Related papers: Superset model problem
We introduce a novel rule-based approach for handling regression problems. The new methodology carries elements from two frameworks: (i) it provides information about the uncertainty of the parameters of interest using Bayesian inference,…
Survival models are used in various fields, such as the development of cancer treatment protocols. Although many statistical and machine learning models have been proposed to achieve accurate survival predictions, little attention has been…
This paper presents a Bayesian framework for assessing the adequacy of a model without the necessity of explicitly enumerating a specific alternate model. A test statistic is developed for tracking the performance of the model across…
Our understanding of physical systems generally depends on our ability to match complex computational modelling with measured experimental outcomes. However, simulations with large parameter spaces suffer from inverse problem instabilities,…
Quantile regression is a powerful tool for inferring how covariates affect specific percentiles of the response distribution. Existing methods either estimate conditional quantiles separately for each quantile of interest or estimate the…
Identifying the parameters of a model and rating competitive models based on measured data has been among the most important but challenging topics in modern science and engineering, with great potential of application in structural system…
We reexamine the classical linear regression model when the model is subject to two types of uncertainty: (i) some of covariates are either missing or completely inaccessible, and (ii) the variance of the measurement error is undetermined…
Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…
In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…
Model inadequacy and measurement uncertainty are two of the most confounding aspects of inference and prediction in quantitative sciences. The process of scientific inference (the inverse problem) and prediction (the forward problem)…
We introduce a general framework that extends Bayesian inference by allowing the researcher to explicitly encode confidence in each source of uncertainty within the model. This mechanism provides a new handle for model design and…
These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental…
Robust Bayesian models are appealing alternatives to standard models, providing protection from data that contains outliers or other departures from the model assumptions. Historically, robust models were mostly developed on a case-by-case…
Probabilistic models analyze data by relying on a set of assumptions. Data that exhibit deviations from these assumptions can undermine inference and prediction quality. Robust models offer protection against mismatch between a model's…
Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…
We empirically show that Bayesian inference can be inconsistent under misspecification in simple linear regression problems, both in a model averaging/selection and in a Bayesian ridge regression setting. We use the standard linear model,…
This paper offers a qualitative insight into the convergence of Bayesian parameter inference in a setup which mimics the modeling of the spread of a disease with associated disease measurements. Specifically, we are interested in the…
Although machine learning tasks are highly sensitive to the quality of input data, relevant datasets can often be challenging for firms to acquire, especially when held privately by a variety of owners. For instance, if these owners are…
Bayesian model comparison is often based on the posterior distribution over the set of compared models. This distribution is often observed to concentrate on a single model even when other measures of model fit or forecasting ability…
A key problem in statistical modeling is model selection, how to choose a model at an appropriate level of complexity. This problem appears in many settings, most prominently in choosing the number ofclusters in mixture models or the number…