Related papers: Approximating the marginal likelihood in mixture m…
The key distinguishing property of a Bayesian approach is marginalization, rather than using a single setting of weights. Bayesian marginalization can particularly improve the accuracy and calibration of modern deep neural networks, which…
We propose a Likelihood Matching approach for training diffusion models by first establishing an equivalence between the likelihood of the target data distribution and a likelihood along the sample path of the reverse diffusion. To…
Laplace approximation is a very useful tool in Bayesian inference and it claims a nearly Gaussian behavior of the posterior. \cite{SpLaplace2022} established some rather accurate finite sample results about the quality of Laplace…
Bayesian analysis has become an indispensable tool across many different cosmological fields including the study of gravitational waves, the Cosmic Microwave Background and the 21-cm signal from the Cosmic Dawn among other phenomena. The…
We propose a fast and theoretically grounded method for Bayesian variable selection and model averaging in latent variable regression models. Our framework addresses three interrelated challenges: (i) intractable marginal likelihoods, (ii)…
One of the core problems of modern statistics is to approximate difficult-to-compute probability densities. This problem is especially important in Bayesian statistics, which frames all inference about unknown quantities as a calculation…
Comparisons between observed and predicted strong lensing properties of galaxy clusters have been routinely used to claim either tension or consistency with $\Lambda$CDM cosmology. However, standard approaches to such cosmological tests are…
The paper derives new results on the marginal likelihood of a two-way table which clarify the conditions under which Ecological inference is possible and lead to an efficient algorithm for maximizing the exact multinomial likelihood. The…
Dirichlet process (DP) mixture models provide a flexible Bayesian framework for density estimation. Unfortunately, their flexibility comes at a cost: inference in DP mixture models is computationally expensive, even when conjugate…
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…
In this note we study a quantitative version of Bernstein's approximation problem when the polynomials are dense in weighted spaces on the real line completing a result of S.~N.~Mergelyan (1960). We estimate in the logarithmic scale the…
Although Bayesian density estimation using discrete mixtures has good performance in modest dimensions, there is a lack of statistical and computational scalability to high-dimensional multivariate cases. To combat the curse of…
Marginal likelihood, also known as model evidence, is a fundamental quantity in Bayesian statistics. It is used for model selection using Bayes factors or for empirical Bayes tuning of prior hyper-parameters. Yet, the calculation of…
A method for implicit variable selection in mixture of experts frameworks is proposed. We introduce a prior structure where information is taken from a set of independent covariates. Robust class membership predictors are identified using a…
We develop Bayesian models for density regression with emphasis on discrete outcomes. The problem of density regression is approached by considering methods for multivariate density estimation of mixed scale variables, and obtaining…
In this paper, we develop local expansions for the ratio of the centered matrix-variate $T$ density to the centered matrix-variate normal density with the same covariances. The approximations are used to derive upper bounds on several…
Models with intractable likelihood functions arise in areas including network analysis and spatial statistics, especially those involving Gibbs random fields. Posterior parameter es timation in these settings is termed a doubly-intractable…
Bayesian analysis of data from the general linear mixed model is challenging because any nontrivial prior leads to an intractable posterior density. However, if a conditionally conjugate prior density is adopted, then there is a simple…
It is shown that the variable bandwidth density estimator proposed by McKay (1993a and b) following earlier findings by Abramson (1982) approximates density functions in $C^4(\mathbb R^d)$ at the minimax rate in the supremum norm over…
Bayesian methods are appealing in their flexibility in modeling complex data and ability in capturing uncertainty in parameters. However, when Bayes' rule does not result in tractable closed-form, most approximate inference algorithms lack…