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Kernel-based hypothesis tests offer a flexible, non-parametric tool to detect high-order interactions in multivariate data, beyond pairwise relationships. Yet the scalability of such tests is limited by the computationally demanding…
As Basu (1977) writes, "Eliminating nuisance parameters from a model is universally recognized as a major problem of statistics," but after more than 50 years since Basu wrote these words, the two mainstream schools of thought in statistics…
Background: Clinical prediction models are increasingly used to inform healthcare decisions, but determining the minimum sample size for their development remains a critical and unresolved challenge. Inadequate sample sizes can lead to…
Hypothesis testing of random forest (RF) variable importance measures (VIMP) remains the subject of ongoing research. Among recent developments, heuristic approaches to parametric testing have been proposed whose distributional assumptions…
The marginal likelihood is a central tool for drawing Bayesian inference about the number of components in mixture models. It is often approximated since the exact form is unavailable. A bias in the approximation may be due to an incomplete…
Mixtures of Linear Regressions (MLR) is an important mixture model with many applications. In this model, each observation is generated from one of the several unknown linear regression components, where the identity of the generated…
The pseudo-marginal (PM) approach is increasingly used for Bayesian inference in statistical models, where the likelihood is intractable but can be estimated unbiasedly. %Examples include random effect models, state-space models and data…
Until recently, the use of Bayesian inference in population genetics was limited to a few cases because for many realistic population genetic models the likelihood function cannot be calculated analytically . The situation changed with the…
Non-parametric two-sample tests based on energy distance or maximum mean discrepancy are widely used statistical tests for comparing multivariate data from two populations. While these tests enjoy desirable statistical properties, their…
Many recent statistical applications involve inference under complex models, where it is computationally prohibitive to calculate likelihoods but possible to simulate data. Approximate Bayesian Computation (ABC) is devoted to these complex…
Bayesian phylogenetic methods are generating noticeable enthusiasm in the field of molecular systematics. Many phylogenetic models are often at stake and different approaches are used to compare them within a Bayesian framework. The Bayes…
High-dimensional longitudinal data is increasingly used in a wide range of scientific studies. To properly account for dependence between longitudinal observations, statistical methods for high-dimensional linear mixed models (LMMs) have…
Modeling binary and categorical data is one of the most commonly encountered tasks of applied statisticians and econometricians. While Bayesian methods in this context have been available for decades now, they often require a high level of…
Measurement error and missing data in variables used in statistical models are common, and can at worst lead to serious biases in analyses if they are ignored. Yet, these problems are often not dealt with adequately, presumably in part…
Bayesian likelihood-free methods implement Bayesian inference using simulation of data from the model to substitute for intractable likelihood evaluations. Most likelihood-free inference methods replace the full data set with a summary…
We study Martin-L\"{o}f random (ML-random) points on computable probability measures on sample and parameter spaces (Bayes models). We consider variants of conditional randomness defined by ML-randomness on Bayes models and those of…
Efficient estimation methods for simultaneous autoregressive (SAR) models with missing data in the response variable have been well-explored in the literature. A common practice is to introduce measurement error into SAR models to separate…
The random-effects or normal-normal hierarchical model is commonly utilized in a wide range of meta-analysis applications. A Bayesian approach to inference is very attractive in this context, especially when a meta-analysis is based only on…
Dirichlet process mixture model (DPMM) is a popular Bayesian nonparametric model. In this paper, we apply this model to weighted data and then estimate the un-weighted distribution from the corresponding weighted distribution using the…
BayesMallows is an R package for analyzing data in the form of rankings or preferences with the Mallows rank model, and its finite mixture extension, in a Bayesian probabilistic framework. The Mallows model is a well-known model, grounded…