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Clustering is a crucial task in various domains of knowledge, including medicine, epidemiology, genomics, environmental science, economics, and visual sciences, among others. Methodologies for inferring the number of clusters have often…

This paper deals with Bayesian inference of a mixture of Gaussian distributions. A novel formulation of the mixture model is introduced, which includes the prior constraint that each Gaussian component is always assigned a minimal number of…

We present a continuation method that entails generating a sequence of transition probability density functions from the prior to the posterior in the context of Bayesian inference for parameter estimation problems. The characterization of…

Imputation of missing values is a strategy for handling non-responses in surveys or data loss in measurement processes, which may be more effective than ignoring them. When the variable represents a count, the literature dealing with this…

We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the…

High-dimensional group inference is an essential part of statistical methods for analysing complex data sets, including hierarchical testing, tests of interaction, detection of heterogeneous treatment effects and inference for local…

Multivariate spatial fields are of interest in many applications, including climate model emulation. Not only can the marginal spatial fields be subject to nonstationarity, but the dependence structure among the marginal fields and between…

Categorical random variables are a common staple in machine learning methods and other applications across disciplines. Many times, correlation within categorical predictors exists, and has been noted to have an effect on various algorithm…

This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We…

In Bayesian theory, calculating a posterior probability distribution is highly important but usually difficult. Therefore, some methods have been put forward to deal with such problem, among which, the most popular one is the asymptotic…

Many existing approaches for estimating parameters in settings with distributional shifts operate under an invariance assumption. For example, under covariate shift, it is assumed that $p(y|x)$ remains invariant. We refer to such…

Bayesian analysis is increasingly popular for use in social science and other application areas where the data are observations from an informative sample. An informative sampling design leads to inclusion probabilities that are correlated…

A family of random probabilities is defined and studied. This family contains the Dirichlet process as a special case, corresponding to an inner point in the appropriate parameter space. The extension makes it possible to have random means…

We introduce a random partition model for Bayesian nonparametric regression. The model is based on infinitely-many disjoint regions of the range of a latent covariate-dependent Gaussian process. Given a realization of the process, the…

Conventional approximations to Bayesian inference rely on either approximations by statistics such as mean and covariance or by point particles. Recent advances such as the ensemble Gaussian mixture filter have generalized these notions to…

Inference is the task of drawing conclusions about unobserved variables given observations of related variables. Applications range from identifying diseases from symptoms to classifying economic regimes from price movements. Unfortunately,…

The analysis of multivariate discrete data is crucial in various scientific research areas, such as epidemiology, the social sciences, genomics, and environmental studies. As the availability of such data increases, developing robust…

This article brings in two new discrete distributions: multidimensional Binomial distribution and multidimensional Poisson distribution. Those distributions were created in eventology as more correct generalizations of Binomial and Poisson…

Bayesian inference on structured models typically relies on the ability to infer posterior distributions of underlying hidden variables. However, inference in implicit models or complex posterior distributions is hard. A popular tool for…

Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…