\boldsymbol{\Sigma})$, where…
Simultaneous tests of superiority and non-inferiority hypotheses on multiple endpoints are often performed in clinical trials to demonstrate that a new treatment is superior over a control on at least one endpoint and non-inferior on the…
An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated. The prior considered is a mixture of an atom of probability at zero and a heavy-tailed density \gamma,…
Modern high-throughput biomedical devices routinely produce data on a large scale, and the analysis of high-dimensional datasets has become commonplace in biomedical studies. However, given thousands or tens of thousands of measured…
Model merging has emerged as an effective approach to combine multiple single-task models into a multitask model. This process typically involves computing a weighted average of the model parameters without any additional training. Existing…
Standardization has been a widely adopted practice in multiple testing, for it takes into account the variability in sampling and makes the test statistics comparable across different study units. However, despite conventional wisdom to the…
The classical binary hypothesis testing problem is revisited. We notice that when one of the hypotheses is composite, there is an inherent difficulty in defining an optimality criterion that is both informative and well-justified. For…
We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We…
Towards understanding the fundamental limits of estimation from data of varied quality, we study the problem of estimating a mean parameter from heteroskedastic Gaussian observations where the variances are unknown and may vary arbitrarily…
Within a Bayesian decision theoretic framework we investigate some asymptotic optimality properties of a large class of multiple testing rules. A parametric setup is considered, in which observations come from a normal scale mixture model…
The estimation of the covariance matrix is an initial step in many multivariate statistical methods such as principal components analysis and factor analysis, but in many practical applications the dimensionality of the sample space is…
This paper considers the problem of detecting equal-shaped non-overlapping unimodal peaks in the presence of Gaussian ergodic stationary noise, where the number, location and heights of the peaks are unknown. A multiple testing approach is…
Regularized linear regression is central to machine learning, yet its high-dimensional behavior with informative priors remains poorly understood. We provide the first exact asymptotic characterization of training and test risks for maximum…
Contemporary approaches frame the color constancy problem as learning camera specific illuminant mappings. While high accuracy can be achieved on camera specific data, these models depend on camera spectral sensitivity and typically exhibit…
We study, to the best of our knowledge, the first Bayesian algorithm for unimodal Multi-Armed Bandit (MAB) problems with graph structure. In this setting, each arm corresponds to a node of a graph and each edge provides a relationship,…