Related papers: An asymptotic approximation of the marginal likeli…
Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…
This paper considers a Bayesian view for estimating a sub-network in a Markov random field. The sub-network corresponds to the Markov blanket of a set of query variables, where the set of potential neighbours here is big. We factorize the…
We consider hidden Markov models indexed by a binary tree where the hidden state space is a general metric space. We study the maximum likelihood estimator (MLE) of the model parameters based only on the observed variables. In both…
Discrete state spaces represent a major computational challenge to statistical inference, since the computation of normalisation constants requires summation over large or possibly infinite sets, which can be impractical. This paper…
Typical Bayesian methods for models with latent variables (or random effects) involve directly sampling the latent variables along with the model parameters. In high-level software code for model definitions (using, e.g., BUGS, JAGS, Stan),…
We present non-asymptotic two-sided bounds to the log-marginal likelihood in Bayesian inference. The classical Laplace approximation is recovered as the leading term. Our derivation permits model misspecification and allows the parameter…
Bayesian model averaging is a practical method for dealing with uncertainty due to model specification. Use of this technique requires the estimation of model probability weights. In this work, we revisit the derivation of estimators for…
We derive a new Bayesian Information Criterion (BIC) by formulating the problem of estimating the number of clusters in an observed data set as maximization of the posterior probability of the candidate models. Given that some mild…
Graphical models or networks describe the statistical dependence among multiple variables and are widely used in biology (e.g., gene regulatory networks). Under appropriate assumptions, directed edges may represent causal relationships. A…
Bayesian networks are now being used in enormous fields, for example, diagnosis of a system, data mining, clustering and so on. In spite of their wide range of applications, the statistical properties have not yet been clarified, because…
We employ the Bayesian improved cross entropy (BiCE) method for rare event estimation in static networks and choose the categorical mixture as the parametric family to capture the dependence among network components. At each iteration of…
Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging "doubly intractable" problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC)…
Low-dimensional probability models for local distribution functions in a Bayesian network include decision trees, decision graphs, and causal independence models. We describe a new probability model for discrete Bayesian networks, which we…
We describe algorithms for learning Bayesian networks from a combination of user knowledge and statistical data. The algorithms have two components: a scoring metric and a search procedure. The scoring metric takes a network structure,…
Prior design is one of the most important problems in both statistics and machine learning. The cross validation (CV) and the widely applicable information criterion (WAIC) are predictive measures of the Bayesian estimation, however, it has…
As observations and student models become complex, educational assessments that exploit advances in technology and cognitive psychology can outstrip familiar testing models and analytic methods. Within the Portal conceptual framework for…
The marginal likelihood is a well established model selection criterion in Bayesian statistics. It also allows to efficiently calculate the marginal posterior model probabilities that can be used for Bayesian model averaging of quantities…
A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…
Marginal likelihood, also known as model evidence, is a fundamental quantity in Bayesian statistics. It is used for model selection using Bayes factors or for empirical Bayes tuning of prior hyper-parameters. Yet, the calculation of…
We consider the problem of estimating the marginal independence structure of a Bayesian network from observational data, learning an undirected graph we call the unconditional dependence graph. We show that unconditional dependence graphs…