Related papers: A Bayesian Multiresolution Independence Test for C…

Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…

If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a…

We propose a general solution to the problem of robust Bayesian inference in complex settings where outliers may be present. In practice, the automation of robust Bayesian analyses is important in the many applications involving large and…

In this article, we study tests of independence for data with arbitrary distributions in the non-serial case, i.e., for independent and identically distributed random vectors, as well as in the serial case, i.e., for time series. These…

We develop a new framework of uncertainty variables to model uncertainty. An uncertainty variable is characterized by an uncertainty set, in which its realization is bound to lie, while the conditional uncertainty is characterized by a set…

We introduce an independence criterion based on entropy regularized optimal transport. Our criterion can be used to test for independence between two samples. We establish non-asymptotic bounds for our test statistic and study its…

Likelihood-free approaches are appealing for performing inference on complex dependence models, either because it is not possible to formulate a likelihood function, or its evaluation is very computationally costly. This is the case for…

Inference in Bayesian statistics involves the evaluation of marginal likelihood integrals. We present algebraic algorithms for computing such integrals exactly for discrete data of small sample size. Our methods apply to both uniform priors…

Probabilistic independence is a useful concept for describing the result of random sampling---a basic operation in all probabilistic languages---and for reasoning about groups of random variables. Nevertheless, existing verification methods…

We study the problem of testing \emph{conditional independence} for discrete distributions. Specifically, given samples from a discrete random variable $(X, Y, Z)$ on domain $[\ell_1]\times[\ell_2] \times [n]$, we want to distinguish, with…

We consider the problem of variable selection in Bayesian multivariate linear regression models, involving multiple response and predictor variables, under multivariate normal errors. In the absence of a known covariance structure,…

We consider fully connected and feedforward deep neural networks with dependent and possibly heavy-tailed weights, as introduced in [26], to address limitations of the standard Gaussian prior. It has been proved in [26] that, as the number…

Predicting the winner of an election is of importance to multiple stakeholders. To formulate the problem, we consider an independent sequence of categorical data with a finite number of possible outcomes in each. The data is assumed to be…

This work addresses testing the independence of two continuous and finite-dimensional random variables from the design of a data-driven partition. The empirical log-likelihood statistic is adopted to approximate the sufficient statistics of…

In an empirical Bayesian setting, we provide a new multiple testing method, useful when an additional covariate is available, that influences the probability of each null hypothesis being true. We measure the posterior significance of each…

Bayesian networks are powerful statistical models to study the probabilistic relationships among set random variables with major applications in disease modeling and prediction. Here, we propose a continuous time Bayesian network with…

Datasets with hundreds of variables and many missing values are commonplace. In this setting, it is both statistically and computationally challenging to detect true predictive relationships between variables and also to suppress false…

Bayesian methods for graphical log-linear marginal models have not been developed in the same extent as traditional frequentist approaches. In this work, we introduce a novel Bayesian approach for quantitative learning for such models.…

An informative sampling design leads to the selection of units whose inclusion probabilities are correlated with the response variable of interest. Model inference performed on the resulting observed sample will be biased for the population…

Multiple imputation has become one of the standard methods in drawing inferences in many incomplete data applications. Applications of multiple imputation in relatively more complex settings, such as high-dimensional clustered data, require…