Related papers: Variational Prior Replacement in Bayesian Inferenc…
Variational Bayes is a popular method for approximate inference but its derivation can be cumbersome. To simplify the process, we give a 3-step recipe to identify the posterior form by explicitly looking for linearity with respect to…
A simulation is useful when the phenomenon of interest is either expensive to regenerate or irreproducible with the same context. Recently, Bayesian inference on the distribution of the simulation input parameter has been implemented…
Bayesian computational strategies for inference can be inefficient in approximating the posterior distribution in models that exhibit some form of periodicity. This is because the probability mass of the marginal posterior distribution of…
Deep learning has revolutionized the last decade, being at the forefront of extraordinary advances in a wide range of tasks including computer vision, natural language processing, and reinforcement learning, to name but a few. However, it…
Bayesian methods estimate a measure of uncertainty by using the posterior distribution. One source of difficulty in these methods is the computation of the normalizing constant. Calculating exact posterior is generally intractable and we…
Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower…
When using complex Bayesian models to combine information, the checking for consistency of the information being combined is good statistical practice. Here a new method is developed for detecting prior-data conflicts in Bayesian models…
Bayesian inference for inverse problems hinges critically on the choice of priors. In the absence of specific prior information, population-level distributions can serve as effective priors for parameters of interest. With the advent of…
This paper develops a methodology for approximating the posterior first two moments of the posterior distribution in Bayesian inference. Partially specified probability models, which are defined only by specifying means and variances, are…
Geoscientists often solve inverse problems to estimate values of parameters of interest given relevant data sets. Bayesian inference solves these problems by combining probability distributions that describe uncertainties in both…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
Vanilla variational inference finds an optimal approximation to the Bayesian posterior distribution, but even the exact Bayesian posterior is often not meaningful under model misspecification. We propose predictive variational inference…
This work considers variational Bayesian inference as an inexpensive and scalable alternative to a fully Bayesian approach in the context of sparsity-promoting priors. In particular, the priors considered arise from scale mixtures of Normal…
We describe the Bedside Patient Rescue (BPR) project, the goal of which is risk prediction of adverse events for non-ICU patients using ~200 variables (vitals, lab results, assessments, ...). There are several missing predictor values for…
We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of interest). The solution, given as a probability measure, is…
Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical…
Variational Bayesian (VB) methods produce posterior inference in a time frame considerably smaller than traditional Markov Chain Monte Carlo approaches. Although the VB posterior is an approximation, it has been shown to produce good…
Bayesian inference offers benefits over maximum likelihood, but it also comes with computational costs. Computing the posterior is typically intractable, as is marginalizing that posterior to form the posterior predictive distribution. In…
Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…
Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance,…