相关论文: Non-trivial informational closure of a Bayesian hy…

For linear models with a diverging number of parameters, it has recently been shown that modified versions of Bayesian information criterion (BIC) can identify the true model consistently. However, in many cases there is little…

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…

Inferring the infinitesimal rates of continuous-time Markov chains (CTMCs) is a central challenge in many scientific domains. This task is hindered by three factors: quadratic growth in the number of rates as the CTMC state space expands,…

We propose a Bayesian nonparametric mixture model for prediction- and information extraction tasks with an efficient inference scheme. It models categorical-valued time series that exhibit dynamics from multiple underlying patterns (e.g.…

Bayesian hierarchical models are frequently used in practical data analysis contexts. One interpretation of these models is that they provide an indirect way of assigning a prior for unknown parameters, through the introduction of…

In this work, we offer a thorough analytical investigation into the role of shared hyperparameters in a hierarchical Bayesian model, examining their impact on information borrowing and posterior inference. Our approach is rooted in a…

The standard Bayesian Information Criterion (BIC) is derived under regularity conditions which are not always satisfied by the graphical models with hidden variables. In this paper we derive the BIC score for Bayesian networks in the case…

Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as…

We extend the Bayesian Information Criterion (BIC), an asymptotic approximation for the marginal likelihood, to Bayesian networks with hidden variables. This approximation can be used to select models given large samples of data. The…

Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…

In the information-based paradigm of inference, model selection is performed by selecting the candidate model with the best estimated predictive performance. The success of this approach depends on the accuracy of the estimate of the…

In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases,…

Inference for continuous-time Markov chains (CTMCs) becomes challenging when the process is only observed at discrete time points. The exact likelihood is intractable, and existing methods often struggle even in medium-dimensional…

We present a Bayesian methodology for infinite as well as finite dimensional parameter identification for partial differential equation models. The Bayesian framework provides a rigorous mathematical framework for incorporating prior…

Modeling of the dependence structure across heterogeneous data is crucial for Bayesian inference since it directly impacts the borrowing of information. Despite the extensive advances over the last two decades, most available proposals…

This paper introduces a framework for speeding up Bayesian inference conducted in presence of large datasets. We design a Markov chain whose transition kernel uses an (unknown) fraction of (fixed size) of the available data that is randomly…

In this article a flexible Bayesian non-parametric model is proposed for non-homogeneous hidden Markov models. The model is developed through the amalgamation of the ideas of hidden Markov models and predictor dependent stick-breaking…

The use of Bayesian information criterion (BIC) in the model selection procedure is under the assumption that the observations are independent and identically distributed (i.i.d.). However, in practice, we do not always have i.i.d. samples.…

Multivariate point processes are widely applied to model event-type data such as natural disasters, online message exchanges, financial transactions or neuronal spike trains. One very popular point process model in which the probability of…

Information-theoretic quantities play a crucial role in understanding non-linear relationships between random variables and are widely used across scientific disciplines. However, estimating these quantities remains an open problem,…