Related papers: Bayesian Copula Density Estimation Using Bernstein…
We introduce a new family of copula densities constructed from univariate distributions on $[0,1]$. Although our construction is structurally simple, the resulting family is versatile: it includes both smooth and irregular examples, and…
Estimating the marginal and joint densities of the long-term average intakes of different dietary components is an important problem in nutritional epidemiology. Since these variables cannot be directly measured, data are usually collected…
Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…
This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. In particular, we improve on current rates of…
Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…
We present a new Bayesian nonparametric approach to estimating the spectral density of a stationary time series. A nonparametric prior based on a mixture of B-spline distributions is specified and can be regarded as a generalization of the…
We present a multi-fidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution. In the Bayesian inference setting, traditional…
We consider the problem of estimating the joint distribution $P$ of $n$ independent random variables within the Bayes paradigm from a non-asymptotic point of view. Assuming that $P$ admits some density $s$ with respect to a given reference…
Multivariate mixed-type outcomes are difficult to model jointly, and additional complexity arises when both marginal effects and dependence structures vary with a covariate such as age or time. Existing approaches often impose restrictive…
We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than…
We propose a class of dynamic vine copula models. This is an extension of static vine copulas and a generalization of dynamic C-vine and D-vine copulas studied by Almeida et al (2016) and Goel and Mehra (2019). Within this class, we allow…
Modeling of high order multivariate probability distribution is a difficult problem which occurs in many fields. Copula approach is a good choice for this purpose, but the curse of dimensionality still remains a problem. In this paper we…
Continuous proportions measured on the same experimental unit often pose two challenges: interior outliers that inflate variance beyond the beta ceiling and residual dependence that invalidates independent-margin models. We introduce a…
Learning the multivariate distribution of data is a core challenge in statistics and machine learning. Traditional methods aim for the probability density function (PDF) and are limited by the curse of dimensionality. Modern neural methods…
By sampling from the latent space of an autoencoder and decoding the latent space samples to the original data space, any autoencoder can simply be turned into a generative model. For this to work, it is necessary to model the autoencoder's…
Normalizing flows, which learn a distribution by transforming the data to samples from a Gaussian base distribution, have proven powerful density approximations. But their expressive power is limited by this choice of the base distribution.…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
Bayesian clustering methods have the widely touted advantage of providing a probabilistic characterization of uncertainty in clustering through the posterior distribution. An amazing variety of priors and likelihoods have been proposed for…
We introduce a density basis of the trigonometric polynomials that is suitable to mixture modelling. Statistical and geometric properties are derived, suggesting it as a circular analogue to the Bernstein polynomial densities. Nonparametric…
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…