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Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is a popular iterative method where a Gaussian process posterior of the underlying function is sequentially…
I propose a novel approach for nonlinear Logistic regression using a two-layer neural network (NN) model structure with hierarchical priors on the network weights. I present a hybrid of expectation propagation called Variational Expectation…
Many probabilistic models of interest in scientific computing and machine learning have expensive, black-box likelihoods that prevent the application of standard techniques for Bayesian inference, such as MCMC, which would require access to…
Many spatial processes exhibit nonstationary features. We estimate a variance function from a single process observation where the errors are nonstationary and correlated. We propose a difference-based approach for a one-dimensional…
Bayesian inference for Markov processes has become increasingly relevant in recent years. Problems of this type often have intractable likelihoods and prior knowledge about model rate parameters is often poor. Markov Chain Monte Carlo…
The detection of rare variants is important for understanding the genetic heterogeneity in mixed samples. Recently, next-generation sequencing (NGS) technologies have enabled the identification of single nucleotide variants (SNVs) in mixed…
Latent space models are popular for analyzing dynamic network data. We propose a variational approach to estimate the model parameters as well as the latent positions of the nodes in the network. The variational approach is much faster than…
We show how the notion of message passing can be used to streamline the algebra and computer coding for fast approximate inference in large Bayesian semiparametric regression models. In particular, this approach is amenable to handling…
We consider the problem of static Bayesian inference for partially observed Levy-process models. We develop a methodology which allows one to infer static parameters and some states of the process, without a bias from the…
Using theoretical and numerical results, we document the accuracy of commonly applied variational Bayes methods across a range of state space models. The results demonstrate that, in terms of accuracy on fixed parameters, there is a clear…
Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a…
The article describe the model, derivation, and implementation of variational Bayesian inference for linear and logistic regression, both with and without automatic relevance determination. It has the dual function of acting as a tutorial…
In this paper we propose a wavelet-based methodology for estimation and variable selection in partially linear models. The inference is conducted in the wavelet domain, which provides a sparse and localized decomposition appropriate for…
Variational inference has recently emerged as a popular alternative to the classical Markov chain Monte Carlo (MCMC) in large-scale Bayesian inference. The core idea is to trade statistical accuracy for computational efficiency. In this…
Bayesian inference has been broadly applied to statistical network analysis, but suffers from the expensive computational costs due to the nature of Markov chain Monte Carlo sampling algorithms. This paper proposes a novel and…
Well-calibrated probabilistic regression models are a crucial learning component in robotics applications as datasets grow rapidly and tasks become more complex. Unfortunately, classical regression models are usually either probabilistic…
We develop an empirical Bayes procedure for estimating the cell means in an unbalanced, two-way additive model with fixed effects. We employ a hierarchical model, which reflects exchangeability of the effects within treatment and within…
Variational Bayes (VB) provides a computationally efficient alternative to Markov Chain Monte Carlo, especially for high-dimensional and large-scale inference. However, existing theory on VB primarily focuses on fixed-dimensional settings…
The mean field variational Bayes (VB) algorithm implemented in Stan is relatively fast and efficient, making it feasible to produce model-estimated official statistics on a rapid timeline. Yet, while consistent point estimates of parameters…
Bayesian graphical models have been shown to be a powerful tool for discovering uncertainty and causal structure from real-world data in many application fields. Current inference methods primarily follow different kinds of trade-offs…