Related papers: Bayesian computation for statistical models with i…
Doubly intractable problems occur when both the likelihood and the posterior are available only in unnormalised form, with computationally intractable normalisation constants. Bayesian inference then typically requires direct approximation…
Rich data generating mechanisms are ubiquitous in this age of information and require complex statistical models to draw meaningful inference. While Bayesian analysis has seen enormous development in the last 30 years, benefitting from the…
In performing a Bayesian analysis, two difficult problems often emerge. First, in estimating the parameters of some model for the data, the resulting posterior distribution may be multi-modal or exhibit pronounced (curving) degeneracies.…
Bayesian learning in undirected graphical models|computing posterior distributions over parameters and predictive quantities is exceptionally difficult. We conjecture that for general undirected models, there are no tractable MCMC (Markov…
Many statistical applications involve models for which it is difficult to evaluate the likelihood, but from which it is relatively easy to sample. Approximate Bayesian computation is a likelihood-free method for implementing Bayesian…
Astronomers are often confronted with funky populations and distributions of objects: brighter objects are more likely to be detected; targets are selected based on colour cuts; imperfect classification yields impure samples. Failing to…
Probabilistic (or Bayesian) modeling and learning offers interesting possibilities for systematic representation of uncertainty using probability theory. However, probabilistic learning often leads to computationally challenging problems.…
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…
This work considers the problem of sampling from a probability distribution known up to a normalization constant while satisfying a set of statistical constraints specified by the expected values of general nonlinear functions. This problem…
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…
This article surveys computational methods for posterior inference with intractable likelihoods, that is where the likelihood function is unavailable in closed form, or where evaluation of the likelihood is infeasible. We review recent…
We propose a Bayesian elastic net that uses empirical likelihood and develop an efficient tuning of Hamiltonian Monte Carlo for posterior sampling. The proposed model relaxes the assumptions on the identity of the error distribution,…
Markov chain Monte Carlo (MCMC) methods have not been broadly adopted in Bayesian neural networks (BNNs). This paper initially reviews the main challenges in sampling from the parameter posterior of a neural network via MCMC. Such…
The Bayesian elastic net regression model is characterized by the regression coefficient prior distribution, the negative log density of which corresponds to the elastic net penalty function. While Markov chain Monte Carlo (MCMC) methods…
This paper proposes Bayesian mosaic, a parallelizable composite posterior, for scalable Bayesian inference on a broad class of multivariate discrete data models. Sampling is embarrassingly parallel since Bayesian mosaic is a multiplication…
Despite recent advances, sampling-based inference for Bayesian Neural Networks (BNNs) remains a significant challenge in probabilistic deep learning. While sampling-based approaches do not require a variational distribution assumption,…
Bayesian statistical inference for Generalized Linear Models (GLMs) with parameters lying on a constrained space is of general interest (e.g., in monotonic or convex regression), but often constructing valid prior distributions supported on…
Estimating the predictive uncertainty of a Bayesian learning model is critical in various decision-making problems, e.g., reinforcement learning, detecting adversarial attack, self-driving car. As the model posterior is almost always…
In many complex statistical models maximum likelihood estimators cannot be calculated. In the paper we solve this problem using Markov chain Monte Carlo approximation of the true likelihood. In the main result we prove asymptotic normality…
The methodology developed in this article is motivated by a wide range of prediction and uncertainty quantification problems that arise in Statistics, Machine Learning and Applied Mathematics, such as non-parametric regression, multi-class…