Related papers: Bayesian two-sample tests
A key problem in statistical modeling is model selection, how to choose a model at an appropriate level of complexity. This problem appears in many settings, most prominently in choosing the number ofclusters in mixture models or the number…
In this article we describe Bayesian nonparametric procedures for two-sample hypothesis testing. Namely, given two sets of samples $\mathbf{y}^{\scriptscriptstyle(1)}\;$\stackrel{\scriptscriptstyle{iid}}{\s im}$\;F^{\scriptscriptstyle(1)}$…
We propose optimal Bayesian two-sample tests for testing equality of high-dimensional mean vectors and covariance matrices between two populations. In many applications including genomics and medical imaging, it is natural to assume that…
Exponential random graph models (ERGMs) are a widely used framework for network data, enabling hypothesis testing on the structural mechanisms underlying observed networks. Bayesian ERGMs provide principled uncertainty quantification and…
In this paper, a novel Bayesian nonparametric test for assessing multivariate normal models is presented. While there are extensive frequentist and graphical methods for testing multivariate normality, it is challenging to find Bayesian…
In this paper we show that there is a link between approximate Bayesian methods and prior robustness. We show that what is typically recognized as an approximation to the likelihood, either due to the simulated data as in the Approximate…
In the case of informative sampling the sampling scheme explicitly or implicitly depends on the response variable. As a result, the sample distribution of response variable can- not be used for making inference about the population. In this…
In population studies, it is standard to sample data via designs in which the population is divided into strata, with the different strata assigned different probabilities of inclusion. Although there have been some proposals for including…
In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…
Combining evidence from different sources can be achieved with Bayesian or Dempster-Shafer methods. The first requires an estimate of the priors and likelihoods while the second only needs an estimate of the posterior probabilities and…
This paper develops Bayesian sample size formulae for experiments comparing two groups. We assume the experimental data will be analysed in the Bayesian framework, where pre-experimental information from multiple sources can be represented…
Diffusion models have emerged as powerful tools for solving inverse problems, yet prior work has primarily focused on observations with Gaussian measurement noise, restricting their use in real-world scenarios. This limitation persists due…
In this paper we propose a Bayesian answer to testing problems when the hypotheses are not well separated. The idea of the method is to study the posterior distribution of a discrepancy measure between the parameter and the model we want to…
We characterize conjugate nonparametric Bayesian models as projective limits of conjugate, finite-dimensional Bayesian models. In particular, we identify a large class of nonparametric models representable as infinite-dimensional analogues…
Bi-clustering is a useful approach in analyzing biological data when observations come from heterogeneous groups and have a large number of features. We outline a general Bayesian approach in tackling bi-clustering problems in moderate to…
Testing the equality of two proportions is a common procedure in science, especially in medicine and public health. In these domains it is crucial to be able to quantify evidence for the absence of a treatment effect. Bayesian hypothesis…
We consider the statistical linear inverse problem of making inference on an unknown source function in an elliptic partial differential equation from noisy observations of its solution. We employ nonparametric Bayesian procedures based on…
We propose a two-sample testing procedure based on learned deep neural network representations. To this end, we define two test statistics that perform an asymptotic location test on data samples mapped onto a hidden layer. The tests are…
Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…
In this paper, we provide an explicit probability distribution for classification purposes. It is derived from the Bayesian nonparametric mixture of Dirichlet process model, but with suitable modifications which remove unsuitable aspects of…