Related papers: Bayesian model selection consistency and oracle in…
We consider Bayesian model selection in generalized linear models that are high-dimensional, with the number of covariates p being large relative to the sample size n, but sparse in that the number of active covariates is small compared to…
Statistical analyses of multipopulation studies often use the data to select a particular population as the target of inference. For example, a confidence interval may be constructed for a population only in the event that its sample mean…
Real-life statistical samples are often plagued by selection bias, which complicates drawing conclusions about the general population. When learning causal relationships between the variables is of interest, the sample may be assumed to be…
Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable…
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…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
Bayesian model selection is premised on the assumption that the data are generated from one of the postulated models. However, in many applications, all of these models are incorrect (that is, there is misspecification). When the models are…
We consider the problem of choosing between parametric models for a discrete observable, taking a Bayesian approach in which the within-model prior distributions are allowed to be improper. In order to avoid the ambiguity in the marginal…
We develop a set of scalable Bayesian inference procedures for a general class of nonparametric regression models. Specifically, nonparametric Bayesian inferences are separately performed on each subset randomly split from a massive…
Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…
In objective Bayesian model selection, no single criterion has emerged as dominant in defining objective prior distributions. Indeed, many criteria have been separately proposed and utilized to propose differing prior choices. We first…
Approximate Bayesian computation (ABC) methods, which are applicable when the likelihood is difficult or impossible to calculate, are an active topic of current research. Most current ABC algorithms directly approximate the posterior…
We have developed a frequentist approach for model selection which determines the consistency between any cosmological model and the data using the distribution of likelihoods from the iterative smoothing method. Using this approach, we…
Sample size criteria are often expressed in terms of the concentration of the posterior density, as controlled by some sort of error bound. Since this is done pre-experimentally, one can regard the posterior density as a function of the…
The stochastic block model (SBM) is a generative model revealing macroscopic structures in graphs. Bayesian methods are used for (i) cluster assignment inference and (ii) model selection for the number of clusters. In this paper, we study…
Comparison of competing statistical models is an essential part of psychological research. From a Bayesian perspective, various approaches to model comparison and selection have been proposed in the literature. However, the applicability of…
This study establishes the consistency of Bayesian adaptive testing methods under the Rasch model, addressing a gap in the literature on their large-sample guarantees. Although Bayesian approaches are recognized for their finite-sample…
In the class of normal regression models with a finite number of regressors, and for a wide class of prior distributions, a Bayesian model selection procedure based on the Bayes factor is consistent [Casella and Moreno J. Amer. Statist.…
Preferential sampling is a common feature in geostatistics and occurs when the locations to be sampled are chosen based on information about the phenomena under study. In this case, point pattern models are commonly used as the probability…
We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…