We present a general approach to visualizing uncertainty in static 2-D statistical graphics. If we treat a visualization as a function of its underlying quantities, uncertainty in those quantities induces a distribution over images. We show how to aggregate these images into a single visualization that represents the uncertainty. The approach can be viewed as a generalization of sample-based approaches that use overlay. Notably, standard representations, such as confidence intervals and bands, emerge with their usual coverage guarantees without being explicitly quantified or visualized. As a proof of concept, we implement our approach in the IID setting using resampling, provided as an open-source Python library. Because the approach operates directly on images, the user needs only to supply the data and the code for visualizing the quantities of interest without uncertainty. Through several examples, we show how both familiar and novel forms of uncertainty visualization can be created. The implementation is not only a practical validation of the underlying theory but also an immediately usable tool that can complement existing uncertainty-visualization libraries.

Abstract Recent advances in MCMC use normalizing flows to precondition target distributions and enable jumps to distant regions. However, there is currently no systematic comparison of different normalizing flow architectures for MCMC. As such, many works choose simple flow architectures that are readily available and do not consider other models. Guidelines for choosing an appropriate architecture would reduce analysis time for practitioners and motivate researchers to take the recommended models as foundations to be improved. We provide the first such guideline by extensively evaluating many normalizing flow architectures on various flow-based MCMC methods and target distributions. When the target density gradient is available, we show that flow-based MCMC outperforms classic MCMC for suitable NF architecture choices with minor hyperparameter tuning. When the gradient is unavailable, flow-based MCMC wins with off-the-shelf architectures. We find contractive residual flows to be the best general-purpose models with relatively low sensitivity to hyperparameter choice. We also provide various insights into normalizing flow behavior within MCMC when varying their hyperparameters, properties of target distributions, and the overall computational budget.

Ensemble methods are a powerful tool, often outperforming individual prediction models. Existing Bayesian ensembles either do not model the correlations between sources, or they are only capable of combining non-probabilistic predictions. We propose a new model, which overcomes these disadvantages. Transforming the probabilistic predictions with the inverse additive logistic transformation allows us to model the correlations with multivariate normal mixtures. We derive an efficient Gibbs sampler for the proposed model and implement a regularization method to make it more robust. We compare our method to related work and the classical linear opinion pool. Empirical evaluation on several toy and real-world data sets, including a case study on air-pollution forecasting, shows that the method outperforms other methods, while being robust and easy to use.

A probabilistic radial basis function (PRBF) network is an effective non-linear classifier. However, similar to most other neural network models it is non-transparent, which makes its predictions difficult to interpret. In this paper we show how a one-variable-at-a-time and an all-subsets explanation method can be modified for an equivalent and more efficient use with PRBF network classifiers. We use several artificial and real-life data sets to demonstrate the usefulness of the visualizations and explanations of the PRBF network classifier.