In a binary response regression model, classical residuals are diicult to deene and interpret due to the discrete nature of the response variable. In contrast, Bayesian residuals have continuous-valued posterior distributions which can be graphed to learn about outlying observations. Two deenitions of Bayesian residuals are proposed for binary regression data. Plots of the posterior distributio...

compared to conventional chlorination methods which apply chlorine at water treatment plant, booster chlorination has almost solved the problems of high dosages of chlorine residuals near water sources and lack of chlorine residuals in the remote points of a water distribution system (wds). however, control of trihalomethane (thm) formation as a potentially carcinogenic disinfection by-product ...

Variational auto-encoders (VAEs) are a popular and powerful deep generative model. Previous works on VAEs have assumed a factorised likelihood model, whereby the output uncertainty of each pixel is assumed to be independent. This approximation is clearly limited as demonstrated by observing a residual image from a VAE reconstruction, which often possess a high level of structure. This paper dem...

Residuals have been studied for various forms of rewriting and residual systems have been defined to capture residuals in an abstract setting. In this article we study residuals in orthogonal Pattern Rewriting Systems (PRSs). First, the rewrite relation is defined by means of a higher-order rewriting logic, and proof terms are defined that witness reductions. Then, we have the formal machinery ...