Related papers: The data augmentation algorithm
Gaussian errors are sometimes inappropriate in a multivariate linear regression setting because, for example, the data contain outliers. In such situations, it is often assumed that the error density is a scale mixture of multivariate…
Markov Chain Monte Carlo (MCMC) algorithms are commonly used for their versatility in sampling from complicated probability distributions. However, as the dimension of the distribution gets larger, the computational costs for a satisfactory…
Data augmentation (DA) is indispensable in modern machine learning and deep neural networks. The basic idea of DA is to construct new training data to improve the model's generalization by adding slightly disturbed versions of existing data…
The reversible Markov chains that drive the data augmentation (DA) and sandwich algorithms define self-adjoint operators whose spectra encode the convergence properties of the algorithms. When the target distribution has uncountable…
Monte Carlo algorithms, such as Markov chain Monte Carlo (MCMC) and Hamiltonian Monte Carlo (HMC), are routinely used for Bayesian inference in generalized linear models; however, these algorithms are prohibitively slow in massive data…
Stochastic gradient Markov chain Monte Carlo (MCMC) algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed…
Let $\pi$ denote the intractable posterior density that results when the likelihood from a multivariate linear regression model with errors from a scale mixture of normals is combined with the standard non-informative prior. There is a…
Data Augmentation (DA) has become an essential tool to improve robustness and generalization of modern machine learning. However, when deciding on DA strategies it is critical to choose parameters carefully, and this can be a daunting task…
We present a data augmentation scheme to perform Markov chain Monte Carlo inference for models where data generation involves a rejection sampling algorithm. Our idea, which seems to be missing in the literature, is a simple scheme 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…
Markov chain Monte Carlo is a class of algorithms for drawing Markovian samples from high-dimensional target densities to approximate the numerical integration associated with computing statistical expectation, especially in Bayesian…
In sampling tasks, it is common for target distributions to be known up to a normalizing constant. However, in many situations, even evaluating the unnormalized distribution can be costly or infeasible. This issue arises in scenarios such…
We propose a generic Markov Chain Monte Carlo (MCMC) algorithm to speed up computations for datasets with many observations. A key feature of our approach is the use of the highly efficient difference estimator from the survey sampling…
Markov Chain Monte Carlo (MCMC) is a popular class of statistical methods for simulating autocorrelated draws from target distributions, including posterior distributions in Bayesian analysis. An important consideration in using simulated…
The mixed effects model for repeated measures (MMRM) has been widely used for the analysis of longitudinal clinical data collected at a number of fixed time points. We propose a robust extension of the MMRM for skewed and heavy-tailed data…
Stochastic epidemic models describe the dynamics of an epidemic as a disease spreads through a population. Typically, only a fraction of cases are observed at a set of discrete times. The absence of complete information about the time…
Markov chain Monte Calro methods (MCMC) are commonly used in Bayesian statistics. In the last twenty years, many results have been established for the calculation of the exact convergence rate of MCMC methods. We introduce another rate of…
Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from…
Markov chain Monte Carlo (MCMC) algorithms are generally regarded as the gold standard technique for Bayesian inference. They are theoretically well-understood and conceptually simple to apply in practice. The drawback of MCMC is that in…
Markov Chain Monte Carlo (MCMC) algorithms are routinely used to draw samples from distributions with intractable normalization constants. However, standard MCMC algorithms do not apply to doubly-intractable distributions in which there are…