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Many modern statistical applications involve inference for complicated stochastic models for which the likelihood function is difficult or even impossible to calculate, and hence conventional likelihood-based inferential echniques cannot be…
This study introduces a computationally efficient algorithm, delayed acceptance Markov chain Monte Carlo (DA-MCMC), designed to improve posterior simulation in quasi-Bayesian inference. Quasi-Bayesian methods, which do not require fully…
Bayesian Neural Networks (BNNs) offer a principled and natural framework for proper uncertainty quantification in the context of deep learning. They address the typical challenges associated with conventional deep learning methods, such as…
Bayesian methods are critical for quantifying the behaviors of systems. They capture our uncertainty about a system's behavior using probability distributions and update this understanding as new information becomes available. Probabilistic…
Models of biological systems often have many unknown parameters that must be determined in order for model behavior to match experimental observations. Commonly-used methods for parameter estimation that return point estimates of the…
Panel Vector Autoregressions (PVARs) are a popular tool for analyzing multi-country datasets. However, the number of estimated parameters can be enormous, leading to computational and statistical issues. In this paper, we develop fast…
Approximate Bayesian inference for models with computationally expensive, black-box likelihoods poses a significant challenge, especially when the posterior distribution is complex. Many inference methods struggle to explore the parameter…
The current standard Bayesian approach to model calibration, which assigns a Gaussian process prior to the discrepancy term, often suffers from issues of unidentifiability and computational complexity and instability. When the goal is to…
Approximate Bayesian computation (ABC) is an approach for sampling from an approximate posterior distribution in the presence of a computationally intractable likelihood function. A common implementation is based on simulating model,…
In the context of computer models, calibration is the process of estimating unknown simulator parameters from observational data. Calibration is variously referred to as model fitting, parameter estimation/inference, an inverse problem, and…
Approximate Bayesian Computation (ABC) is a useful class of methods for Bayesian inference when the likelihood function is computationally intractable. In practice, the basic ABC algorithm may be inefficient in the presence of discrepancy…
In high-dimensions, the prior tails can have a significant effect on both posterior computation and asymptotic concentration rates. To achieve optimal rates while keeping the posterior computations relatively simple, an empirical Bayes…
As modern neural networks get more complex, specifying a model with high predictive performance and sound uncertainty quantification becomes a more challenging task. Despite some promising theoretical results on the true posterior…
Approximate Bayesian Computation (ABC) enables statistical inference in simulator-based models whose likelihoods are difficult to calculate but easy to simulate from. ABC constructs a kernel-type approximation to the posterior distribution…
The Laplace approximation is a popular method for constructing a Gaussian approximation to the Bayesian posterior and thereby approximating the posterior mean and variance. But approximation quality is a concern. One might consider using…
Bayesian regression remains a simple but effective tool based on Bayesian inference techniques. For large-scale applications, with complicated posterior distributions, Markov Chain Monte Carlo methods are applied. To improve the well-known…
Bayesian phylogenetic inference is often conducted via local or sequential search over topologies and branch lengths using algorithms such as random-walk Markov chain Monte Carlo (MCMC) or Combinatorial Sequential Monte Carlo (CSMC).…
We propose a novel method for computing $p$-values based on nested sampling (NS) applied to the sampling space rather than the parameter space of the problem, in contrast to its usage in Bayesian computation. The computational cost of NS…
Radial velocity (RV) planet searches are increasingly finding planets with small velocity amplitudes, with long orbital periods, or in multiple planet systems. Bayesian inference has the potential to improve the interpretation of existing…
Spatial whole-brain Bayesian modeling of task-related functional magnetic resonance imaging (fMRI) is a great computational challenge. Most of the currently proposed methods therefore do inference in subregions of the brain separately or do…