Related papers: Insufficient Gibbs Sampling
Simulator-based models are models for which the likelihood is intractable but simulation of synthetic data is possible. They are often used to describe complex real-world phenomena, and as such can often be misspecified in practice.…
In mathematical finance, Levy processes are widely used for their ability to model both continuous variation and abrupt, discontinuous jumps. These jumps are practically relevant, so reliable inference on the feature that controls jump…
Learning Gibbs distributions using only sufficient statistics has long been recognized as a computationally hard problem. On the other hand, computationally efficient algorithms for learning Gibbs distributions rely on access to full sample…
We consider discrete nonparametric priors which induce Gibbs-type exchangeable random partitions and investigate their posterior behavior in detail. In particular, we deduce conditional distributions and the corresponding Bayesian…
Hybrid Gibbs samplers represent a prominent class of approximated Gibbs algorithms that utilize Markov chains to approximate conditional distributions, with the Metropolis-within-Gibbs algorithm standing out as a well-known example. Despite…
In this paper, we consider objective Bayesian inference of the generalized exponential distribution using the independence Jeffreys prior and validate the propriety of the posterior distribution under a family of structured priors. We…
Replicated network data are increasingly available in many research fields. In connectomic applications, inter-connections among brain regions are collected for each patient under study, motivating statistical models which can flexibly…
Variational Bayesian inference and (collapsed) Gibbs sampling are the two important classes of inference algorithms for Bayesian networks. Both have their advantages and disadvantages: collapsed Gibbs sampling is unbiased but is also…
Statistical models are central to machine learning with broad applicability across a range of downstream tasks. The models are controlled by free parameters that are typically estimated from data by maximum-likelihood estimation or…
This paper derives two new optimization-driven Monte Carlo algorithms inspired from variable splitting and data augmentation. In particular, the formulation of one of the proposed approaches is closely related to the alternating direction…
We propose a methodology for modeling and comparing probability distributions within a Bayesian nonparametric framework. Building on dependent normalized random measures, we consider a prior distribution for a collection of discrete random…
Motivated by the analysis of the distribution of university grades, which is usually asymmetric, we discuss two informative priors for the shape parameter of the skew-normal distribution, showing that they lead to closed-form…
Sequential Monte Carlo has become a standard tool for Bayesian Inference of complex models. This approach can be computationally demanding, especially when initialized from the prior distribution. On the other hand, deter-ministic…
Constraints are a natural choice for prior information in Bayesian inference. In various applications, the parameters of interest lie on the boundary of the constraint set. In this paper, we use a method that implicitly defines a…
We consider the problem of sampling from a product-of-experts-type model that encompasses many standard prior and posterior distributions commonly found in Bayesian imaging. We show that this model can be easily lifted into a novel latent…
A one-to-one correspondence is established between the bridge path space of birth-death processes and the exclusive union of the product spaces of simplexes and integer grids. Formulae are derived for the exact counting of the integer grid…
In Bayesian inverse problems, the posterior distribution is used to quantify uncertainty about the reconstructed solution. In practice, Markov chain Monte Carlo algorithms often are used to draw samples from the posterior distribution.…
Non-Gaussian mixture models are gaining increasing attention for mixture model-based clustering particularly when dealing with data that exhibit features such as skewness and heavy tails. Here, such a mixture distribution is presented,…
Approximate Bayesian computation (ABC) is commonly used for parameter estimation and model comparison for intractable simulator-based models whose likelihood function cannot be evaluated. In this paper we instead investigate the feasibility…
A new methodology for model determination in decomposable graphical Gaussian models is developed. The Bayesian paradigm is used and, for each given graph, a hyper inverse Wishart prior distribution on the covariance matrix is considered.…