Related papers: Objective Climate Model Predictions Using Jeffreys…

The application of Bayesian inference for the purpose of model selection is very popular nowadays. In this framework, models are compared through their marginal likelihoods, or their quotients, called Bayes factors. However, marginal…

Numerical climate models are used to project future climate change due to both anthropogenic and natural causes. Differences between projections from different climate models are a major source of uncertainty about future climate. Emergent…

This paper considers the topic of finding prior distributions when a major component of the statistical model depends on a nonlinear function. Using results on how to construct uniform distributions in general metric spaces, we propose a…

Quantifying and reducing uncertainty in Earth system model parameterizations is essential to improving their reliability in decision-making. Forward uncertainty propagation is used to derive parameter sensitivity but requires physically…

The construction of objective priors is, at best, challenging for multidimensional parameter spaces. A common practice is to assume independence and set up the joint prior as the product of marginal distributions obtained via "standard"…

We introduce a computational efficient data-driven framework suitable for quantifying the uncertainty in physical parameters and model formulation of computer models, represented by differential equations. We construct physics-informed…

The properties of the normal distribution under linear transformation, as well the easy way to compute the covariance matrix of marginals and conditionals, offer a unique opportunity to get an insight about several aspects of uncertainties…

Multi-model ensembles provide a pragmatic approach to the representation of model uncertainty in climate prediction. However, such representations are inherently ad hoc, and, as shown, probability distributions of climate variables based on…

In objective Bayesian model selection, no single criterion has emerged as dominant in defining objective prior distributions. Indeed, many criteria have been separately proposed and utilized to propose differing prior choices. We first…

The Rician distribution, a well-known statistical distribution frequently encountered in fields like magnetic resonance imaging and wireless communications, is particularly useful for describing many real phenomena such as signal process…

Objective priors for sequential experiments are considered. Common priors, such as the Jeffreys prior and the reference prior, will typically depend on the stopping rule used for the sequential experiment. New expressions for reference…

We advocate for a new statistical principle that combines the most desirable aspects of both parameter inference and density estimation. This leads us to the predictively oriented (PrO) posterior, which expresses uncertainty as a…

Probability forecasting is common in the geosciences, the finance sector, and elsewhere. It is sometimes the case that one has multiple probability-forecasts for the same target. How is the information in these multiple forecast systems…

Specifying a Bayesian prior is notoriously difficult for complex models such as neural networks. Reasoning about parameters is made challenging by the high-dimensionality and over-parameterization of the space. Priors that seem benign and…

Predicting the winner of an election is of importance to multiple stakeholders. To formulate the problem, we consider an independent sequence of categorical data with a finite number of possible outcomes in each. The data is assumed to be…

We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior…

Fitted probabilities from widely used Bayesian multinomial probit models can depend strongly on the choice of a base category, which is used to uniquely identify the parameters of the model. This paper proposes a novel identification…

In our contemporary era, meteorological weather forecasts increasingly incorporate ensemble predictions of visibility - a parameter of great importance in aviation, maritime navigation, and air quality assessment, with direct implications…

Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially under covariate distribution shifts between training and testing. To address this problem, we propose a Bayesian framework for…

The gaussian spread regression model for the calibration of site specific ensemble temperature forecasts depends on the apparently restrictive assumption that the uncertainty around temperature forecasts is normally distributed. We…