Related papers: Constrained Fiducial Inference for Gaussian Models
Performing numerical integration when the integrand itself cannot be evaluated point-wise is a challenging task that arises in statistical analysis, notably in Bayesian inference for models with intractable likelihood functions. Markov…
Quasi-Monte Carlo (QMC) methods for estimating integrals are attractive since the resulting estimators typically converge at a faster rate than pseudo-random Monte Carlo. However, they can be difficult to set up on arbitrary posterior…
We propose efficient computational methods to fit multivariate Gaussian additive models, where the mean vector and the covariance matrix are allowed to vary with covariates, in an empirical Bayes framework. To guarantee the…
Gaussian processes (GPs) are commonly used for prediction and inference for spatial data analyses. However, since estimation and prediction tasks have cubic time and quadratic memory complexity in number of locations, GPs are difficult to…
Markov chain Monte Carlo (MCMC) algorithms provide a very general recipe for estimating properties of complicated distributions. While their use has become commonplace and there is a large literature on MCMC theory and practice, MCMC users…
We have made a Markov Chain Monte Carlo (MCMC) analysis of primordial non-Gaussianity (f_NL) using the WMAP bispectrum and power spectrum. In our analysis, we have simultaneously constrained f_NL and cosmological parameters so that 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…
Solving Bayesian inference problems approximately with variational approaches can provide fast and accurate results. Capturing correlation within the approximation requires an explicit parametrization. This intrinsically limits this…
Despite having various attractive qualities such as high prediction accuracy and the ability to quantify uncertainty and avoid over-fitting, Bayesian Matrix Factorization has not been widely adopted because of the prohibitive cost of…
This paper presents a new approach to automatically discovering accurate models of complex time series data. Working within a Bayesian nonparametric prior over a symbolic space of Gaussian process time series models, we present a novel…
Sampling from a lattice Gaussian distribution is emerging as an important problem in various areas such as coding and cryptography. The default sampling algorithm --- Klein's algorithm yields a distribution close to the lattice Gaussian…
We propose a Markov chain Monte Carlo (MCMC) scheme to perform state inference in non-linear non-Gaussian state-space models. Current state-of-the-art methods to address this problem rely on particle MCMC techniques and its variants, such…
Bayesian inference for Markov processes has become increasingly relevant in recent years. Problems of this type often have intractable likelihoods and prior knowledge about model rate parameters is often poor. Markov Chain Monte Carlo…
Markov Chain Monte Carlo (MCMC) techniques are now widely used for cosmological parameter estimation. Chains are generated to sample the posterior probability distribution obtained following the Bayesian approach. An important issue is how…
Markov Chain Monte Carlo (MCMC) algorithms are often used for approximate inference inside learning, but their slow mixing can be difficult to diagnose and the approximations can seriously degrade learning. To alleviate these issues, we…
Factors models are routinely used to analyze high-dimensional data in both single-study and multi-study settings. Bayesian inference for such models relies on Markov Chain Monte Carlo (MCMC) methods which scale poorly as the number of…
We apply Markov Chain Monte Carlo (MCMC) to the problem of parametric galaxy modeling, estimating posterior distributions of galaxy properties such as ellipticity and brightness for more than 100,000 images of galaxies taken from DC2, a…
Markov Chain Monte Carlo methods become increasingly popular in applied mathematics as a tool for numerical integration with respect to complex and high-dimensional distributions. However, application of MCMC methods to heavy tailed…
Recently, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) methods have been proposed for scaling up Monte Carlo computations to large data problems. Whilst these approaches have proven useful in many applications, vanilla SG-MCMC…
The use of Cauchy Markov random field priors in statistical inverse problems can potentially lead to posterior distributions which are non-Gaussian, high-dimensional, multimodal and heavy-tailed. In order to use such priors successfully,…