Related papers: Bayesian nonparametric tests via sliced inverse mo…
Testing conditional independence between two random vectors given a third is a fundamental and challenging problem in statistics, particularly in multivariate nonparametric settings due to the complexity of conditional structures. We…
A Bayesian multivariate model with a structured covariance matrix for multi-way nested data is proposed. This flexible modeling framework allows for positive and for negative associations among clustered observations, and generalizes the…
Causal phenomena associated with rare events occur across a wide range of engineering problems, such as risk-sensitive safety analysis, accident analysis and prevention, and extreme value theory. However, current methods for causal…
Joint Bayesian factor models are popular for characterizing relationships between multivariate correlated predictors and a response variable. Standard models assume that all variables, including both the predictors and the response, are…
Hypothesis testing of structure in covariance matrices is of significant importance, but faces great challenges in high-dimensional settings. Although consistent frequentist one-sample covariance tests have been proposed, there is a lack of…
We propose a new class of models for random permutations, which we call log-linear models, by the analogy with log-linear models used in the analysis of contingency tables. As a special case, we study the family of all Luce-decomposable…
Testing independence among a number of (ultra) high-dimensional random samples is a fundamental and challenging problem. By arranging $n$ identically distributed $p$-dimensional random vectors into a $p \times n$ data matrix, we investigate…
This paper studies model checking for general parametric regression models having no dimension reduction structures on the predictor vector. Using any U-statistic type test as an initial test, this paper combines the sample-splitting and…
We consider a linear regression model and propose an omnibus test to simultaneously check the assumption of independence between the error and the predictor variables, and the goodness-of-fit of the parametric model. Our approach is based…
This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for…
So far, one-factor copulas induce conditional independence with respect to a latent factor. In this paper, we extend one-factor copulas to conditionally dependent models. This is achieved through new representations which allow to build new…
Independence screening is a powerful method for variable selection for `Big Data' when the number of variables is massive. Commonly used independence screening methods are based on marginal correlations or variations of it. In many…
The ratio of Bayesian evidences is a popular tool in cosmology to compare different models. There are however several issues with this method: Bayes' ratio depends on the prior even in the limit of non-informative priors, and Jeffrey's…
The discovery of rare genetic variants through Next Generation Sequencing is a very challenging issue in the field of human genetics. We propose a novel region-based statistical approach based on a Bayes Factor (BF) to assess evidence of…
In this article we propose novel Bayesian nonparametric methods using Dirichlet Process Mixture (DPM) models for detecting pairwise dependence between random variables while accounting for uncertainty in the form of the underlying…
Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…
The model-X conditional randomization test is a generic framework for conditional independence testing, unlocking new possibilities to discover features that are conditionally associated with a response of interest while controlling type-I…
Model Selections in Bayesian Statistics are primarily made with statistics known as Bayes Factors, which are directly related to Posterior Probabilities of models. Bayes Factors require a careful assessment of prior distributions as in the…
A fundamental task in AI is to assess (in)dependence between mixed-type variables (text, image, sound). We propose a Bayesian kernelised correlation test of (in)dependence using a Dirichlet process model. The new measure of (in)dependence…
It is a common saying that testing for conditional independence, i.e., testing whether whether two random vectors $X$ and $Y$ are independent, given $Z$, is a hard statistical problem if $Z$ is a continuous random variable (or vector). In…